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Rainbow Deals - hours only!Up to 80% off on all courses and bundles.-Close Introduction 3. Table project Function COUNT Function AVG Functions SUM, MAX, MIN Revision ## Instruction Good, let's take a look at the very last table. ## Exercise Select all the information from the last table: project. The last table is a bit more complicated. You can find the project_id, client_id and translator_id, of course. These columns should be clear. Then, you can see: • the start - that is, when the client commissioned the project, • the deadline - when the project is due. Afterwards, we can see the price the client paid, the number of words to translate and two languages: • the source language (lang_from), • the target language (lang_to). The final column (feedback) provides the client's feedback. Positive numbers mean that the client was very satisfied, negative ones mean that the client complained to some extent about the quality.
New Page 1 TORNA ALLA HOME DI ENGLISH GRATIS  •  Tel. 02-78622122  •  [email protected]  • WIKIBOOKS DISPONIBILI ••••••••• ART - Great Painters - Accounting - Fundamentals of Law - Marketing - Shorthand CARS - Concept Cars GAMES&SPORT - Videogames - The World of Sports COMPUTER TECHNOLOGY - Blogs - Free Software - My Computer - PHP Language and Applications - Wikipedia - Windows Vista EDUCATION - Education LITERATURE - Masterpieces of English Literature LINGUISTICS - American English - English Dictionaries - The English Language MEDICINE - Medical Emergencies - The Theory of Memory MUSIC&DANCE - The Beatles - Dances - Microphones - Musical Notation - Music Instruments SCIENCE - Batteries - Nanotechnology LIFESTYLE - Cosmetics - Diets - Vegetarianism and Veganism NATURE - Animals - Fruits And Vegetables ARTICLES IN THE BOOK BATTERIES http://en.wikipedia.org/wiki/Coulomb All text is available under the terms of the GNU Free Documentation License: http://en.wikipedia.org/wiki/Wikipedia:Text_of_the_GNU_Free_Documentation_License # Coulomb The coulomb (symbol: C) is the SI unit of electric charge. It is named after Charles-Augustin de Coulomb. ## Definition 1 coulomb is the amount of electric charge carried by a current of 1 ampere flowing for 1 second. $1 \ \mathrm{C} = 1 \ \mathrm{A} \cdot 1 \ \mathrm{s}$ It can also be defined in terms of capacitance and voltage, where one coulomb is defined as one farad of capacitance times one volt of electric potential difference: $1 \ \mathrm{C} = 1 \ \mathrm{F} \cdot 1 \ \mathrm{V}$ ## Explanation The coulomb is also the unit of electric flux. (See Gauss Law.) In principle, the coulomb could be defined in terms of the charge of an electron or elementary charge. Since the values of the Josephson (CIPM (1988) Recommendation 1, PV 56; 19) and von Klitzing (CIPM (1988), Recommendation 2, PV 56; 20) constants have been given conventional values (KJ ≡ 4.835 979×1014 Hz/V and RK ≡ 2.581 280 7×104 Ω), it is possible to combine these values to form an alternative (not yet official) definition of the coulomb. A coulomb is then equal to exactly 6.241 509 629 152 65×1018 elementary charges. Combined with the current definition of the ampere, this proposed definition would make the kilogram a derived unit. If two point charges of + 1 C are held one meter away from each other, the repulsive force they will feel is given by Coulomb's Law as 8.988×109 N [1]. This is roughly equal to the gravitational force of 900,000 metric tons of mass at the surface of the Earth. Because these forces are so large, it can be informally stated that "a coulomb is a lot of charge." In everyday life, most things don't have a large surplus of charge -- e.g. normal human beings standing one meter away from each other generally don't feel any electrostatic force between them, and have a capacity to feel a force of ~10 N (~1 kg). From this, it can be conjectured that they generally have a net charge of less than 30 µC [2]. ## Historical note The ampere was historically a derived unit - being defined as 1 coulomb per second. Therefore the coulomb, rather than the ampere, was the SI base electrical unit. In 1960 the SI system made the ampere the base unit (See http://alpha.montclair.edu/~kowalskiL/SI/SI_PAGE.HTML). ## Conversions • The electrical charge of one mole of electrons (approximately 6.022×1023, or Avogadro's number) is known as a faraday (actually -1 faraday, since electrons are negatively charged). One faraday equals 96.485 341 5 kC (the Faraday constant). In terms of Avogadro's number (NA), one coulomb is equal to approximately 1.036 × NA ×10−5 elementary charges. • one ampere-hour = 3600 C • The elementary charge is approximately 160.2176 zC. • One statcoulomb (statC), the CGS electrostatic unit of charge (esu), is approximately 3.3356×10-10 C or about 1/3 nC. • 1 coulomb is the amount of electrical charge in 6.241506×1018 electrons or other elementary charged particles. • The charge of one electron is equal to -1.6022×10-19 C • Statcoulomb, the cgs unit of charge • Coulomb's law • Current (electricity) • Quantity of electricity • SI • Ampere
Copied to clipboard ## G = C11×3- 1+2order 297 = 33·11 ### Direct product of C11 and 3- 1+2 direct product, metacyclic, nilpotent (class 2), monomial, 3-elementary Aliases: C11×3- 1+2, C99⋊C3, C9⋊C33, C32.C33, C33.2C32, (C3×C33).C3, C3.2(C3×C33), SmallGroup(297,4) Series: Derived Chief Lower central Upper central Derived series C1 — C3 — C11×3- 1+2 Chief series C1 — C3 — C33 — C99 — C11×3- 1+2 Lower central C1 — C3 — C11×3- 1+2 Upper central C1 — C33 — C11×3- 1+2 Generators and relations for C11×3- 1+2 G = < a,b,c | a11=b9=c3=1, ab=ba, ac=ca, cbc-1=b4 > Smallest permutation representation of C11×3- 1+2 On 99 points Generators in S99 (1 2 3 4 5 6 7 8 9 10 11)(12 13 14 15 16 17 18 19 20 21 22)(23 24 25 26 27 28 29 30 31 32 33)(34 35 36 37 38 39 40 41 42 43 44)(45 46 47 48 49 50 51 52 53 54 55)(56 57 58 59 60 61 62 63 64 65 66)(67 68 69 70 71 72 73 74 75 76 77)(78 79 80 81 82 83 84 85 86 87 88)(89 90 91 92 93 94 95 96 97 98 99) (1 20 71 38 30 58 49 91 85)(2 21 72 39 31 59 50 92 86)(3 22 73 40 32 60 51 93 87)(4 12 74 41 33 61 52 94 88)(5 13 75 42 23 62 53 95 78)(6 14 76 43 24 63 54 96 79)(7 15 77 44 25 64 55 97 80)(8 16 67 34 26 65 45 98 81)(9 17 68 35 27 66 46 99 82)(10 18 69 36 28 56 47 89 83)(11 19 70 37 29 57 48 90 84) (12 94 33)(13 95 23)(14 96 24)(15 97 25)(16 98 26)(17 99 27)(18 89 28)(19 90 29)(20 91 30)(21 92 31)(22 93 32)(56 83 69)(57 84 70)(58 85 71)(59 86 72)(60 87 73)(61 88 74)(62 78 75)(63 79 76)(64 80 77)(65 81 67)(66 82 68) G:=sub<Sym(99)| (1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22)(23,24,25,26,27,28,29,30,31,32,33)(34,35,36,37,38,39,40,41,42,43,44)(45,46,47,48,49,50,51,52,53,54,55)(56,57,58,59,60,61,62,63,64,65,66)(67,68,69,70,71,72,73,74,75,76,77)(78,79,80,81,82,83,84,85,86,87,88)(89,90,91,92,93,94,95,96,97,98,99), (1,20,71,38,30,58,49,91,85)(2,21,72,39,31,59,50,92,86)(3,22,73,40,32,60,51,93,87)(4,12,74,41,33,61,52,94,88)(5,13,75,42,23,62,53,95,78)(6,14,76,43,24,63,54,96,79)(7,15,77,44,25,64,55,97,80)(8,16,67,34,26,65,45,98,81)(9,17,68,35,27,66,46,99,82)(10,18,69,36,28,56,47,89,83)(11,19,70,37,29,57,48,90,84), (12,94,33)(13,95,23)(14,96,24)(15,97,25)(16,98,26)(17,99,27)(18,89,28)(19,90,29)(20,91,30)(21,92,31)(22,93,32)(56,83,69)(57,84,70)(58,85,71)(59,86,72)(60,87,73)(61,88,74)(62,78,75)(63,79,76)(64,80,77)(65,81,67)(66,82,68)>; G:=Group( (1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22)(23,24,25,26,27,28,29,30,31,32,33)(34,35,36,37,38,39,40,41,42,43,44)(45,46,47,48,49,50,51,52,53,54,55)(56,57,58,59,60,61,62,63,64,65,66)(67,68,69,70,71,72,73,74,75,76,77)(78,79,80,81,82,83,84,85,86,87,88)(89,90,91,92,93,94,95,96,97,98,99), (1,20,71,38,30,58,49,91,85)(2,21,72,39,31,59,50,92,86)(3,22,73,40,32,60,51,93,87)(4,12,74,41,33,61,52,94,88)(5,13,75,42,23,62,53,95,78)(6,14,76,43,24,63,54,96,79)(7,15,77,44,25,64,55,97,80)(8,16,67,34,26,65,45,98,81)(9,17,68,35,27,66,46,99,82)(10,18,69,36,28,56,47,89,83)(11,19,70,37,29,57,48,90,84), (12,94,33)(13,95,23)(14,96,24)(15,97,25)(16,98,26)(17,99,27)(18,89,28)(19,90,29)(20,91,30)(21,92,31)(22,93,32)(56,83,69)(57,84,70)(58,85,71)(59,86,72)(60,87,73)(61,88,74)(62,78,75)(63,79,76)(64,80,77)(65,81,67)(66,82,68) ); G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11),(12,13,14,15,16,17,18,19,20,21,22),(23,24,25,26,27,28,29,30,31,32,33),(34,35,36,37,38,39,40,41,42,43,44),(45,46,47,48,49,50,51,52,53,54,55),(56,57,58,59,60,61,62,63,64,65,66),(67,68,69,70,71,72,73,74,75,76,77),(78,79,80,81,82,83,84,85,86,87,88),(89,90,91,92,93,94,95,96,97,98,99)], [(1,20,71,38,30,58,49,91,85),(2,21,72,39,31,59,50,92,86),(3,22,73,40,32,60,51,93,87),(4,12,74,41,33,61,52,94,88),(5,13,75,42,23,62,53,95,78),(6,14,76,43,24,63,54,96,79),(7,15,77,44,25,64,55,97,80),(8,16,67,34,26,65,45,98,81),(9,17,68,35,27,66,46,99,82),(10,18,69,36,28,56,47,89,83),(11,19,70,37,29,57,48,90,84)], [(12,94,33),(13,95,23),(14,96,24),(15,97,25),(16,98,26),(17,99,27),(18,89,28),(19,90,29),(20,91,30),(21,92,31),(22,93,32),(56,83,69),(57,84,70),(58,85,71),(59,86,72),(60,87,73),(61,88,74),(62,78,75),(63,79,76),(64,80,77),(65,81,67),(66,82,68)]]) 121 conjugacy classes class 1 3A 3B 3C 3D 9A ··· 9F 11A ··· 11J 33A ··· 33T 33U ··· 33AN 99A ··· 99BH order 1 3 3 3 3 9 ··· 9 11 ··· 11 33 ··· 33 33 ··· 33 99 ··· 99 size 1 1 1 3 3 3 ··· 3 1 ··· 1 1 ··· 1 3 ··· 3 3 ··· 3 121 irreducible representations dim 1 1 1 1 1 1 3 3 type + image C1 C3 C3 C11 C33 C33 3- 1+2 C11×3- 1+2 kernel C11×3- 1+2 C99 C3×C33 3- 1+2 C9 C32 C11 C1 # reps 1 6 2 10 60 20 2 20 Matrix representation of C11×3- 1+2 in GL3(𝔽199) generated by 61 0 0 0 61 0 0 0 61 , 106 91 0 92 93 92 0 107 0 , 1 0 0 106 92 0 198 0 106 G:=sub<GL(3,GF(199))| [61,0,0,0,61,0,0,0,61],[106,92,0,91,93,107,0,92,0],[1,106,198,0,92,0,0,0,106] >; C11×3- 1+2 in GAP, Magma, Sage, TeX C_{11}\times 3_-^{1+2} % in TeX G:=Group("C11xES-(3,1)"); // GroupNames label G:=SmallGroup(297,4); // by ID G=gap.SmallGroup(297,4); # by ID G:=PCGroup([4,-3,-3,-11,-3,396,817]); // Polycyclic G:=Group<a,b,c|a^11=b^9=c^3=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^4>; // generators/relations Export ׿ × 𝔽
Astronomy Answers: From the Astronomical Dictionary # Astronomy AnswersFrom the Astronomical Dictionary $$\def\|{&}$$ The description of the word you requested from the astronomical dictionary is given below. Suttungr A moon of 7 km diameter at about 19,459,000 km from the planet Saturn. The gravity at its surface is about 0.0001 times as strong as on Earth. The moon goes once around its planet in about 2.8 years. The moon was discovered in 2000. Also called SXXIII (Saturn twenty-three). Its provisional designation was S/2000 S12.
# Find the difference between two consecutive sensor readings in real-time in C I am working on a Micromouse and it has three sensors. Call it S1,S2 and S3. For now, I have to use S1. The idea is this S1 controls the left motor and S3, the right motor. S2 will detect wall in the front. Anyways, I am trying to write a code in C for the dsPIC30F4011 MCU which would continuously read Sensor values and after reading two consecutive values, it will compare the two values. Read happens every 0.1ms. The Flow of the Code is as follows: // Initialize timer for generating interrupts every 0.1ms // Pseudo-Code void __attribute__((interrupt, auto_psv)) _T1Interrupt(void) { int count = 0; //Read Sensor1 and store value in Sensor1Value Sensor1Value = Sensor1; int i = count++; //Now this is part where I am lost :( // I want to do this * diff_S1Value = Sensor1Value(i = n+1) - Sensor1Value(i = n); // n is in the mathematical sense, like n+1 is 2 and n is 1 // So I want to compare the new value with the previous sensor value if (diff_S1Value != 0) // Checks if the difference is zero { //Duty Cycle of PWM that controls the Speed of the Motor Sensor1Value = Sensor1Value(i = n+2) + or - diff_S1Value; PDC1 = float k/Sensor1Value; } } So if you look at the line with the *, how do I compare two sensor values in real-time every 0.1ms ? Let me know if one wants to more info!! You need to store the previous value somewhere, e.g. in a static: void ...
## Quantum Gravity Seminar ### Week 9, Track 2 #### November 27, 2000 "Okay," said the Wiz. "We're almost done working out the equations of motion for a bunch of Lagrangians. First we looked at "Chern theory", which has Lagrangian tr(F ^ ... ^ F) where F is the curvature of a connection A on some G-bundle P over the spacetime M. This Lagrangian vacuous equations of motion, which follow from the Bianchi identity d_A F = 0 Then we looked at the Yang-Mills Lagrangian tr(F ^ *F) This gives the Yang-Mills equation d_A *F = 0 The quantized version of Yang-Mills theory describes all the forces *except* gravity. It relies on a background metric, which we need to define the Hodge * operator. To avoid this, we can introduce an extra field E, which like *F is an Ad(P)-valued (n-2)-form. This lets us write down the Lagrangian tr(E ^ F) This gives the equations of "EF theory": F = 0 d_A E = 0 In dimensions 2, 3 and 4 we can add extra terms to the EF Lagrangian, making the field equations more interesting. We talked about this already in Week 2! What can we do in dimension 4?" Miguel said, "We can add a term like tr(E ^ E)..." "... or tr(F ^ F)!" added Jay. "Right!" said the Wiz. "The Chern theory Lagrangian tr(F ^ F) gives vacuous equations of motion, so adding a term like this won't affect the classical equations of motion in EF theory. It can still be interesting in the quantized theory, but let's not worry about that -- let's just try tr(E ^ F + Lambda E ^ E) What equations of motion do we get? How do we figure this out?" "Well," said Jay, "We start with the action S = \int tr(E ^ F + Lambda E ^ E) and then vary it: DS = D \int tr(E ^ F + Lambda E ^ E) Pushing the D in and using the Leibniz law, we get DS = \int tr(DE ^ F + E ^ DF + Lambda DE ^ E + Lambda E ^ DE) And then...." He hesitated. "Those last two terms look awfully similar," commented the Wiz. "Oh!" said Toby. "If E and DE were 2-forms, we'd have E ^ DE = DE ^ E. They're actually Ad(P)-valued 2-forms, but they still commute after we take the trace, so we get DS = \int tr(DE ^ F + E ^ DF + 2 Lambda DE ^ E) or DS = \int tr(E ^ DF + DE ^ (F + 2 Lambda E)) after we simplify." "Good!" said the Wiz. "Now what?" "The magic formula!" cried John. "Right! Never forget the magic formula DF = d_A DA! This gives DS = \int tr(E ^ d_A DA + DE ^ (F + 2 Lambda E)) Then what?" "When in doubt," said Miguel, "integrate by parts. So: DS = \int tr(d_A E ^ DA + DE ^ (F + 2 Lambda E)) I'm not completely sure about the sign of the first term, but it doesn't matter: the whole thing can only be zero for all variations DA and DE if both these equations hold: d_A E = 0 F + 2 Lambda E = 0 These are the equations of motion." "Excellent!" said the Wizard. "Notice anything funny about them?" The class stared intently at the equations. "Hmm," said Jay. "You can solve for E in the second equation and plug it into the first one...." The Wizard growled and tossed a low-intensity fireball in Jay's general direction, singing him slightly. "Ouch!" said Jay. "Why'd you do that?" "It was a nice idea," said the Wiz, "but you forgot a crucial clause: *if Lambda is nonzero*, we can solve the second equation for E and get E = F / 2 Lambda Then the first equation says d_A F = 0 But this is just a tautology: the Bianchi identity." "Hey!" said Miguel. "That's weird! When Lambda is nonzero, the equations say: take any connection A you like, work out F, and let E = F / 2 Lambda. Just as in Chern theory, any connection gives a solution. But when Lambda is zero, they say: A is flat and d_A E = 0. The two cases are utterly different!" "Yup!" said the Wiz. "But believe it or not, some people study the theory for arbitrary Lambda by doing perturbation about the Lambda = 0 theory." The class gasped in horror. "We'll talk more about that later. Now let's go down to 3 dimensions. What terms can we add to the EF theory Lagrangian here?" "Just tr(E ^ E ^ E)," said Toby. "Okay, so take this Lagrangian tr(E ^ F + Lambda E ^ E ^ E) and work out the equations of motion. Any takers?" "I bet I can do it," said Jay, striding confidently towards the board. "We write down the action S = \int tr(E ^ F + Lambda E ^ E ^ E) and vary it: DS = \int tr(DE ^ F + E ^ DF + Lambda (DE ^ E ^ E + E ^ DE ^ E + E ^ E ^ DE)) Then, hmm... are those last 3 terms all equal?" "Sure!" said Toby. "Use the cyclic property of the trace, and the fact that cyclic permutations are even, so we don't get nasty minus signs from switching the 1-form parts...." "Okay, so it's just DS = \int tr(DE ^ F + E ^ DF + 3 Lambda DE ^ E ^ E) Then I'll collect like terms and use the magic formula: DS = \int tr(E ^ d_A DA + DE ^ (F + 3 Lambda E ^ E)) To complete my performance, I'll integrate by parts: DS = \int tr(-d_A E ^ DA + DE ^ (F + 3 Lambda E ^ E)) I'm not sure about the sign of the first term, but it doesn't matter: this mess can only vanish for all variations of A and E if both these equations hold: d_A E = 0 F + 3 Lambda E ^ E = 0 These are the equations of motion!" The class erupted in applause; Jay took a bow and walked back to his desk. "Excellent!" said the Wiz. "And when G = SO(2,1), they're the equations for Lorentzian 3d gravity with cosmological constant Lambda. By the way... do you notice anything funny about these equations?" The Acolytes tried various tricks to derive one of the equations from the other, but failed miserably. "Oh well," said the Wiz, looking down and flipping through his notes for the next topic. "It never hurts to try." "... unless you get hit with a fireball!" someone quipped. The Wiz glanced up and glowered, but couldn't spot the culprit. Was Jay still smarting from that last one? "Okay. To finish things off, I'll work out the equations of motion for Lorentzian *4d* gravity with cosmological constant. Here our basic fields are an \so(3,1) connection A and an \R^4-valued 1-form e, and the Lagrangian is tr(e ^ e ^ F + Lambda e ^ e ^ e ^ e) I explained what this means in Week 2. The same Lagrangian works for the Riemannian theory if we use \so(4) instead of \so(3,1), but let's talk about the Lorentzian theory, since that's more like real physics. It's easy to work out the equations of motion. The action is S = \int tr(e ^ e ^ F + Lambda e ^ e ^ e ^ e) so we get DS = \int tr(2 De ^ e ^ F + e ^ e ^ DF + 4 Lambda De ^ e ^ e ^ e) where I've used the Leibniz law, the cyclic property of the trace, and the fact that De ^ e = e ^ De Grouping like terms and using the magic formula, DS = \int tr(e ^ e ^ d_A DA + De ^ (2 e ^ F + 4 Lambda e ^ e ^ e)) Integrating by parts, DS = \int tr(d_A(e ^ e) ^ DA + De ^ (2 e ^ F + 4 Lambda e ^ e ^ e)) so the equations of motion are d_A(e ^ e) = 0 e ^ F + 2 Lambda e ^ e ^ e = 0 Believe it or not, these are the usual vacuum Einstein equations in slight disguise, at least when the metric g(v,w) = tr((ev) (ew) is nondegenerate. I'll prove this some other time; it works like the 3d case I discussed last week. For now, just compare these equations to those for 4d EF theory with cosmological constant: d_A E = 0 F + 2 Lambda E = 0 Notice anything funny?" "Yeah," said Miguel, "e ^ e acts a lot like E." "Right! More precisely, given any solution of the EF equations for which E is of the form e ^ e, we get a solution of the equations of general relativity! We only get a special class of solutions this way, but it's still pretty interesting. It hints at a relation between gravity and EF theory, and this relation is the key to "spin foam models". But we can talk about that over dinner. I'm famished!" The class closed their notebooks and went down the winding stairs of the castle, out into the cool moonlit night. They hiked over to a nearby tavern, where they had dinner, laughing and talking into the wee hours of the morning. The conversation was very interesting -- but unfortunately, too secret for you. [email protected] © 2001 John Baez
## Stream: general ### Topic: HoTT3 universe errors #### Thomas Eckl (Aug 29 2020 at 12:14): I started to port my Lean2 - HoTT files to HoTT3, but run almost immediately into trouble: import hott.init universes u v w hott_theory namespace hott @[hott, hsimp, reducible] def id {A : Type u} (a : A) : A := a @[hott, hsimp, reducible] def id_map (A : Set) : A -> A := @id A @[hott] lemma id_map_is_right_neutral {A B : Set} (map : A -> B) : map ∘ (id_map A) = map := by { hsimp, exact rfl } end hott says goals accomplished at the last } but attaches a problem to the equality sign in id_map_is_right_neutral: kernel failed to type check declaration 'id_map_is_right_neutral' this is usually due to a buggy tactic or a bug in the builtin elaborator elaborated type: Π {A : Set} {B : Set} (map : ↥A → ↥B), map ∘ id_map A = map elaborated value: λ {A : Set} {B : Set} (map : ↥A → ↥B), cast idp⁻¹ rfl nested exception message: type mismatch at application @eq (↥A → ↥B) term ↥A → ↥B has type Type (max u_1 u_2) but is expected to have type Type u_3 I never understand these universe error messages. Why is ↥A → ↥B expected to have type Type u_3? Why can't u_3 be unified with max u_1 u_2? You get more or less the same message when replacing exact rfl by exact @hott.eq.refl (A -> B) map. I also wonder why you can't use reflexivity for hott.eq. #### Thomas Eckl (Aug 29 2020 at 12:17): I also have some fundamental questions about the implementation of HoTT in Lean 3: Why can't you just check whether terms use objects of type Prop in their construction? Isn't that the only way how HoTT and Lean 3 can produce contradiction? #### Gabriel Ebner (Aug 29 2020 at 13:32): The error happens, as the error message explains, because the tactic is probably buggy (because it generates an incorrect proof term). But I don't have time to debug that right now. Feel free to file an issue though. #### Gabriel Ebner (Aug 29 2020 at 13:33): You can definitely use reflexivity for hott.eq, we use it all over the place. If it doesn't work here, then that might be related to same issue as above. #### Gabriel Ebner (Aug 29 2020 at 13:36): Why can't you just check whether terms use objects of type Prop in their construction? That is, very generally speaking, exactly what the @[hott] attribute does. It is a bit more permissive though, it allows everything except eq.rec, acc.rec, heq.rec and choice (those are the only recursors/axioms that produce something outside of Prop). #### Thomas Eckl (Aug 29 2020 at 19:48): My guess would be the bug in the builtin elaborator, because the issue remains when you replace by ... with sorry. Is it then a Lean 3 problem? #### Floris van Doorn (Aug 29 2020 at 23:09): This is strange. I have minimized the problem, and here is a code snippet that fails in the latest version of Lean, without using anything HoTT-specific: -- set_option trace.elaborator_detail true def my_eq {A : Type*} (a b : A) : Prop := true lemma id_map_is_right_neutral {A : Type} (map : A -> A) : my_eq (function.comp.{1 1 _} map map) map := sorry #### Kevin Buzzard (Aug 29 2020 at 23:13): Does changing Type* to Type u help? #### Floris van Doorn (Aug 29 2020 at 23:25): no (changing it to Type/Sort*/Sort u does) #### Floris van Doorn (Aug 29 2020 at 23:27): It is strange that @Thomas Eckl runs into this problem, but apparently it wasn't a problem for the rest of the HoTT library. #### Kevin Buzzard (Aug 29 2020 at 23:28): universe u def my_eq {A : Type u} (a b : A) : Prop := true lemma id_map_is_right_neutral {A : Type} (maap : A -> A) : my_eq (function.comp maap maap) maap := trivial -> kernel failed to type check declaration 'id_map_is_right_neutral' this is usually due to a buggy tactic or a bug in the builtin elaborator elaborated type: ∀ {A : Type} (maap : A → A), my_eq (maap ∘ maap) maap elaborated value: λ {A : Type} (maap : A → A), trivial nested exception message: type mismatch at application @my_eq (A → A) term A → A has type Type but is expected to have type Type u_1 Interesting! #### Thomas Eckl (Sep 01 2020 at 16:51): I've got the same error message when stating the universal property of injective maps (of sets): @[hott] lemma univ_prop_of_inj {A B : Set} (i : A -> B) (i_inj : is_set_injective i) : forall (C : Set) (f g : C -> A), i ∘ f = i ∘ g -> f = g := sorry I hope is_set_injective is self-explaining, but you can produce the error message also by omitting the parameteri_inj. The scientist in me immediately induces from these two observations that the problem might be related to the composition of functions. Hovering over the ∘ shows that composition is taken from the general Lean3 library (init.function), not from HoTT3. And in Lean3, all the domains and codomains of the maps are sorts, not types - maybe that clashes with = of maps between types? Since I did not find a definition of ∘ in hott.init.function, I guess it does not exist anywhere. Should it be added to hott.init.function? #### Thomas Eckl (Sep 01 2020 at 17:07): Just tried: Inserting in my file namespace function @[inline, reducible] def comp {α β φ : Type _} (f : β → φ) (g : α → β) : α → φ := λ x, f (g x) infixr ∘ʰ :80 := hott.function.comp end function solves the problem. The new symbol is not perfect, but also not too bad ... #### Floris van Doorn (Sep 01 2020 at 17:09): Yes, it has to do with the interaction of Sort and Type between hott.eq and function.comp. I don't know why though, I feel like Lean should be able to figure it out. Moreover, Lean managed to figure out all the occurrences of composition in init. #### Floris van Doorn (Sep 01 2020 at 17:10): If in the hott namespace you write def function.comp {A B C : Type _} (g : B → C) (f : A → B) (x : A) := g (f x) hott_theory_cmd "local infix ∘ := hott.function.comp" then you override the notation ∘ to mean hott.function.comp (so you can use the same symbol) Last updated: May 18 2021 at 17:44 UTC
contraction mapping theorem Printable View • December 20th 2012, 08:15 AM Plato13 contraction mapping theorem I need to show f:[0,1]->[0,1] is a contraction mapping. $f(x)=sinx|x^{0.5}-g(x)|$ where g is continous map form [0,1] to itself When I try |f(x)-f(y)|, using triangle inequality and sinx<1, I get it is less that or equal to $|x^{0.5}-f(x)|-|y^{0.5}-f(y)|$ which I can't seem to manipulate (even aware that x,f(x) are in [0,1]) to k|x-y| as required. • December 21st 2012, 12:13 AM Plato13 Re: contraction mapping theorem I require to show that |f(x)-f(y)| is less that or equal to k|x-y| for some 0<k<1
# PolyGamma PolyGamma[z] gives the digamma function . PolyGamma[n,z] gives the n derivative of the digamma function . # Details • Mathematical function, suitable for both symbolic and numerical manipulation. • PolyGamma[z] is the logarithmic derivative of the gamma function, given by . • PolyGamma[n,z] is given for positive integer by . • For arbitrary complex n, the polygamma function is defined by fractional calculus analytic continuation. • PolyGamma[z] and PolyGamma[n,z] are meromorphic functions of z with no branch cut discontinuities. • For certain special arguments, PolyGamma automatically evaluates to exact values. • PolyGamma can be evaluated to arbitrary numerical precision. • PolyGamma automatically threads over lists. • PolyGamma can be used with Interval and CenteredInterval objects. » # Examples open allclose all ## Basic Examples(7) Evaluate the digamma function: Derivative of the gamma function: Plot the digamma function over a subset of the reals: Plot over a subset of the complexes: Series expansion at the origin: Series expansion at Infinity: Series expansion at a singular point: ## Scope(47) ### Numerical Evaluation(7) Evaluate numerically: Evaluate for integer arguments of any size: Evaluate for complex arguments and orders: Evaluate to any precision: The precision of the output tracks the precision of the input: Evaluate PolyGamma efficiently at high precision: PolyGamma can be used with Interval and CenteredInterval objects: ### Specific Values(6) Some singular points of PolyGamma: Values at infinity: Find a zero of : Use FunctionExpand to expand higher-order polygamma functions: Special case: Evaluate at exact arguments: ### Visualization(3) Plot the digamma function: Plot the real part of : Plot the imaginary part of : Plot PolyGamma for half-integer values of parameter : ### Function Properties(9) Real domain of PolyGamma: Approximate function ranges of PolyGamma for half-integer parameters: PolyGamma is not an analytic function: It has both singularities and discontinuities: is a meromorphic function: For fixed nonnegative , is an analytic function of : It is not meromorphic for other values of : is neither nondecreasing nor nonincreasing: is not injective: is surjective: is neither non-negative nor non-positive: is neither convex nor concave: ### Differentiation(3) First derivative of PolyGamma: Higher derivatives of Euler gamma function: Formula for the derivative: ### Integration(3) Indefinite integral of PolyGamma: Indefinite integral involving a power function: Definite integral : ### Series Expansions(7) Taylor expansion for the digamma function around : Plot the first three approximations for the Euler gamma function around : General term in the series expansion of the digamma function: Series expansion at infinities: Series expansion at poles: Series expansion at a generic point: Series expansion near a singularity: PolyGamma can be applied to a power series: ### Function Identities and Simplifications(5) Use FullSimplify to simplify polygamma functions: PolyGamma identity : PolyGamma of a double argument: Other argument simplifications: Recurrence relation: ### Function Representations(4) Digamma function definition: Integral representation: PolyGamma can be represented as a DifferenceRoot: ## Applications(3) Plot of the absolute value of PolyGamma over the complex plane: The electric field energy of a charge at a fraction of the distance between parallel conducting plates: Expand near the left wall: Final speed of a rocket with discrete propulsion events: Final velocity in the limit of constant continuous propulsion: ## Properties & Relations(7) Use FullSimplify to simplify polygamma functions: Express rational arguments through elementary functions: Numerically find a root of a transcendental equation: Sums and integrals: Generate PolyGamma from integrals, sums, and limits: Generating function: Obtain as special cases of hypergeometric functions: ## Possible Issues(3) The oneargument form evaluates to the two-argument form: Large orders can give results too large to be computed explicitly: Machinenumber inputs can give highprecision results: Wolfram Research (1988), PolyGamma, Wolfram Language function, https://reference.wolfram.com/language/ref/PolyGamma.html (updated 2022). #### Text Wolfram Research (1988), PolyGamma, Wolfram Language function, https://reference.wolfram.com/language/ref/PolyGamma.html (updated 2022). #### CMS Wolfram Language. 1988. "PolyGamma." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/PolyGamma.html. #### APA Wolfram Language. (1988). PolyGamma. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PolyGamma.html #### BibTeX @misc{reference.wolfram_2022_polygamma, author="Wolfram Research", title="{PolyGamma}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/PolyGamma.html}", note=[Accessed: 05-October-2022 ]} #### BibLaTeX @online{reference.wolfram_2022_polygamma, organization={Wolfram Research}, title={PolyGamma}, year={2022}, url={https://reference.wolfram.com/language/ref/PolyGamma.html}, note=[Accessed: 05-October-2022 ]}
# All Questions 18 views ### winding number partial fractions I need to compute the winding numbers for a particular contour integration (which I understand and is not relevant for this question). However, before doing so I need to use partial fractions to get ... 23 views ### Expected Value of the product of an indicator R.V. and continuous R.V. I have an indicator random variable $X \in \{0,1\}$ and a continuous random variable $Y$. I am looking for $E[XY]$. Intuitively, it seems $E[XY] = P(X=1)E[Y|X=1]$, but am having a hard time ... 30 views Let V be an inner product space,and suppose that $x$ and $y$ are orthogonal vectors in V.We also know $\left\lVert x+y \right\rVert^2=\left\lVert x \right\rVert^2+\left\lVert y \right\rVert^2$.My ...
# Reciprocal Frequency Counter Mean I have designed a high precision frequency counter circuit. I am using it to measure a frequency of around 35kHz that is stable to 0.1mHz. I can measure the frequency using a Stanford Research Systems SR620 and the only digits that change are 0.000XXX. My frequency counter varies by about 1Hz with the same signal. The SR620 uses some sort of Mean calculation to provide a more precise result. I am looking to learn how to do the same. How the circuit works There are two counters. A count down counter and a count up counter. The count down counter is loaded with the base frequency (or expected perfect input frequency) multiplied by the sample time in seconds. The count down counter decrements on each period of the 35kHz input. The count up counter counts a 2GHz signal while the count down is counting to zero. The count up counter stops when the count down counter reaches zero. Then frequency = (base frequency * sample time in seconds) / (count up counter / 2GHz) or (count down counter start count) / (count up counter / 2GHz) My circuit uses a PLL chip locked to a 10ppb 100MHz OCXO to generate a 2GHz signal. Using a rubidium standards 1pps output my counter is accurate to 2,000,000,000 +-15 for a 1 second reading. I need to be able to read a 35kHz signal and be accurate to 100uHz for a 1 second reading. The 35kHz signal can vary to as low as 31kHz and to as high as 39kHz but my readings are not performed while the frequency is changing. What kind of calculation would make these readings more accurate and does anyone know of a resource that explains it? My Solution My issue ended up being a circuit logic to software issue. My standard deviation went from 1Hz to 100uHz after the fix. I did not need to modify my firmware math. • Finally! A correct use of the unit "mHz"! – Dave Tweed May 4 '18 at 18:01 • The SR620 manual and application note give a lot of detail. Impressive list of parts, but no schematic or block diagram. Includes a Z80 processor, so a lot can be done in firmware. – Dave Tweed May 4 '18 at 18:14 • @DaveTweed Actually, the paper version of the SR620 includes also the schematic. – Massimo Ortolano May 4 '18 at 18:16 • From the equation you posted, it doesn't seem you've implemented a reciprocal counter. – Massimo Ortolano May 4 '18 at 18:18 • How much does the frequency vary? What is the range of values? How often does it change? How closely do you know the frequency? – Henry Crun May 4 '18 at 18:47 A plain reciprocal counter should give F-Clock/T-Measurement resolution. i.e 0.0035Hz/second with 10MHz clock. A pic/avr should achieve this by simple reciprocal counting with its timer capture registers. That is what you should be achieving. Your measurements must be coherent for accuracy to increase linearly i.e. the capture counter must be running continuously to count N through M multiple edges of the input signal. If you average incoherent measurements, accuracy only increases by sqrt() they long ago used an analog interpolator {linear ramp and samplers) to go between the clock resolution e,g to add 3 digits resolution eg 100M clock =11 digits/second For stable or almost known frequencies, you can mix down then measure period of the beat frequency. this increases resolution dramatically in fact right to the phase noise/allen variance limit of the clock source, even just using an ordinary uP as the counter I don't know how the SR620 does it, but this is how I suggest doing it. Suppose you want at least 10 readings per second. Divide the 35000+/- frequency by about 3500. Maybe you pick 4096 or 2048, say the latter. That gives you an edge every 58.514285714 ms, dividing by 2^n where n = 11. Use that with a reasonable clock, say Fosc = 25MHz. You will have 1462857 clocks per cycle, giving you solid 6-digit resolution at 17Hz sample rate. If you need more resolution, increase n or Fosc. If you increase n you reduce the sample rate, of course. If you increase Fosc the logic has to work faster and the sharpness of the edges on your 35kHz becomes more important. To get the measured frequency F from the number of clocks k, F =$\frac{F_{OSC}\cdot 2^n}{k}$ I see you've added the clock frequency to your question- at 2GHz, the edges of the input signal have to be very sharp, the comparator very fast, the reference voltage and signal amplitude very stable etc. to get full benefit from the high clock frequency. • Yes the PLL outputs a differential 2GHz signal that is read with an 8-bit ECL logic ripple counter that is good to I believe 2.4GHz. When the ripple counter overflows, it increments a lower speed 32-bit counter. – ozziwald May 4 '18 at 20:59 Given a stable time base, a desired readout interval equal to N cycles of that time base, and a stable input signal whose frequency is equal to at least twice the readout frequency, one may relatively easily measure the frequency with an uncertainty fraction of 3/N. Each time an input pulse occurs, sample the time and the number of pulses that have occurred to date. At each readout interval, capture the sampled time and count values. Divide the difference in counts by the difference in time, and that will be the frequency. For any signal whose frequency is greater than some integer K times the readout frequency, the interval being measured will be at least (K-1)/(K+1) of the readout interval. In the worst case where the input frequency is just below 3x the readout frequency, the interval will be just over 1/3 the readout period. Here is an Arxiv paper that should be helpful. It gives an overview of precision frequency measurement and then proposes a new improved statistical based measurement method. From the paper: Higher resolution is obtained by measuring fractions of the clock period with a suitable interpolator. Simple and precise interpolators work only at fixed frequency. The most widely used techniques are described underneath. Surprisingly, all them are rather old and feature picosecond range resolution. HP used analog charge-storage interpolation in a reciprocal time-pulse counter beast in the 1960s.. The transistors were 2N5179.
# Distance between quaternion with opposite signs I want to compute the distance between two unit quaternions to know if the angle between them is too big, because I don't want to apply the rotation if the angle between the quaternions is higher than $\pi$. I have a problem with quaternion of opposite sign. Between $Q_1 = (-0.33, 0.13, -0.93, 0.05)$ and $Q_2 = (-0.37, 0.10, -0.92, 0.00)$ I compute a distance of $0.15$, but between $Q_1$ and $Q_3 = (0.37, -0.09, 0.92, -0.00)$ I've got $6.14 = 2\pi -0.15$. Both $Q_2$ and $Q_3$ represents the same orientation but with opposite sign. I wonder why I don't have the same result. The calculations I have to compute the distance between $Q_1$ and $Q_2$ are : (1)$$QuatProjection = Q_1 \times Q_2^{-1}$$ where $\times$ is the Hamilton product and $Q_2^{-1}$ is the conjugate of $Q_2$. (2)$$angle = 2arctan \Bigl(\frac{||QuatProjection||}{qw}\Bigr)$$ with $qw$ the $lambda$ of the quaternion $QuatProjection = (qx, qy, qz, qw)$ and $||Q||$ the norm of $Q$ (3)$$QuatProjection = QuatProjection.\frac{angle}{||QuatProjection||}$$ with $.$ the scalar multiplication with each members of the quaternion. Finally, (4)$$distance = || QuatProjection ||$$ It seems that if I use the absolute value of $qw$, I've got the correct result but I don't understand why. It might just be fortuitous. Although, I don't understand the purpose of the (3) equation, the scalar multiplication. I will be really grateful if someone can help me with my problem. • It seems that my use of atan2() instead of atan() is part of the answer, so I edited the question to match exactly my computation – mlel Nov 20 '17 at 16:04 It took some days to figure out the answer. The purpose of equation (3) We are using unit quaternions so $distance$ in (4) is equivalent to $angle$ in (2): (3) + (4) gives $distance = ||\Bigl(\frac{QuatProjection}{||QuatProjection||}\Bigr).angle||$ $distance = ||\Bigl(\frac{QuatProjection}{||QuatProjection||}\Bigr)||.||angle||$ with angle a scalar and $\frac{QuatProjection}{||QuatProjection||} = 1$ , for unit quaternion $distance = angle$ So, in this case equations (3) and (4) are useless. atan() vs atan2() The use of atan or atan2 has a big influence on the result because: $0 <= atan() <= π$ $0 <= atan2() <= 2π$ To detect angles higher than $\pi$, we shall use $atan2()$. Quaternion with opposite sign To get the same angle value with $Q_2$ and $Q_3$, we can make the $QuatProjection$ positive if its scalar part is negative, between (1) and (2): (1b) if $qw < 0$ $qx = -qx$, $qy = -qy$, $qz = -qz$ and $qw=-qw$ It conserves the value of the norm of $QuatProjection$.
# Concurrent request scheduling explained It’s quite an interesting way that’s used to implement concurrent request schedules in Oracle Applications. In this post I’ll describe how “Periodic” and “On Specific Day” type of schedules are stored in the Database and if you will be patient enough to read all the story, I’ll give you a query that can be used to report all the request schedules in the environment. I’ll pay attention to the repeating schedules only as requests submitted for one-time execution are not too interesting, basically, they use the fnd_concurrent_requests.requested_start_date field to store the time the request has to be executed. This field is used in repeating schedules to specify the time of next execution. There are just 2 normal types of repeating schedules. Defining a ‘periodic’ schedule Periodic – the request is submitted for execution in pre-defined intervals of specified number of months, weeks, days, hours or minutes. Definig a ‘on Specific Days’ schedule On Specific Days – user can choose exact dates of month or days of week when the request will be executed. There’s an option to schedule requests for the last day of months too. There’s also a 3rd option – Advanced – this is a special option that implements possibility to run requests based on schedules, that depend on different financial calendars and financial periods. This kind of scheduling is rarely used as it’s available in few Applications products only, e.g. GL. These schedules are managed by Scheduler/Prereleaser Concurrent Manager. There are 2 tables invoved in storing the information about schedules: fnd_concurrent_requests that stores all basic information about concurrent requests including the next time the request is scheduled for, andfnd_conc_release_classes that stores information about the schedules. Both tables can be joined byrelease_class_id. The fields we are interested in are: fnd_conc_release_classes.CLASS_TYPE – contains value ‘P’ for “Periodic” schedules, “S” – for “on Specific Days” schedules and “X” – for advanced schedules. fnd_conc_release_classes.DATE1 – start date of the schedule (“Start at” field in the form) fnd_conc_release_classes.DATE2 – end date of the schedule (“End at” field in the form) – this information is doubled in fnd_concurrent_requests.resubmit_end_date. fnd_conc_release_classes.CLASS_INFO – this is the most interesting field as it contains all the information needed for reschedulingThe format of the field depends on the type of schedule. “PERIODIC” schedule In case of Periodic schedule fnd_conc_release_classes.CLASS_INFO field contains values like “2:D:S” orX:Y:Z where: • X – number of months/weeks/days/hours/minutes the request has to be rescheduled from prior run. • Y – contains a single letter representing units • “M” – months; • “D” – days; • “H” – hours; • “N” – minutes; • (there is no representation of “weeks” option. If you specify interval in weeks, it’s automatically calculated and stored in “days”). • Z – contains a single letter to represent if the rescheduling has to be done from start or from completion of the prior run • S – from the start of the prior run; • C – from the completion of the prior run. Some samples: • 30:N:S – Repeat every 30 minutes from the start of the prior run • 5:N:C – Repeat every 5 minutes from the completion of the prior run • 12:H:S – Repeat every 12 hours from the start of the prior run It’s interesting that information about intervals of periodic schedules is duplicated in fnd_concurrent_requeststable fields RESUBMIT_INTERVAL, RESUBMIT_INTERVAL_TYPE_CODE andRESUBMIT_INTERVAL_UNIT_CODE. I haven’t yet found why’s that so. “ON SPECIFIC DAY” schedule In case of on Specific Day schedule fnd_conc_release_classes.CLASS_INFO field contains values like “000010000000000000000000000000010000000” – a 39 character value consisting of 0 and 1. The idea is that the placement of 1-s represent the options selected through form: • 1-s at places 1 to 31 – represent dates, when request has to be run, eg, if the 10th character is “1” – the request is scheduled to run on 10th day of each month; • character “1” at the 32nd position – specifies that the request has to be run at the last day of each month; • 1-s at places 33 to 39 – specifies days of week (Sunday – Saturday)the request has to be run. if the 33rd character is “1” – the request is scheduled to run each Sunday, if 34th – on Monday and so on. Some samples: • 000000000000000000000000000000000000001 – Days of week: Sa • 111111111000000000000000000000000111110 – Dates: 1 2 3 4 5 6 7 8 9. Days of week: Mo Tu We Th Fr • 000000000000000000000000000000010000000 – Last day of month Reporting all schedules Using the information given above I wrote a “small” query to provide a report like this: Reporting all schedules The query was tested in Oracle Applications versions 11.5.9, 11.5.10.1, 12.0.1 and 12.0.4 so there’s a good chance it will work on others as well. The performance of the query was OK.  but I have to say – test/analyze it before running in productio. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 select r.request_id,        p.user_concurrent_program_name || case          when p.user_concurrent_program_name = 'Report Set' then           (select ' - ' || s.user_request_set_name              from fnd_request_sets_tl s             where s.application_id = r.argument1               and s.request_set_id = r.argument2               and language = 'US')          when p.user_concurrent_program_name = 'Check Periodic Alert' then           (select ' - ' || a.alert_name              from alr_alerts a             where a.application_id = r.argument1               and a.alert_id = r.argument2               and language = 'US')        end concurrent_program_name,        case          when p.user_concurrent_program_name != 'Report Set' and               p.user_concurrent_program_name != 'Check Periodic Alert' then           r.argument_text        end argument_text,        r.requested_start_date next_run,        r.hold_flag on_hold,        decode(c.class_type,               'P',               'Periodic',               'S',               'On Specific Days',               'X',               'Advanced',               c.class_type) schedule_type,        case          when c.class_type = 'P' then           'Repeat every ' ||           substr(c.class_info, 1, instr(c.class_info, ':') - 1) ||           decode(substr(c.class_info, instr(c.class_info, ':', 1, 1) + 1, 1),                  'N',                  ' minutes',                  'M',                  ' months',                  'H',                  ' hours',                  'D',                  ' days') ||           decode(substr(c.class_info, instr(c.class_info, ':', 1, 2) + 1, 1),                  'S',                  ' from the start of the prior run',                  'C',                  ' from the completion of the prior run')          when c.class_type = 'S' then           nvl2(dates.dates, 'Dates: ' || dates.dates || '. ', null) ||           decode(substr(c.class_info, 32, 1), '1', 'Last day of month ') ||           decode(sign(to_number(substr(c.class_info, 33))),                  '1',                  'Days of week: ' ||                  decode(substr(c.class_info, 33, 1), '1', 'Su ') ||                  decode(substr(c.class_info, 34, 1), '1', 'Mo ') ||                  decode(substr(c.class_info, 35, 1), '1', 'Tu ') ||                  decode(substr(c.class_info, 36, 1), '1', 'We ') ||                  decode(substr(c.class_info, 37, 1), '1', 'Th ') ||                  decode(substr(c.class_info, 38, 1), '1', 'Fr ') ||                  decode(substr(c.class_info, 39, 1), '1', 'Sa '))        end schedule,        c.date1 start_date,        c.date2 end_date,        c.class_info   from fnd_concurrent_requests r,        fnd_conc_release_classes c,        fnd_concurrent_programs_tl p,        (SELECT release_class_id,                substr(max(SYS_CONNECT_BY_PATH(s, ' ')), 2) dates           FROM (select release_class_id,                        rank() over(partition by release_class_id order by s) a,                        s                   from (select c.class_info,                                l,                                c.release_class_id,                                decode(substr(c.class_info, l, 1),                                       '1',                                       to_char(l)) s                           from (select level l from dual connect by level <= 31),                                fnd_conc_release_classes c                          where c.class_type = 'S')                  where s is not null)         CONNECT BY PRIOR                     (a || release_class_id) = (a - 1) || release_class_id          START WITH a = 1          group by release_class_id) dates  where r.phase_code = 'P'    and c.application_id = r.release_class_app_id    and c.release_class_id = r.release_class_id    and nvl(c.date2, sysdate + 1) > sysdate    and c.class_type is not null    and p.concurrent_program_id = r.concurrent_program_id    and p.application_id = r.program_application_id    and p.language = 'US'    and dates.release_class_id(+) = r.release_class_id  order by on_hold, next_run; I know there are some interesting lines in this query that might need some explanation, but as that is not directly connected to the topic of this post I’ll provide explanation in comments if you will ask for it. • 本文已收录于以下专栏: ## SA-Concurrent request scheduling explained Concurrent request scheduling explained 摘自:http://appsdbalife.wordpress.com/2008/09/16/concurrent-r... • kikiwhq • 2014年08月12日 14:24 • 305 ## Scheduling a Concurrent program EBS中的Program是可以根据需求周期性运行的,比如‘Purge Logs and Closed System Alerts’ Program,我们需要每天运行来清理日渐庞大的日志表,周期性运行P... ## How To Kill runaway processes After Terminating Concurrent Request Every concurrent Request uses some resources for running. If we find that the concurrent request is ... ## [Script]Long Running Concurrent Request in Oracle EBS Looking on how to check long running concurrent request in Oracle Apps 11i or R12? Here’s the overvi... ## 如何收集Concurrent Request的SQL Trace 1. System Administrator > Concurrent > Program > Define 注意:如果仅仅是"Enable Trace",收集到的Sql Trace并不包... ## Oracle EBS Concurrent Request:Gather Schema Statistics Oracle EBS 的Concurrent Request"Gather Schema Statistics"是一个和性能相关的Concurrent Program,它会对表,列和索引的做数据采样,... 举报原因: 您举报文章:Concurrent request scheduling explained 色情 政治 抄袭 广告 招聘 骂人 其他 (最多只允许输入30个字)
# Problem: Lithium hydroxide may be used to absorb carbon dioxide in enclosed environments, such as manned spacecraft and submarines. Write an equation for the reaction that involves 2 mol of LiOH per 1 mol of CO2. (Hint: Water is one of the products.) ⚠️Our tutors found the solution shown to be helpful for the problem you're searching for. We don't have the exact solution yet. ###### Problem Details Lithium hydroxide may be used to absorb carbon dioxide in enclosed environments, such as manned spacecraft and submarines. Write an equation for the reaction that involves 2 mol of LiOH per 1 mol of CO2. (Hint: Water is one of the products.)
# Matrix multiplication (works with 2 but not with more) This topic is 4900 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic. ## Recommended Posts I'm making a 3D game using 3D rotation matrixes, and multiplying them together to add different effects. I've documented myself on this subject on google and made a function to mutiply matrices, etc. it works efficiently when using 2 matrices, but when using more than one i multiply like this (AxB)xC and all i get is my objet screwed up all ways on screen. How must i multiply more than 2 matrices together? thanks ;) i've not found any website mentionning those here's the method i'm using, just in case matrix format: double matrix[] 0, 1, 2, 3, 4, 5, 6, 7, 8 void mulMatrix(double* MatrixA, double* MatrixB, double* dest_matrix){ dest_matrix[0] = MatrixA[0] * MatrixB[0] + MatrixA[1] * MatrixB[3] + MatrixA[2] * MatrixB[6]; dest_matrix[1] = MatrixA[0] * MatrixB[1] + MatrixA[1] * MatrixB[4] + MatrixA[2] * MatrixB[7]; dest_matrix[2] = MatrixA[0] * MatrixB[2] + MatrixA[1] * MatrixB[5] + MatrixA[2] * MatrixB[8]; dest_matrix[3] = MatrixA[3] * MatrixB[3] + MatrixA[4] * MatrixB[3] + MatrixA[5] * MatrixB[6]; dest_matrix[4] = MatrixA[3] * MatrixB[4] + MatrixA[4] * MatrixB[4] + MatrixA[5] * MatrixB[7]; dest_matrix[5] = MatrixA[3] * MatrixB[5] + MatrixA[4] * MatrixB[5] + MatrixA[5] * MatrixB[8]; dest_matrix[6] = MatrixA[6] * MatrixB[6] + MatrixA[7] * MatrixB[3] + MatrixA[8] * MatrixB[6]; dest_matrix[7] = MatrixA[6] * MatrixB[7] + MatrixA[7] * MatrixB[4] + MatrixA[8] * MatrixB[7]; dest_matrix[8] = MatrixA[6] * MatrixB[8] + MatrixA[7] * MatrixB[5] + MatrixA[8] * MatrixB[8]; } ##### Share on other sites Matrix multiplication is associative. It shouldn't matter if you multiply A and B together first or B and C together first. ##### Share on other sites > Matrix multiplication is associative. It shouldn't matter if you multiply A and B together first or B and C together first. i know, but it doesn't work... i do something like: C= AxB E= CxD and i use E, however it just manages to screw up my object instead of doing nice rotations like each matrix does separately ##### Share on other sites Quote: Original post by Marianne dest_matrix[3] = MatrixA[3] * MatrixB[3] + MatrixA[4] * MatrixB[3] + MatrixA[5] * MatrixB[6]; dest_matrix[4] = MatrixA[3] * MatrixB[4] + MatrixA[4] * MatrixB[4] + MatrixA[5] * MatrixB[7]; dest_matrix[5] = MatrixA[3] * MatrixB[5] + MatrixA[4] * MatrixB[5] + MatrixA[5] * MatrixB[8]; should be dest_matrix[3] = MatrixA[3] * MatrixB[0] + MatrixA[4] * MatrixB[3] + MatrixA[5] * MatrixB[6]; dest_matrix[4] = MatrixA[3] * MatrixB[1] + MatrixA[4] * MatrixB[4] + MatrixA[5] * MatrixB[7]; dest_matrix[5] = MatrixA[3] * MatrixB[2] + MatrixA[4] * MatrixB[5] + MatrixA[5] * MatrixB[8]; and Quote: Original post by Marianne dest_matrix[6] = MatrixA[6] * MatrixB[6] + MatrixA[7] * MatrixB[3] + MatrixA[8] * MatrixB[6]; dest_matrix[7] = MatrixA[6] * MatrixB[7] + MatrixA[7] * MatrixB[4] + MatrixA[8] * MatrixB[7]; dest_matrix[8] = MatrixA[6] * MatrixB[8] + MatrixA[7] * MatrixB[5] + MatrixA[8] * MatrixB[8]; should be dest_matrix[6] = MatrixA[6] * MatrixB[0] + MatrixA[7] * MatrixB[3] + MatrixA[8] * MatrixB[6]; dest_matrix[7] = MatrixA[6] * MatrixB[1] + MatrixA[7] * MatrixB[4] + MatrixA[8] * MatrixB[7]; dest_matrix[8] = MatrixA[6] * MatrixB[2] + MatrixA[7] * MatrixB[5] + MatrixA[8] * MatrixB[8]; ##### Share on other sites thanks! it works great! the site i've been on must have been wrong (i don't reckon i made an error cause it did work for simple mul) ##### Share on other sites quote: >> Matrix multiplication is associative. It shouldn't matter if you multiply A and B together first or B and C together first. >i know, but it doesn't work... You are both wrong. And I think you mean commutative instead of associative. AND matrix multiplication are in general NOT commutative so it does matter whether you multiply like this AxB or this BxA. A clear example of this is the multiplaication of a 2x3 matrix with a 3x2 matrix... One way around it gives a 2x2 matrix. The other way around, a 3x3 matrix comes out as result.. ##### Share on other sites For multiplication: Associative means (a*b)*c = a*(b*c) Commutative means a*b = b*a so Marianne and SiCrane were correct in using the term associative, and correct in saying that it applies to matrix multiplication. Matrix multiplication is not commutative, but then that was never an issue... ##### Share on other sites Yes I know what associative and communicative means. Reading the post again I see I missread it. I see he was actually talking about the associative rule..=) Geez.. My mistake - sorry! • ### What is your GameDev Story? In 2019 we are celebrating 20 years of GameDev.net! Share your GameDev Story with us. • 11 • 15 • 11 • 11 • 9 • ### Forum Statistics • Total Topics 634151 • Total Posts 3015825 ×
# Wald-test & T-test confusion #### alex.wendland ##### New Member Hi, I'm trying to test the linear restriction b1-b2=0 in my MNL-Modell to find if the coefficients b1 and b2 are equal or not. My Wald-statistic has a value of 30.46 and my text-book tells me that with Wald-values exceeding the critical chi-squared value (here 3.84) I can assume that the coefficients are equal. This confuses me because with the T-test values exceeding the critical t-value result in rejecting the Ho (which is b1-b2=0) and I have to assume that b1 and b2 are different. Can anybody pitch me his ideas and thoughts on this? alex #### antonis11 ##### New Member Hi alex, In order to test for Ho: β1 -β2=0 you cannot use the individual t statistics for β1 and β2 (estimates). The t statistic is calculated like this t=(β1-β2)/se(β1-β2). The βi used in the t statistic are all estimates and not actual β. Hope this helps! #### fed1 ##### TS Contributor I cant remember the details, but the wald test is less efficient(not as good) because of the way it estimates the variance. Wald is asymptotically efficient. Do you know what exact formula is for denominator of wald in this case? I cant remember/too lazy to look up. #### Dragan ##### Super Moderator Hi, My Wald-statistic has a value of 30.46 and my text-book tells me that with Wald-values exceeding the critical chi-squared value (here 3.84) I can assume that the coefficients are equal. Can anybody pitch me his ideas and thoughts on this? alex Well, yes I can. Either you are misinterpreting the (perhaps entire) discussion in your textbook or the authors of this textbook are wrong. So, which is it?...you tell me.
# Fermi levels in p-n junction under voltage 1. Nov 27, 2007 ### smallphi I understand that for a semiconductor p-n junction under zero voltage, the Fermi level is constant throughout the junction because that is the condition for a system in thermodynamic equilibrium. I also understand that p-n junction under applied voltage (forward or reverse) is not a system in thermal equilibrium because there is a nonzero total current that obviously tries to revert the system back to equilibrium. Then I don't understand how come away from the junction we still use two Fermi levels to describe the electron distribution in energies, one for the left side and one for the right. Most importantly how come those Fermi levels differ exactly by the applied voltage? I've consulted 2 textbooks in semiconductor devices and Ashcroft-Mermin solid state textbook. They all state the difference in the Fermi levels must be equal to the applied voltage without any derivation as if that is something obvious. Can someone enlighten me where that formula comes from? 2. Nov 27, 2007 ### rbj maybe post this under the "Atomic, Solid State, Comp. Physics" forum. semi-conductor physics is very tough, and i don't remember half of it. 3. Nov 27, 2007 ### marcusl Think of the Fermi level as an energy level (it's often called that and we use E_f to denote it). If you apply a potential across the junction, you impose an energy difference between the two sides (that's the definition of a voltage or potential drop). The Fermi levels simply shift to reflect that. By the way, you will sometimes see the Fermi level called "chemical potential," which is technically the correct term for a semiconductor. 4. Nov 27, 2007 ### smallphi It's not so simple. In equilibrium (junction with no external voltage) there is a potential difference across the junction (the so called built-in potential). The conduction bands on both sides of junction differ by that potential difference but the Fermi levels are at the same level. On the other hand, the external potential difference is ZERO in equilibrium case. So the picture is that the electric potential difference across the junction is measured by the difference of the conduction bands on both sides of the junction. The battery voltage, which may not be the actual voltage applied on the semiconductor sample, is measured by difference in the Fermi levels and is NOT equal to the electric potential difference across the junction. That are the things I can't comprehend: 1. Why the Fermi levels measure the battery voltage but the conduction bands don't? 2. Why the conduction bands measure the potential difference across the junction but the Fermi levels don't? 3. Why the battery voltage is NOT equal to the potential difference across the junction? Where is the missing voltage applied ? 4. Is the potential difference on the part of semiconductor away from the junction zero? The band edges and the Fermi levels are drawn horizontal there, no bending, and that makes me think it must be zero. If so then how come there is a current flowing there? Last edited: Nov 27, 2007 5. Nov 27, 2007 ### marcusl The conduction and valence bands on the two sides are shifted relative to Ef because of the different dopings there. That is, Ef is not in the center of the band gap for a bulk material but is higher or lower for n and p materials. When Ef is equalized as the sides are joined, charges move to either side because of the relative shifts in the energy of the conduction band edge Ec, until space charge balances it out. This is where thinking in terms of the chemical potential mu is helpful, because mu describes diffusion along a concentration gradient just as in a chemistry problem. The built in potential essentially arises, then, from the difference in work functions of the two materials. The "actual" potential across the junction is V_applied - V_builtin. Your textbook probably covers this; if not, see any of the excellent semiconductor books out there like Sze, Physics of Semiconductor Devices. Section 4.2 in this link also covers it briefly You can't see V_builtin directly because as soon as you apply contacts and attach a meter, additional potentials arise at those interfaces that cancel it and prevent any current flow. 6. Nov 27, 2007 ### smallphi I know what the textbooks say. I have a whole tower of them on my desk right now. The problem is it doesn't make sense at all. The most ridiculous statements go like this: A: The applied potential V appears mostly across the transition junction region because it has way bigger resistance compared to the neutral semiconductor regions away from it. B: The electrostatic potential across the junction is Vb - V (Vb is the built-in). Now statements A and B obviously contradict each other. If the total electrostatic potential difference on the sample is indeed V then crossing the whole sample we have V = -(Vb - V) + Vx, so the missing potential is Vx = Vb and it must be applied somewhere. Statement A, claims it can't be on the neutral bulk of the semiconductor because the voltage drop on that is much smaller than V and Vb supposedly. Statement B claims it is not on the junction region. So where is Waldo ? Electrostatic potentials have to add up, doesn't matter if you can or cannot measure them. Last edited: Nov 27, 2007 7. Nov 28, 2007 ### marcusl It's hard to interpret A from that small snip. I imgaine it's just saying that you can ignore ohmic drop in the bulk regions since the resistance there is low due to heavy doping. In other words, all points in a good conductor are at the same potential. Accordingly, all the drops are at the junction. B is correct. Imagine joining a piece of n to a piece of p material (abrupt junction). There is a large concentration gradient, so electrons leave the n side, leaving behind a positively charged depletion zone there. The same occurs with holes from the p side. Together, these create a space charge field across the junction that balances out the original flow. The junction is now in equilibrium, and the electric field in the junction is triangular as shown in sect. 4.3 of the link I posted, and also presumably in your textbooks. Since $$\vec{E}=-\vec{\nabla}\phi$$, or $$E(x)=-\frac{d\phi}{dx}$$ in this 1-D problem, we can find phi by integrating -E resulting in a smooth curve that is parabolic on each side. The potential difference across the junction (that is, the difference between values of $$\phi$$ measured well away from the junction) is the built in potential $$\phi_i$$. It's around 0.7V in silicon. The junction is not a battery, however. The built-in potential arises from the depletion zones, which in turn arose from carrier diffusion that balanced the charge or carrier gradient between n and p when the junction was (virtually) created. That diffusion brought the chemical potential to a constant level throughout the material (indeed, it was mu that caused the carriers to move in the first place if you want to think of it that way), so equilibrium is reached. Connecting the two sides via a wire cannot support a current flow because the chemical potential is constant throughout the entire circuit including at each semiconductor/metal contact, which has its own fields, potentials, etc. And if there's no current flow, there's no emf or potential driving the flow, hence you can't directly see the built-in potential. Finally, any externally applied voltage gets added onto/subtracted from $$\phi_i$$. 8. Nov 28, 2007 ### smallphi I am talking about forward biased junction not junction in equilibrium. What you said can be found in any textbook but it doesn't address the question of the missing potential drop in forward bias. This is question 3 from my list above. Just because you can't measure the built-in voltage doesn't mean it's should be treated as 'special voltage that is actually not there'! It's created by static total charge distribution and as such it obeys laws of electrostatics: the total potential difference between points A and B is the same irrespective of the path you use to sum it up. So if it's V between the terminals of the battery, and there are negligible potential drops on wires, on contacts between semiconductor and wires and on bulk semiconductor away from junction, then it must be V on the junction which contradicts the statement it's Vb - V. The only resolution I see is that actually the potential drop on the semiconductor sample is Vb-V. And the missing potential drop is between the sample and the metalic contacts - a statement I've never seen discussed in any textbook. That is not obvious at all. Forward biased junction is a system totally different from junction in equilibrium. The extra voltage V-Vb could be distributed between the p-n junction and the semiconductor-wire junctions. Assuming the potential change V is applied on the junction only is a bit of a stretch that needs deeper explanation. Otherwise it's like solving the problem by assuming the solution. Last edited: Nov 28, 2007 9. Nov 28, 2007 ### marcusl It seems we agree with the description of the static system, so now we apply bias. The forward biased case is more complex in details as you say (away from equilibrium we use quasi-Fermi levels, for instance) but conceptually the picture is still simple. When you look at the static band diagram, the “potential hill” (different height on left and right) reflects the built-in potential discussed above, about 0.7V for silicon. Suppose you apply an external potential of 0.2V in the forward direction, that is, positive applied to the p side. This has the effect of flattening the diagram, reducing the barrier that a carrier must overcome to move from one side to the other. A hole, for instance, now “sees” a barrier of 0.5V. The simple addition really holds here, and there is no "missing" potential because we assume that the other parts of the circuit have low resistance. At 1 or 10 mA, for instance, the ohmic drop across the wires and extrinsic (heavily doped) bulk regions can simply be ignored. If the applied potential is $$\phi$$ then the potential barrier seen by a carrier near the junction is $$\phi_i-\phi$$. A small current begins to flow, at room temperature anyway, because a tiny fraction of carriers have enough thermal energy to cross the barrier. Flow remains small, however, until phi applied approaches 0.7V where the barrier flattens enough for carriers to flood across. The junction “turns on” in the language of the engineer, and in this regime the applied voltage changes little regardless of the current. You still don’t directly access $$\phi_i$$, but its effects are indirectly seen: there is little flow at small forward bias, increasing exponentially and becoming large as $$\phi=\phi_i$$ is approached. This is very different than for a regular conductor where current flow is directly proportional to impressed potential. 10. Nov 28, 2007 ### smallphi My questions are not answered by citing the textbooks. In fact, what you have said so far doesn't even address my questions. 11. Nov 28, 2007 ### Reality_Patrol This is a good question, it's something I've really never seen a good explanation of in standard semiconductor texts. It is explained in electrochemical texts but with respect to electrochemical applications. I think your problem is you haven't been taught about the electrochemical potential - which is really the driving force in electrochemical systems. Roughly speaking it's the sum of the chemical potential (think Fermi level for electrons/holes in unbiased junctions) and electrostatic potential (uhh, the externally applied voltage, which is zero with no bias). Equilibrium thermodynamics shows the electrochemical potential difference is driven to zero. So, if the unbiased junction has a chemical potential difference equal to the difference in the fermi levels, then a biased junction in equilibrium (constant current) can only be produced via an applied electrostatic potential "equal and opposite" to original chemical potential difference. Hope this helps. 12. Nov 28, 2007 ### smallphi No it doesn't help. You can combine the electrostatic potential in whatever potentials you want but there is a simple law of electrostatics that can't be broken when the circuit is in steady state: electrostatic drop around a closed loop must be zero. So involving electrochemical potential doesn't resolve the missing electrostatic drop in the closed circuit. How come the total electrostatic drop between the battery terminals is V but the drop on the junction is (V-Vb). Apparently there is electrostatic drop Vb, created by accumulated charge somewhere in the circuit and my guess was it is at the contacts between the semiconductor and the metal wires. Not a single textbook discusses that and they should cause that missing potential drop is the first thing all beginners notice. The existence of that electrostatic potential drop on the contacts raises the second question. How come the total increase on electrostatic potential given by the battery voltage V is applied as an increase entirely on the junction. How come the contacts didn't get any increase? After all the voltage on the contacts Vb is bigger than V or V-Vb so they have more charge there. How come only the junction responds and not the contacts. The fake 'explanation' that it is 'simply addition of voltage' doesn't pass. Imagine a capacitor charged to some voltage Vc. Now imagine that you connect it to a battery of voltage V. Following the fake logic of 'voltage addition' now the capacitor voltage must be V + Vc. Systems do NOT respond in that way. When the applied voltage changes the system reconfigures, it doesn't simply 'add voltage only at its special point'. Last edited: Nov 28, 2007 13. Nov 29, 2007 ### Reality_Patrol Sorry. You do have some genuinely valid questions, but you're also really confused on some points. This is a complex subject. The texts, as I said above, do not offer entirely valid explanations. On this point you are correct. So, if your objective here is to pass a course the most practical advice I can give is to study the texts, memorize their explanation, and spit that back out on any exams. If your objective is to really understand a PN junction the bad news is you will have to learn about several other subjects as well. I will give a little more detail below just in case your interested. The "fermi level" is just a name given to a quantity generally referred to as the chemical potential. It is NOT a field quantity, an exact "position" can not be assigned to it. It can't be "measured" using voltmeters or oscilloscopes. It comes from statistical thermodynamics. Every statistical system has one. Systems whose chemical potential is a "fermi level" are those that obey Fermi-Dirac statistics. There are other types of statistics and if a system behaves in one of those ways it is not appropriate to call the chemical potential a fermi level. If a system has more than one component (phase), like a chemical mixture or PN junction, then each phase has it's own chemical potential. Thus we can talk about differences in chemical potentials. These are what drive chemical reactions in purely chemical systems, i.e. reactions occur until the chemical potentials are equal (equilibrium). In systems that have an external FIELD applied to them thermodynamics shows that the a new quantity is needed, i.e. the so-called electrochemical potential I mentioned above, which is more generally the sum of the chemical potential and external potential. It is what drives processes until all are equal. Here the external potential is a FIELD, and one can talk about how it is distributed spatially across the system - as some of your questions point to. But THERMODYNAMICS doesn't allow such treatment. This is a limit introduced due to the lack of more robust thermodynamic field theory. In thermodynamic treatments, each phase (component, i.e. P or N semiconductor) are modeled as if the external potential is constant across the phase (no spatial variation). Thus, the measurable external potential drop must be treated as if it occurs entirely across the phase interface (PN junction). So, what the texts are really trying to say is that whenever an external potential difference is applied to a PN junction, an equal and opposite difference in chemical potential (fermi levels) develops. Again, this is because the system is trying to get back to equilibrium (zero electrochemical potential difference). Such an explanation would require a solid background in statistical physics, electromagnetics and general thermodynamics - something most students simply don't possess at the time they look at this material. In short it's not really practical to give an accurate, consistent, simple explanation. 14. Nov 29, 2007 ### smallphi I appreciate your trials, but like the previous poster, you are NOT addressing my questions: 1. Where is the missing electrostatic potential drop in p-n junction under forward/reverse bias? 2. The external voltage is not 'applied on the p-n junction'. It's applied on a circuit of two metal-semiconductor junctions and the p-n junction. Why would the p-n junction alone get the total increase in external voltage but the metal-semicondor junctions get no change at all? The electrochemical potential cannot prevent the electrostatic potential obey the laws of electrostatics. The very notion of electrostatic potential is not defined if it doesn't obey them - if it jumps across a closed loop then you will have multi-valued function with several values at the same point. The equalizing of electrochemical potential in equilibrium leads to certain charge distribution in the system. Now you can imagine that you make a copy of that charge distribution but using charges that are frozen in place by some external forces (you can imagine a daemon holding each charge in place). Are you trying to tell me that the electrostatic potential drop around any closed loop in that system would not be zero? And by the way, forward bias in p-n junction is NOT equilibrium situation, there is nonzero total current. They even have to describe electrons and holes with two different quasi-Fermi potentials inside the transition region. The Fermi levels match only for junction in equilibrium with no applied external voltage. If you claim that the Fermi levels on the usual diagrams of forward biased junction are the 'chemical' potentials not the electrochemical ones, then adding the electrostatic potential energy represented by the edge of the conduction band to them will lead to even bigger jump between the p and n side because the fermi levels and the conduction band jump by the same amount in the SAME direction, they don't compensate each other. So no matter how you define the electrochemical potential, like the fermi levels or fermi levels plus conduction band, it jumps for forward or reverse biased p-n junction. Last edited: Nov 29, 2007 15. Nov 29, 2007 ### Reality_Patrol Do you appreciate it? I don't get the impression you realize how convoluted some of your questions really are. It's tough to answer some because they're confusing multiple concepts simultaneously. Also, I wasn't trying to answer your questions in my last reply. I was replying to your last post and trying to providing some general guidance. I used caps in places where I was trying to highlight places that concepts from different theories were being introduced. There simply isn't a "missing" electrostatic potential drop under either bias. Each metal-semi junction has a very small drop, compared to the drop across the semi-semi junction. This drop is sometimes called a contact potential. A reasonable estimate would be around 1% of the total applied voltage at each metal-semi junction. For this reason these drops are typically neglected in simple explanations and first, sometimes even, second order mathematical models. In the forward bias case, when current flows, there is also some drop through each semi region, due to the ohmic loss of the materials. This is also usually neglected, because it is likewise usually quite small. I can't give a useful % for that though it depends on to many different factors. This is why simple models treat the "applied voltage" as if it were dropped entirely across the junction. It's a very good approximation. I will also point out this "drop distribution" I've just described is really a description of how the electrostatic field behaves spatially. This has nothing to do with chemical potentials (fermi levels). Again, chemical potentials are merely numbers calculated from a statistical ensemble, nothing to do with spatial distributions in any way. Not at all. This is an example of a poorly phrased question founded on a faulty claim. Again, there is no "missing" electrostatic potential drop. You are correct, when steady current flows in the forward bias case the system is described thermodynamically as "near equilibrium". This is exactly the type of state where the electrochemical potential gradient is used to describe system dynamics. I claim "fermi level" is merely a name generally used to describe the chemical potential of systems who obey fermi statistics. The texts you are looking at may be doing something non-standard in their terminology. I have no way of knowing so I will have to leave my answer at this. I hope all this hard work pays off for you. This will be my last reply. I don't have enough time to type all this out! Good luck. 16. Nov 29, 2007 ### smallphi Direct citation from "Solid state electronic devices" Ben Streetman, page 152: "Indeed the contact potential cannot be measured by placing a voltmeter across the device, because new contact potentials are formed at each probe, just canceling V0 (the built-in potential". Potentials canceling V0 are NOT small compared to V0. Those are the missing electrostatic potentials for a closed circuit with zero external voltage. The same potentials have to appear in circuit with battery to balance the electrostatic potential change around a loop to zero. Last edited: Nov 29, 2007 17. Nov 29, 2007 ### smallphi I finally found an explanation in William Shockley's "Electrons and holes in semiconductors", 7th edition, 1959, section 4.3 On the nature of metal semiconductor contacts: So the missing electrostatic potential drops are indeed between the semiconductor and the metal probes. The 'surface states' explain why those potential drops remain rigidly constant when the potential of the metal changes, producing exactly the same potential change on the semiconductor. That explains why the p-n junction voltage changes by V. The book gives a reference to article discussing the surface states: J. Bardeen, "Surface states and rectification at metal semiconductor contact", Phys. Rev. 71, 717-727 (1947) Last edited: Nov 29, 2007 18. Nov 29, 2007 ### marcusl Interesting! We also have "You can't see V_builtin directly because as soon as you apply contacts and attach a meter, additional potentials arise at those interfaces that cancel it and prevent any current flow." earlier in this thread, and also "Connecting the two sides via a wire cannot support a current flow because the chemical potential is constant throughout the entire circuit including at each semiconductor/metal contact, which has its own fields, potentials, etc." Seriously, glad you understand it now. 19. Dec 6, 2007 ### Reality_Patrol smallphi, In case you're still interested I have a reference that explains the PN junction in electrochemical terms: "Solid-State Physics, An Introduction to Principles of Material Science, 2nd Ed, 1995", see sections 12.6.1 (equilibrium) and 12.6.2 (biased). In particular note eq 12.48, where the "electric field" is introduced/defined. If you follow closely, you'll see it's NOT an electrostatic field. It's a type of non-conservative field usually called a "concentration potential" in electrochemistry. You may or may not know yet that there are 2 types of electric fields in general, conservative (e.g. eletrostatic) and non-conservative (e.g. transformer, motional and diffusional). Nonconservative fields don't have to sum to zero around a loop. I hope this information doesn't cause you too much grief. You're working very hard to understand something that's not being explained correctly in the texts you're studying. Your solution above, re contact potentials, is also incorrect. But who am I, right? I like your spirit so when I came across this section in this text today I remembered this thread. If nothing else I think you'll find in interesting and hopefully credible. I'll share something with you as a final comment: personally I think even this description is incomplete physically, though less so than the ones you've seen. 20. Dec 6, 2007 ### smallphi I was talking about the electrostatic field created by a static electrical charge distribution. There may be charges drifting and diffusing around but the total charge density at every point of the circuit is constant with time after the stationary state is reached (I am assuming DC circuit). The field of the static total charge is always conservative and its potential drops have to be zero across a closed loop - it comes from Maxwell equations and there is no way around it. If there are other forces in the problem, they do not change the fact that the electrostatic force is conservative. The built-in potential is a real electrostatic potential - they calculate it from the charge distribution. Last edited: Dec 6, 2007
# Evaluation of Trigonometric Functions Trigonometry is a stream of mathematics which performs operations on angles and sides of a triangle. Trigonometric Functions are defined as the Functions including the various Trigonometric Equations. There are six Trigonometric Functions defined in Trigonometry these are: sin x, cos x, tan x, cot x, sec x and cosec x. Cosec x is inversely proportional to sine x. If for any function the value of sin x= ½ then it will be reciprocated for cosec x and the value will be obtained as 2. The identities defined for evaluation of trigonometric functions are as follows: sin2x + cos2 x=1 sec2x – tan2x =1 cosec2 x -cot2 x =1 Reciprocal identities are as follows: sin x= 1/cosec x cos x= 1/sec x tan x= sin x / cos x cot x= cos x / sin x To evaluate trigonometric functions, one must know about the values of function at those different intervals or at different points. The value of trigonometric functions is different at different points. Six trigonometric functions are evaluated using same above equations. Let’s understand it using an example, suppose the value of sin x= 1/2 and we need to find the value of cot x. then using the identity cosec x= 1/sin x we get, cosec x= 2. Now using identity, cosec2x – cot2 x=1 cot2x=cosec2x-1 that gives, cot2x= 4-1=3 and cot x= √3 In the above example, we are given with the value of sin and for determining cot function; cosec is used as an intermediate function. The value of cot can be determined by cosec. Thus, using the identities various trigonometric functions can be determined. Evaluation of trigonometric functions is not a difficult task to do; we just need to make proper use of identities at right place. Imaginary values cannot be defined for trigonometric functions as their values are not specified yet.
# Capacitor and Pith Ball experiment Suppose I first charge a capacitor so that one plate is positively charged and another negatively. Now I remove the charging source and ground only one of the terminals say negative terminal, will there be a net positive charge in the capacitor that can be detected by a pith ball? Can a capacitor be used as static electricity generator? When you connect the negative terminal to ground, why would the negative charge flow anywhere? It has to exist somewhere, and it might as well be close to the positive charge on the other capacitor plate. You could also consider a very similar scenario in which you connect the negative side to ground before disconnecting the charging source. In this case, when you disconnect the source no charge will flow. • Suppose I have 2 copper balls . One having +ve Q charge & other having -ve Q charge. They are at a separation x which is very less. I connect the -ve charge ball to an equal ball having charge 0 with a wire. Will the -ve charge of the ball flow to the other ball or will it stay there because of attraction be +be charge on the 1st ball ? – Shashaank Mar 25 '17 at 16:36 • @shashaank it will stay.The charges are said to be bound in this case – Panda Apr 4 '18 at 3:36 When you ground a terminal there will be no charge flow, as those negative charges are attracted by the positive charges of the other plate. Or use Gauss's Law, construct a cuboidal gaussian surface with 4 sides perpendicular to plates and 2 sides inside each plate (I chose cuboidal only because it's easy to explain). There will be no flux through this surface (inside conductor $$\vec E=0$$ and outside it,$$\vec {E}\bot \vec {dA}$$) , so no net charge within it. If some charges are lost from neg plate then will be a net charge inside our surface, which can't happen. I believe some of the other answers are wrong. The charges on opposite plates of a capacitor do attract each other, but not as much as they repel themselves. That's why a capacitor will discharge if it gets a chance to. So a capacitor that can discharge, will discharge. If the side that has more elections is connected to a place electrons can go, and the other side is connected to a place that supplies electrons, some of them will move. Yes, there will be a charge at one terminal, whether or not the other terminal is grounded. How much charge? So you need a capacitor which can do that. "The accumulation of enough charge to detect with an electroscope requires hundreds or thousands of volts, so electroscopes are used with high voltage sources such as static electricity and electrostatic machines." So you need a capacitor which can do that, charged that much.
MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4). 2 format, tag; edited tags My question is: "Is it possible to have a sound and rigorous legitimation of the following construction ?". This construction is: 0/ Let ZFC be the usuel set theory, and let us add to the language capital latin letters as names for classes.Let V={x/x=x} be the usual universal class (that is a proper class, directly by foundation, or by Russel's paradox and separation) and P(x)={y/y⊆x} be the usual Pow⊆er Power set fonction. 1/ Let us now extend the domain of the power set fonction to all classes, so that P(A)={y/y⊆A} We have that P(A)is a set if A is a set by the power set axiom;but as F(x)={x} in an injection from A into P(A), we also hav}e that P(A) must be a proper class if A is such. So that P(A) is a set iff A is a set. The universal class V being transitive and well-founded, we have that V={x/x⊆V}={x/x⊆V}=P(V); So that: V=P(0,V)=P(V)=P(1,V)=P(P(n,V))=P(n+1,V). Let us also remark that for every class A, we have A⊆V, so tat V is the greater possible class. 2/ Now, let us recursively build the following Q construction: Q(0,V)=P(V)=V{x/x⊆V}=V and Q(n+1,V)={A/(B∈A-->B∈Q(n,V)}={A/A Q(n,V)} Moreover let the collection Q be the union of the collections Q(n,V): Q=∪〈n∈N〉Q(n,V); By induction, we have Q(n,V)⊆Q(n+1,V). We already know that the elements of Q(0,V)=V are axactly sets, and that the elements of Q(1,V)={A/A⊆V} are exactly usual classes. So that Q(0,V)⊆Q(1,V); moreover, the elements of the difference Q(1,V)/Q(0,V) are exactly usual proper classes and V is such an element. We also have Q(n,V)⊆Q(n+1,V)-->Q(n+1,V)⊆Q(n+2,V) because A∈Q(n+1,V)<-->(∀B∈A(B∈Q(n,V)) and by hypothesis B∈Q(n,V)-->B∈Q(n+1,V), so that A∈Q(n+2,V). It is now natural to name sets as level 0 super-classes, proper classes as level 1 super-classes, and more generally elements of the difference Q(n+1,V)/Q(n,V) as level (n+1) super-classes, and also members of Q as super-classes. We alreaduy already know that Q(0,V) and Q(1,V)/Q(0,V) are non-void. more generally we have that Q(n+1,V)/Q(n,V) is non-void. To see this, let A and B be two level n super-classes and consider R(A,B)={D∈Q(n,V)/A⊆D⊆B}. It is clear that R(A,B) is a level (n+1) super-class that is non-void as soon as A⊆B. Particularly R(∅,A)={B/B⊆A} and R(A,A)={A} are such level (n+1) super-classes. So, we have by induction that Q(n,V)⊆Q(n+1,V) and also that Q(n,V)∈Q(n+1,V); for every level n, Q(n,V) is the greater element of Q(n+1,V) for inclusion. 3/ We also obtain that the difference of two super-classes (of level n) is a super-class (of level n), and that the union (the intersection) of a finite (of any family, but what can be the collection of indices ?) family of super-classes (of level n) is a super-class (of level n; of level ≤n). Gérard Lang 1 # Finite level super classes over ZFC My question is: "Is it possible to have a sound and rigorous legitimation of the following construction ?". This construction is: 0/ Let ZFC be the usuel set theory, and let us add to the language capital latin letters as names for classes.Let V={x/x=x} be the usual universal class (that is a proper class, directly by foundation, or by Russel's paradox and separation) and P(x)={y/y⊆x} be the usual Pow⊆er set fonction. 1/ Let us now extend the domain of the power set fonction to all classes, so that P(A)={y/y⊆A} We have that P(A)is a set if A is a set by the power set axiom;but as F(x)={x} in an injection from A into P(A), we also hav}e that P(A) must be a proper class if A is such. So that P(A) is a set iff A is a set. The universal class V being transitive and well-founded, we have that V={x/x⊆V}={x/x⊆V}=P(V); So that: V=P(0,V)=P(V)=P(1,V)=P(P(n,V))=P(n+1,V). Let us also remark that for every class A, we have A⊆V, so tat V is the greater possible class. 2/ Now, let us recursively build the following Q construction: Q(0,V)=P(V)=V{x/x⊆V}=V and Q(n+1,V)={A/(B∈A-->B∈Q(n,V)}={A/A Q(n,V)} Moreover let the collection Q be the union of the collections Q(n,V): Q=∪〈n∈N〉Q(n,V); By induction, we have Q(n,V)⊆Q(n+1,V). We already know that the elements of Q(0,V)=V are axactly sets, and that the elements of Q(1,V)={A/A⊆V} are exactly usual classes. So that Q(0,V)⊆Q(1,V); moreover, the elements of the difference Q(1,V)/Q(0,V) are exactly usual proper classes and V is such an element. We also have Q(n,V)⊆Q(n+1,V)-->Q(n+1,V)⊆Q(n+2,V) because A∈Q(n+1,V)<-->(∀B∈A(B∈Q(n,V)) and by hypothesis B∈Q(n,V)-->B∈Q(n+1,V), so that A∈Q(n+2,V). It is now natural to name sets as level 0 super-classes, proper classes as level 1 super-classes, and more generally elements of the difference Q(n+1,V)/Q(n,V) as level (n+1) super-classes, and also members of Q as super-classes. We alreaduy know that Q(0,V) and Q(1,V)/Q(0,V) are non-void. more generally we have that Q(n+1,V)/Q(n,V) is non-void. To see this, let A and B be two level n super-classes and consider R(A,B)={D∈Q(n,V)/A⊆D⊆B}. It is clear that R(A,B) is a level (n+1) super-class that is non-void as soon as A⊆B. Particularly R(∅,A)={B/B⊆A} and R(A,A)={A} are such level (n+1) super-classes. So, we have by induction that Q(n,V)⊆Q(n+1,V) and also that Q(n,V)∈Q(n+1,V); for every level n, Q(n,V) is the greater element of Q(n+1,V) for inclusion. 3/ We also obtain that the difference of two super-classes (of level n) is a super-class (of level n), and that the union (the intersection) of a finite (of any family, but what can be the collection of indices ?) family of super-classes (of level n) is a super-class (of level n; of level ≤n). Gérard Lang
# Uniformly Converging Metrization of Uniform Structure This is related to trying to resolve the currently faulty second part of my answer to this question, but is by itself a purely real analysis question. Let $$X$$ be a set with a uniform structure presented by a function $$f:X^2 \rightarrow [0,1]$$ satisfying the following conditions: • $$f(x,x) = 0$$ • $$f(x,y) = f(y,x)$$ • For some fixed parameter $$1 < \beta \leq 2$$, $$f(x_0,x_3)\leq \beta \max(f(x_0 ,x_1 ),f(x_1 ,x_2),f(x_2,x_3))$$. It's clear that the sets $$\{(x,y)\in X^2 : f(x,y) < \varepsilon\}$$ generate a (pseudo-)uniformity on the set $$X$$. (I say 'pseudo-' because we haven't guaranteed that points are separated by $$f$$ but it's not really important for this question.) Let $$f_1(x,y) = f(x,y)$$ and for $$k>1$$, let $$f_k(x,y) = \inf_{z_1,\dots,z_{k-1}} f(x,z_1)+f(z_1,z_2) + \dots + f(z_{k-1},y) .$$ It's clear that $$f_k(x,x)=0$$, $$f_k(x,y)=f_k(y,x)$$, and $$0\leq f_{k+1}(x,y)\leq f_k(x,y) \leq f(x,y) \leq 1$$. This last one implies that the sequence $$f_k(x,y)$$ is monotonically decreasing and bounded from below and so converges for any $$x,y$$. Let $$d(x,y)=\lim_{k\rightarrow \infty}f_k(x,y)$$. It's clear that $$d(x,x)=0$$, $$d(x,y)=d(y,x)$$, and $$0 \leq d(x,y) \leq f_k(x,y) \leq 1)$$. It's also fairly clear that $$d(x,y)$$ obeys the triangle inequality so in particular it is a pseudo-metric. You can show with an argument similar to the one around page 16 of this document (page 18 according to the pdf) that $$\beta^{-1} f(x,y) \leq d(x,y) \leq f(x,y)$$, so $$d(x,y)$$ induces the same (pseudo-)uniform structure on $$X$$ as $$f$$ does. (In the document $$\beta = 2$$.) What would allow me to resolve the other question is the sequence $$f_k$$ converging uniformly. I've gone back and forth on how I feel it's going to turn out for a while now but I can neither prove it nor provide a counterexample. So the question is Under what conditions does the sequence $$f_k$$ converge uniformly? The best I've been able to do is under the assumption that $$\beta < \sqrt{2}$$ which ends up implying that the chains witnessing the values of $$f_k(x,y)$$ are very 'clumpy' in that there's a single $$f(z_i,z_{i+1})$$ which accounts for 'most' of the value of $$f_k(x,y)$$, but the bound on $$f_{k+1}$$ in terms of $$f_k$$ I can compute from this seems to be too marginal to get uniform convergence. EDIT: This is adapted from this document. Lemma. If $$1 < \beta \leq 2$$ then $$f(x,y) \leq \beta d(x,y)$$. Proof. We will show that $$f(x,y) \leq \beta f_k(x,y)$$ for every $$k$$. Clearly this is true for $$f_1(x,y)=f(x,y)$$, since $$\beta >1$$. Assume that we have shown this result for all $$\ell. Let $$z_1,\dots,z_{k-1}$$ be some chain and let $$z_0 = x$$ and $$z_k = y$$. Let $$r=\sum_{i. Find $$m maximal such that $$\sum_{i. (It may be the case that $$m=0$$.) Note that since $$m$$ is chosen maximally, it must also be the case that $$\sum_{m. Also it's certainly the case that $$f(z_m,z_{m+1})\leq r$$. By the induction hypothesis $$f(z_0,z_m)\leq \beta f_m(z_0,z_m) \leq \beta \sum_{i and $$f(z_{m+1},z_k) \leq \beta f_{k-m-1}(z_{m+1},z_k) \leq \beta \sum_{m So now we can apply the assumed inequality to get $$f(z_0,z_k)\leq \beta \max(f(z_0,z_m),f(z_m,z_{m+1}),f(z_{m+1},z_k)) \leq \beta \max(\beta \frac{r}{2},r).$$ Since $$\beta\leq 2$$, $$\beta\frac{r}{2}\leq r$$, so we get $$f(x,y)=f(z_0,z_k)\leq \beta r$$. Since this is true for any such chain we get $$f(x,y)\leq \beta f_k(x,y)$$, as required. So by induction this is true for all $$k$$ and we get $$f(x,y) \leq \beta d(x,y)$$. $$\Box$$ ## 1 Answer $$f_k$$ converges uniformly for $$1\leq\beta\leq 2.$$ I will argue that for any $$\epsilon>0$$ and any path $$z_0,z_1,\dots,z_{k-1},z_k,$$ there is a sub-path $$z_0,z_{i_1},\dots,z_{i_{m-1}},z_k$$ such that either $$f(z_0,z_{i_1})+\dots+f(z_{i_{m-1}},z_k)\leq (1+\epsilon)(f(z_0,z_1)+\dots+f(z_{k-1},z_k))\tag{1}$$ and $$m$$ is bounded by a function of $$\epsilon$$ and $$\beta,$$ or $$f(z_0,z_{i_1})+\dots+f(z_{i_{m-1}},z_k)\leq f(z_0,z_1)+\dots+f(z_{k-1},z_k)\tag{2}$$ and $$m So by induction on $$k,$$ any path can always be shrunk to satisfy (1) with $$m$$ bounded. The following argument helps to analyse the paths. Lemma. For all $$\delta>0$$ and all integers $$K\geq 3$$ there exists $$n$$ such that for any $$r>0$$ and any set $$A\subseteq [0,r]$$ either: • $$A$$ can be covered by at most $$n$$ intervals of total length at most $$r\delta,$$ or • $$A$$ contains a sequence $$a_1<\dots such that the maximum step $$\max(a_{i+1}-a_i)$$ is at most $$2(a_K-a_1)/(K-2).$$ Proof. By Szemerédi's theorem, for large $$N$$ the set $$A'=\{\lfloor aN/r\rfloor\mid a\in A\}\subseteq\{0,1,\dots,N\}$$ has cardinality less than $$\delta N/2$$ unless $$A'$$ contains an arithmetic progression $$t_1<\dots In the first case we can cover $$A$$ by at most $$n=\lceil \delta N/2\rceil$$ intervals $$[rt/N,r(t+1)/N]$$ for $$t\in A',$$ of total length at most $$r\delta.$$ In the second case we can pick $$a_i\in A$$ such that $$\lfloor a_iN/r\rfloor=t_i.$$ Let $$d$$ be the step size of $$\{t_i\}.$$ Then $$(a_{i+1}-a_i)/(a_K-a_1)\leq (d+1)/((K-2)d)\leq 2/(K-2).$$ $$\Box$$ Take $$r=\sum_{i=0}^{k} f(z_i,z_{i+1})$$ $$A=\{0\}\cup\{\sum_{i=0}^{j} f(z_i,z_{i+1})\mid j\in\{0,1,\dots,k\}\}$$ $$\delta=\epsilon/10$$ and $$K=3^d+1$$ where $$d$$ is an integer large enough that $$2\beta^{d+1}<3^d-1$$ - this uses $$\beta<3.$$ Let $$n$$ be the number given by the lemma. Note $$n$$ is bounded in terms of $$\epsilon$$ and $$\beta.$$ The first case to consider is that $$A$$ can be covered by at most $$n$$ intervals of total length at most $$r\delta.$$ We can modify these intervals so they are disjoint and their endpoints lie in $$A.$$ Form a subpath by removing all the $$z_i$$ lying in the interior of these intervals. This increases the total by at most $$r\beta\epsilon/10$$: each interval corresponds to some $$z_i,\dots,z_j,$$ and we can use the inequality $$f(z_i,z_j)\leq \beta d(z_i,z_j)\leq \beta (f(z_i,z_{i+1})+\dots+f(z_{j-1},z_j)).$$ This small relative error ensures (1) holds. Since each interval has two endpoints, $$m\leq 2n+1.$$ The second case is that $$A$$ contains $$a_1<\dots with $$\max(a_{i+1}-a_i)\leq 2(a_K-a_1)/(K-2).$$ These elements of $$A$$ correspond to some $$z_{j_1},\dots,z_{j_K}$$ which must satisfy $$f(z_{j_{i+1}},z_{j_i})\leq 2\beta(a_K-a_1)/(K-2)$$ (by the inequality used in the previous paragraph). By induction on $$D$$ for $$0\leq D\leq d$$ we have $$f(z_{j_{i+3^D}},z_{j_i})\leq 2\beta^{D+1}(a_K-a_1)/(K-2).$$ Hence $$f(z_{j_K},z_{j_1})\leq a_K-a_1.$$ This means that removing all the $$z_i$$ for $$j_1 gives a sub-path satisfying (2). This gives a uniform bound $$f_k(x,y)\leq (1+\epsilon)d(x,y)$$ where $$k$$ depends only on $$\epsilon$$ and $$\beta.$$ Remarks about the case $$\beta>2$$: The argument goes through for $$2<\beta<3$$ under the extra assumption $$f(x,y)\leq \beta d(x,y).$$ For $$\beta=3$$ we can get arbitrarily slow convergence on $$X=\mathbb N\times\mathbb Z$$ by taking $$f((n,x),(n',y))=\begin{cases} 0&\text{ if n=n' and \{x,y\}=\{2k,2k+1\} for some k\in\mathbb Z}\\ 1&\text{ if n\neq n'}\\ \min(1,|x-y|/n)&\text{ otherwise.} \end{cases}.$$ For even $$n$$ this gives $$f_k((n,0),(n,n/2))\geq (n-k)/2$$ but $$d((n,0),(n,n/2))=1/2.$$ I don't know if the convergence is uniform for $$2<\beta<3$$ without the assumption $$f(x,y)\leq \beta d(x,y).$$ • This is excellent. Thank you very much. One thing though is that I needed $\beta \leq 2$ to prove the inequality $f(x,y) \leq \beta d(x,y)$, which you use in the third and second to last paragraphs. (I'll edit my question to include the proof.) I don't need the case $2 < \beta < 3$, but I'm worried that $3$ might not be optimal. – James Hanson Mar 11 at 15:19 • @JamesHanson: and thank you for the interesting question and for spotting my hasty assumption. I've changed my claims accordingly and moved all remarks about the $\beta>2$ case to the end. – Dap Mar 12 at 0:10
# A conjecture generalization of Karamata inequality Fist I observe function $f(x)=x^2$ in the figure as following I found that when $x_1 \ge y_1$ and $x_2 \le y_2$ $\Rightarrow$ $AB \ge CD$ $\Rightarrow$ $$\frac{f(x_1)+f(x_2)}{2}-f(\frac{x_1+x_2}{2}) \ge \frac{f(y_1)+f(y_2)}{2}-f(\frac{y_1+y_2}{2})$$ (1). Note that: When $x_1+x_2=y_1+y_2$ the inequality (1) is Karamata inequality (with case n=2) $$f(x_1)+f(x_2) \ge f(y_1)+f(y_2)$$ From above observation, I am looking for a proof of a conjecture generalization of Karamata inequality as following: Let $I$ be an interval of the real line and let $f$ denote a real-valued, convex function defined on $I$. If $x_1, . . . , x_n$ and $y_1, . . . , y_n$ are numbers in $I$ such that: 1. $x_1 \ge x_2 \ge x_3...\ge x_n,$ and $y_1 \ge y_2 \ge y_3...\ge y_n$ 2.x_1+x_2+...+x_i \ge y_1+y_2+...+y_i for i=1,...,n-1 and 3. x_n \le y_n 2'. $x_1+...+x_i \ge y_1+...+y_i$ and $x_{i+1}+...+x_n \le y_{i+1}+...+y_n$ for $i=1,...,n-1$ then $$\frac{f(x_1)+f(x_2)+...+f(x_n)}{n}-f(\frac{x_1+x_2+...+x_n}{n}) \ge \frac{f(y_1)+f(y_2)+...+f(y_n)}{n}-f(\frac{y_1+y_2+...+y_n}{n})$$ The inequality holds with equality if and only if $x_i=y_i$ for all $i \in {1, 2,...,n}$ • I don't think MO should be a place for people to keep posting conjectures – Yemon Choi Jul 26 '16 at 3:45 • Dear @YemonChoi I think mathematics developed from conjecture and problem and observation – Oai Thanh Đào Jul 26 '16 at 4:11 • I think, any question like "is the following proposition true?" may be called "a conjecture", and most MO questions are of this type. – Fedor Petrov Jul 26 '16 at 18:19 • I think both Yemon Choi and Fedor Petrov are right. -- It's just that questions should be formulated as such. As you have done this in your last edits, it is no longer unclear what you're asking, and hence I have voted to reopen. – Stefan Kohl Jul 26 '16 at 20:05 • Inequality $\sum f(a_i)\geq \sum f(b_i)$ for any convex function holds if and only if it holds by Karamata, that is, if and only if the multiset $\{a_i\}$ majorates the multiset $\{b_i\}$. In our situation $\{a_i\}$ is the set consisting from $x_1,\dots,x_n$ and $n$ times $(\sum y_i)/n$, another multiset $\{b_i\}$ consists of $y_1,\dots,y_n$ and $n$ times $(\sum x_i)/n$. You may try to prove this by considering many cases or by procedures like 'bring to $x$'s together' or 'move two $y$'s apart', when they do not violate your inequalities. – Fedor Petrov Jul 27 '16 at 10:50 1. Conditions (1,2,3) are not enough for the inequality to hold. Take $n=3$, $x_1=x_2=3,x_3=0$, $y_1=3,y_2=y_3=0$. Then we need the multiset $(3,3,0,1,1,1)$ (all three $x$'s and 3 times mean of $y$'s) to majorate $(3,0,0,2,2,2)$. But four largest elements of the first multiset have sum $3+3+1+1=8$, while in the second it is $3+2+2+2=9$. So, the claim does not hold in full generality. To be more explicit, we get an opposite inequality for $f(x)=\max(x-2,0)$. 2. Conditions (1) and (2') $x_1+...+x_i \geqslant y_1+.....+y_i$ and $x_{i+1}+...+x_n \leqslant y_{i+1}+...+y_n$ for $i=1,....,n-1$ are enough. We prove it by verifying that the multiset of $2n$ numbers $A:=\{x_1,\dots,x_n,y,y,\dots,y\}$ majorates the multiset $B:=\{y_1,\dots,y_n,x,x,\dots,x\}$, where $x=\frac1n \sum x_i$, $y=\frac1n \sum y_i$. Without loss of generality $x\leqslant y$, else change signs of all $x$'s and $y$'s. We have to check that the sum $w_m$ of $m$ largest elements of $B$ does not exceed the sum of $m$ largest elements of $A$. Let $m$ largest elements of $B$ be $y_1,\dots,y_s$ and $(m-s)$ times $x$. Consider two cases. 1-st case. $s\leqslant n-1$. Then $w_m=y_1+\dots+y_s+(m-s)x\leqslant x_1+\dots+x_s+(m-s)y$. 2-nd case. $s=n$. Then $w_m=y_1+\dots+y_n+(m-n)x\leqslant n\cdot y+x_1+\dots+x_{m-n}$. In both cases we found $m$ elements of $A$ with a sum at least $w_m$, as desired. • Thank to dear @FedorPetrov Please let me an example: $f(x)=?$, $n=?$ $x_1, x_2,....,x_n= ?$ and $y_1=?, y_2=?,...y_n=?$ – Oai Thanh Đào Jul 28 '16 at 11:11 • $f=\max(x-2,0)$, other data are in the answer. – Fedor Petrov Jul 28 '16 at 11:37 • Dear Dr. @FedorPetrov , the inequality (1) is hold ? with $x_1 \ge y_1$ and $x_2 \leq y_2$ – Oai Thanh Đào Jul 29 '16 at 14:55 • @OaiThanhĐào yes, the expression $h(x_1,x_2)$ in LHS is increasing in $x_1$ and decreasing in $x_2$ (when $x_1\geqslant x_2$), therefore $h(x_1,x_2)\geqslant h(y_1,x_2)\geqslant h(y_1,y_2)$ if $x_1\geqslant y_1\geqslant y_2\geqslant x_2$. – Fedor Petrov Jul 29 '16 at 15:07 • Dear Dr. @FedorPetrov could you give for condition of xi, yi such that the inequality hold. Please read my ask below. – Oai Thanh Đào Jul 29 '16 at 16:58 1. I prove that the inequality (1) is hold with $x_1 \ge y_1$ and $y_2 \ge x_2$ as followings: $$y(x)=\frac{f(x)+f(x_2)}{2}-f(\frac{x+x_2}{2})- \frac{f(y_1)+f(y_2)}{2}+f(\frac{y_1+y_2}{2})$$ $$y'=\frac{f'(x)}{2}-\frac{1}{2}f'(\frac{x+x_2}{2})$$ Because $f'' \ge 0$ so $y'(x) \ge y'(x_2)=0$ because $x \ge x_2$, because $x_1 \ge y_1$ so $y(x_1) \ge y(y_1)$, therefor $$y(x_1) \ge y(y_1)=\frac{f(y_1)+f(x_2)}{2}-f(\frac{y_1+x_2}{2})- \frac{f(y_1)+f(y_2)}{2}+f(\frac{y_1+y_2}{2})=\frac{f(x_2)}{2}-f(\frac{y_1+x_2}{2})- \frac{f(y_2)}{2}+f(\frac{y_1+y_2}{2})$$ Let $$g(t)=\frac{f(x_2)}{2}-f(\frac{t+x_2}{2})- \frac{f(y_2)}{2}+f(\frac{t+y_2}{2})$$ with $t \ge y_2$, we have: $$g'(t)=-\frac{1}{2}f'(\frac{t+x_2}{2})+\frac{1}{2}f'(\frac{t+y_2}{2})$$ Because $f'' \ge 0$ and $y_2 \ge x_2$ so $g'(t) \ge 0$ so $g(y_1) \ge g(y_2)=\frac{f(x_2)}{2}-f(\frac{y_2+x_2}{2})- \frac{f(y_2)}{2}+f(\frac{y_2+y_2}{2})=\frac{f(x_2)+f(y_2)}{2}-f(\frac{y_2+x_2}{2}) \ge 0$ because $f'' \ge 0$ 1. Remark with the same proof, I can prove the inequality (1) with weights $\lambda_i$ holds. Let $x_1 \ge y_1$ and $x_2 \le y_2$, $\lambda_i >0$ and $\lambda_1+\lambda_2=1$ we have: $$\lambda_1f(x_1)+\lambda_2f(x_2)-f(\lambda_1x_1+\lambda_2x_2) \ge \lambda_1f(y_1)+\lambda_2f(y_2)-f(\lambda_1y_1+\lambda_2y_2)$$ (2) 1. Now let $I$ be an interval of the real line and let $f$ denote a real-valued, convex function defined on $I$. If $x_1, . . . , x_n$ and $y_1, . . . , y_n$ are numbers in $I$ such that: (i). $x_1 \ge x_2 \ge x_3...\ge x_n,$ and $y_1 \ge y_2 \ge y_3...\ge y_n$ (ii). $x_1+...+x_i \ge y_1+...+y_i$ and $x_{i+1}+...+x_n \le y_{i+1}+...+y_n$ for $i=1,...,n-1$ $$\frac{f(x_1)+f(x_2)+...+f(x_n)}{n}-f(\frac{x_1+x_2+...+x_n}{n}) \ge \frac{f(y_1)+f(y_2)+...+f(y_n)}{n}-f(\frac{y_1+y_2+...+y_n}{n})$$ The inequality holds with equality if and only if $x_i=y_i$ for all $i \in {1, 2,...,n}$ • Is your proposition 3 a theorem or conjecture or what? – Fedor Petrov Jul 30 '16 at 4:38 • Proposition 3 is a conjecture. Some days recenterly I think how I can generalization of (1). So I give stronger condition of $x_i$ and $y_i$ in conjecture 3. I am looking for the proof. – Oai Thanh Đào Jul 30 '16 at 4:54 • This new conjecture is correct, see the edit of my answer. – Fedor Petrov Aug 1 '16 at 19:11 • DearDr. @FedorPetrov in case $x \ge y$, is the proof similarly? – Oai Thanh Đào Aug 2 '16 at 0:27 • If $x>y$, we replace $x_i$ to $-x_i$, $y_i$ to $-y_i$ and thus reduce it to the case $x<y$. – Fedor Petrov Aug 2 '16 at 4:38
Population dynamics Map of population trends of native and invasive species of jellyfish[1] Increase (high certainty) Increase (low certainty) Stable/variable Decrease No data Population dynamics is the branch of life sciences that studies the size and age composition of populations as dynamical systems, and the biological and environmental processes driving them (such as birth and death rates, and by immigration and emigration). Example scenarios are ageing populations, population growth, or population decline. History Population dynamics has traditionally been the dominant branch of mathematical biology, which has a history of more than 210 years, although more recently the scope of mathematical biology has greatly expanded. The first principle of population dynamics is widely regarded as the exponential law of Malthus, as modeled by the Malthusian growth model. The early period was dominated by demographic studies such as the work of Benjamin Gompertz and Pierre François Verhulst in the early 19th century, who refined and adjusted the Malthusian demographic model. A more general model formulation was proposed by F.J. Richards in 1959, further expanded by Simon Hopkins, in which the models of Gompertz, Verhulst and also Ludwig von Bertalanffy are covered as special cases of the general formulation. The Lotka–Volterra predator-prey equations are another famous example, as well as the alternative Arditi–Ginzburg equations. The computer game SimCity, Sim Earth and the MMORPG Ultima Online, among others, tried to simulate some of these population dynamics. In the past 30 years, population dynamics has been complemented by evolutionary game theory, developed first by John Maynard Smith. Under these dynamics, evolutionary biology concepts may take a deterministic mathematical form. Population dynamics overlap with another active area of research in mathematical biology: mathematical epidemiology, the study of infectious disease affecting populations. Various models of viral spread have been proposed and analyzed, and provide important results that may be applied to health policy decisions. Intrinsic rate of increase The rate at which a population increases in size if there are no density-dependent forces regulating the population is known as the intrinsic rate of increase. It is ${\displaystyle {\dfrac {dN}{dt}}{\dfrac {1}{N}}=r}$ where the derivative ${\displaystyle dN/dt}$ is the rate of increase of the population, N is the population size, and r is the intrinsic rate of increase. Thus r is the maximum theoretical rate of increase of a population per individual – that is, the maximum population growth rate. The concept is commonly used in insect population biology to determine how environmental factors affect the rate at which pest populations increase. See also exponential population growth and logistic population growth.[2] Fisheries and wildlife management In fisheries and wildlife management, population is affected by three dynamic rate functions. • Natality or birth rate, often recruitment, which means reaching a certain size or reproductive stage. Usually refers to the age a fish can be caught and counted in nets. • Population growth rate, which measures the growth of individuals in size and length. More important in fisheries, where population is often measured in biomass. • Mortality, which includes harvest mortality and natural mortality. Natural mortality includes non-human predation, disease and old age. If N1 is the number of individuals at time 1 then ${\displaystyle N_{1}=N_{0}+B-D+I-E}$ where N0 is the number of individuals at time 0, B is the number of individuals born, D the number that died, I the number that immigrated, and E the number that emigrated between time 0 and time 1. If we measure these rates over many time intervals, we can determine how a population's density changes over time. Immigration and emigration are present, but are usually not measured. All of these are measured to determine the harvestable surplus, which is the number of individuals that can be harvested from a population without affecting long-term population stability or average population size. The harvest within the harvestable surplus is termed "compensatory" mortality, where the harvest deaths are substituted for the deaths that would have occurred naturally. Harvest above that level is termed "additive" mortality, because it adds to the number of deaths that would have occurred naturally. These terms are not necessarily judged as "good" and "bad," respectively, in population management. For example, a fish & game agency might aim to reduce the size of a deer population through additive mortality. Bucks might be targeted to increase buck competition, or does might be targeted to reduce reproduction and thus overall population size. For the management of many fish and other wildlife populations, the goal is often to achieve the largest possible long-run sustainable harvest, also known as maximum sustainable yield (or MSY). Given a population dynamic model, such as any of the ones above, it is possible to calculate the population size that produces the largest harvestable surplus at equilibrium.[3] While the use of population dynamic models along with statistics and optimization to set harvest limits for fish and game is controversial among scientists,[4] it has been shown to be more effective than the use of human judgment in computer experiments where both incorrect models and natural resource management students competed to maximize yield in two hypothetical fisheries.[5][6] To give an example of a non-intuitive result, fisheries produce more fish when there is a nearby refuge from human predation in the form of a nature reserve, resulting in higher catches than if the whole area was open to fishing.[7][8] For control applications Population dynamics have been widely used in several control theory applications. With the use of evolutionary game theory, population games are broadly implemented for different industrial and daily-life contexts. Mostly used in multiple-input-multiple-output (MIMO) systems, although they can be adapted for use in single-input-single-output (SISO) systems. Some examples of applications are military campaigns, resource allocation for water distribution, dispatch of distributed generators, lab experiments, transport problems, communication problems, among others. Furthermore, with the adequate contextualization of industrial problems, population dynamics can be an efficient and easy-to-implement solution for control-related problems. Multiple academic research has been and is continuously carried out.
# Antimatter creation from collision of photons Can you create antimatter by letting photons collide? • – NickD Jul 26 '17 at 20:39 • – heather Jul 26 '17 at 20:40 Photon-photon pair production can be represented by the equation $\gamma + \gamma^{'}\rightarrow e^-+e^+$, which basically means that the collision of two photons produces an electron and a positron (the anti-electron).
# Second Order Numerical Integration w/ Neumann Boundary Conditions I hope this is the right place to post this question. I'm trying to figure out how to run a numeric integration for a nonlinear second order ODE with Neumann B.C. I've started programming up Runge Kutta 4, but clearly without a boundary condition on the function, but only on its derivative I'm stuck. If anyone could point me in the right direction, or refer me to a text that discusses this problem I'd really appreciate it.
# Methods of Information Geometry ### Methods of Information Geometry (repost)eBooks & eLearning Posted by libr at Dec. 10, 2015 Shun-Ichi Amari, Hiroshi Nagaoka, "Methods of Information Geometry" English | 2001-01-20 | ISBN: 0821805312 | 206 pages | DJVU | 4.7 mb ### Methods of Information Geometry (repost)eBooks & eLearning Posted by interes at Nov. 23, 2013 Shun-Ichi Amari, Hiroshi Nagaoka, "Methods of Information Geometry" English | 2001-01-20 | ISBN: 0821805312 | 206 pages | DJVU | 4.7 mb Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the $\alpha$-connections. ### Methods of Algebraic Geometry, Volume 3eBooks & eLearning Posted by step778 at March 5, 2015 W. V. D. Hodge, D. Pedoe, "Methods of Algebraic Geometry, Volume 3" 1953 | pages: 342 | ISBN: 0521467756 | PDF | 3,2 mb ### Methods of Algebraic Geometry: Volume 1eBooks & eLearning Posted by step778 at March 4, 2015 W. V. D. Hodge, D. Pedoe, "Methods of Algebraic Geometry: Volume 1" 1953 | pages: 444 | ISBN: 0521469007 | DJVU | 5,3 mb ### Operators, Geometry and Quanta: Methods of Spectral Geometry in Quantum Field Theory [Repost]eBooks & eLearning Posted by ChrisRedfield at Feb. 10, 2014 Dmitri Fursaev, ‎Dmitri Vassilevich - Operators, Geometry and Quanta: Methods of Spectral Geometry in Quantum Field Theory Published: 2011-06-26 | ISBN: 9400702043 | PDF | 288 pages | 3 MB ### Information GeometryeBooks & eLearning Posted by hill0 at Sept. 27, 2017 Information Geometry (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics) by Nihat Ay English | 20 Sept. 2017 | ISBN: 3319564773 | 420 Pages | EPUB | 9.42 MB The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. ### Information GeometryeBooks & eLearning Posted by AvaxGenius at Sept. 6, 2017 Information Geometry By Nihat AyJürgen JostHông, Vân LêLorenz Schwachhöfer English | PDF | 2017 | 411 Pages | ISBN : 3319564773 | 4.5 MB The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. ### Information Geometry and Its Applications (Applied Mathematical Sciences)eBooks & eLearning Posted by tukotikko at March 7, 2016 Information Geometry and Its Applications (Applied Mathematical Sciences) By Shun-ichi Amari 2016 | 390 Pages | ISBN: 4431559779 | EPUB | 6 MB ### Information Geometry and Its ApplicationseBooks & eLearning Posted by Underaglassmoon at Feb. 5, 2016 Information Geometry and Its Applications Springer | Geometry & Topology | March 4, 2016 | ISBN-10: 4431559779 | 373 pages | pdf | 6.14 mb Authors: Amari, Shun-ichi Introduces information geometry intuitively to readers without knowledge of differential geometry Includes hot topics of applications to machine learning, signal processing, neural networks, and optimization Applies information geometry to statistical inference and time-series analysis ### Geometric Theory of Information [Repost]eBooks & eLearning Posted by ChrisRedfield at Jan. 27, 2015 Frank Nielsen - Geometric Theory of Information Published: 2014-05-08 | ISBN: 3319053167 | PDF | 392 pages | 8 MB
## Jul 11, 2016 ### PUT vs WPUT Analysis Earlier this year Oleg Bondarenko, professor at U of Illinois published an excellent empirical analysis of CBOE's PUT index and more recent WPUT (same as PUT but using weekly options). I will review some of the points in the paper comparing theoretical values with the ones that were empirically observed. Here is a summary, and complete research paper. Professor Bondarenko notes: Selling 1-month ATM puts 12 times a year can produce significant income. From 2006 to 2015, the average monthly premium is 2.01%. From 2006 to 2015, the average weekly premium is 0.75%. Although smaller, the premium is collected more frequently. Intuitively, the premium of the ATM put increases as the square root of maturity. This means that a one-week tenor option rolled over four times per month will approximately generate 2.0x the premium of a one-month tenor option rolled over once per month (i.e., 1/2 premium times 4). Premium by itself, of course, does not guarantee profit. Let's take a look at some basic formulas (assuming ABM,  zero rates, and unit price for simplicity. All formulas were generated using Mathematica ) $\inline&space;\dpi{200}&space;\bg_black&space;\large&space;putprice&space;=&space;\frac{\sigma&space;\sqrt{T}}{\sqrt{2&space;\pi}}$ So, as stated, assuming 4 weeks per month, we would expect theoretically to collect 2x more premium. Since in reality we are collecting about 1.5x more premium, it means that weekly premiums are smaller than expected, which is pretty much what we would expect as vol term structure is in contango most of the time. Similarly, expected vol arb (implied vs realized) PL suffers from contango. $\inline&space;\dpi{200}&space;\bg_black&space;\large&space;volarb&space;=&space;\frac{(\sigma_{implied}&space;-\sigma_{realized})\sqrt{T}}{\sqrt{2&space;\pi}}$ In theory, for the same implied vol value we would expect 2x more profit for WPUT, while in practice WPUT has slightly underperformed PUT. This implies an interesting relationship (not a statistical or theoretical, just merely an observation) if we simply re-arrange the terms, that value of weekly implied volatility is in between monthly implied volatility and realized volatility. As an approximation I took VXST index (available since 2011), VIX, and SPX returns. Because of the period mismatch, the results are not exact - average value of VXST is 17.14, between  average of VIX of 17.47, and realized volatility of 15.54. Now, let's consider another aspect of put selling - what is the risk? We can derive expected volatility of put selling strategy: $\inline&space;\dpi{200}&space;\bg_black&space;\large&space;vol&space;\&space;of&space;\&space;volarb&space;=&space;\frac{\sqrt{\pi-1}&space;}{\sqrt{2&space;\pi}}&space;\sigma_{realized}\sqrt{T}$ Just like in the formulas above, the expression is "per trade". That means that individual weekly trade will have half the volatility of monthly trade, but since there are 4 of them, and vol scales with the square root of # of trades, the expected volatility of PUT and WPUT should be the same. In reality, WPUT has somewhat smaller standard deviation (2.84% vs 3.32% ). Since expected volatility of put selling strategy only (theoretically) depends on realized volatility, the difference is quite surprising. Finally we can derive a formula for sharpe ratio for selling ATM options, it is $\inline&space;\dpi{200}&space;\bg_black&space;\large&space;SR&space;=&space;\frac{\sigma_{implied}-\sigma_{realized}}{\sigma_{realized}} * \frac{1}{\sqrt{\pi-1}}$ We can see that sharpe ratio does not depend on frequency of put sales, but rather proportional to the percent difference in implied vs realized volatility. As expected, SR for WPUT is lower than that of the PUT.
# Finite-quotient-pullbackable automorphism ## Contents BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE] This article defines an automorphism property, viz a property of group automorphisms. Hence, it also defines a function property (property of functions from a group to itself) View other automorphism properties OR View other function properties ## Definition Let $G$ be a finite group and $\sigma$ be an automorphism of $G$. We say that $\sigma$ is a finite-quotient-pullbackable automorphism of $G$ if, for any surjective homomorphism $\rho:K \to G$, there exists an automorphism $\sigma'$ of $K$ such that $\rho \circ \sigma' = \sigma \circ \rho$.
# Relation between the matrix elements of the density matrix Tags: 1. Apr 8, 2017 ### Gabriel Maia Hi. I must prove that, in general, the following relation is valid for the elements of a density matrix $$\rho_{ii}\rho_{jj} \geq |\rho_{ij}|^{2}.$$ I did it for a 2x2 matrix. The density matrix is given by $$\rho = \left[ \begin{array}{cc} \rho_{11} & \rho_{12} \\ \rho^{\ast}_{12} & \rho_{22} \end{array}\right].$$ Now, the trace of the square of the density matrix is $$\rho_{11}^2 + \rho_{22}^{2} + 2|\rho_{12}|^{2} \leq 1 \\ (\rho_{11} + \rho_{22})^2 + 2|\rho_{12}|^{2} - 2\rho_{11}\rho_{22} \leq 1$$ Because the sum of the diagonal elements of the density matrix is 1 we have that $$|\rho_{12}|^{2} \leq \rho_{11}\rho_{22}$$ This is what I've done so far but I have no idea how to prove it in the general way of $$\rho_{ii}\rho_{jj} \geq |\rho_{ij}|^{2}.$$ If, for example, the density matrix is a 3x3 matrix this means that this inequality is valid for any two elements of the diagonal. Do you know how can I approach this? Thank you. 2. Apr 13, 2017 ### PF_Help_Bot Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
Article Text The impact of tobacco control policies in Albania 1. Eduard Zaloshnja1, 2. Hana Ross2, 3. David T Levy3 1. 1Pacific Institute for Research and Evaluation, Beltsville, Maryland, USA 2. 2International Tobacco Surveillance, American Cancer Society, Atlanta, Georgia, USA 3. 3Pacific Institute for Research and Evaluation, University of Baltimore, Baltimore, Maryland, USA 1. Correspondence to Dr Eduard Zaloshnja, Pacific Institute for Research and Evaluation, 11720 Beltsville Dr Suite 900, Beltsville, MD 20705, USA; zaloshnja{at}pire.org ## Abstract Objective To assess the impact of a tobacco control law adopted in Albania in 2007 and to estimate the share of illicit cigarettes on the market. Design Comparative analysis of two waves of a nationally representative household survey, one conducted before the new law went into effect and the other after 2 years. Official sales data were contrasted with the consumption estimate based on the survey. Main outcome measures Smoking prevalence, quit attempts, exposure to cigarette advertising, exposure to second-hand smoke, total cigarette consumption, share of illicit packs among packs possessed by smokers. Results Despite the adoption of strong smoke-free policies and adverting restrictions, smoking prevalence in Albania has risen. The increase in prevalence has been driven by higher smoking rates among females (18.9% in 2007 vs 29.3% in 2009) and young adults (23.2% in 2007 vs 38.5% in 2009 among 18–19 year olds). Self-reported exposure to second-hand smoke and cigarette advertising have been reduced since 2007. The majority of respondents are still exposed to second-hand smoke and more than half are exposed to tobacco advertising. Nevertheless, there are signs that the consumption of illicit cigarettes is declining. Conclusions The impacts of smoke-free policies and an advertising ban have been limited due to lack of enforcement and failure to adopt a comprehensive set of tobacco control measures. These measures should include sizeable and regular tobacco tax increases in excess of the general level of inflation and income growth. The decline in the share of illicit cigarettes should improve the effectiveness of the cigarette tax policy. • Tobacco control • illicit cigarettes • Albania • smoking prevalence • tobacco tax • cessation • economics • prevalence • smuggling This is an open-access article distributed under the terms of the Creative Commons Attribution Non-commercial License, which permits use, distribution, and reproduction in any medium, provided the original work is properly cited, the use is non commercial and is otherwise in compliance with the license. See: http://creativecommons.org/licenses/by-nc/2.0/ and http://creativecommons.org/licenses/by-nc/2.0/legalcode. ## Introduction Until 1990, all cigarettes sold in Albania were produced by a state monopoly and were of poor quality. With economic liberalisation and the freedom to travel after the fall of communism, Albanians' exposure to the outside world dramatically increased the demand for Western-type products including cigarettes. Foreign products symbolised prestige and a promise of future economic prosperity. Cigarette smoking among women, considered socially unacceptable during the communist regime, became a sign of emancipation and a modern lifestyle, especially among the younger generations. The fall of communism created a favourable climate for foreign investment and trade, which led to higher incomes, which encourage higher consumption. International tobacco companies seized the opportunity to profit from the increased purchasing power and limited tobacco control policies, and flooded the market with foreign cigarettes. At the same time cigarettes became heavily advertised while taxes collected on them remained low. During the 1990s, domestic cigarette production was privatised, but could not compete with foreign imports.1 For example, between August 2008 and July 2009, domestic production was only 200 metric tons (conversation between Vice Minister of Finance Mima Florion and H Ross, Tirana, 2009), while imports clearing customs reached 4037 metric tons.2 However, not all cigarettes were legally imported. In 2001, the tobacco industry estimated that illicit cigarettes occupied about 72% of the total market.3 The WHO reported that between 40% and 50% of cigarettes consumed in Albania were illicit in 2007.4 In response to alarming trends in smoking prevalence,5 the Albanian government began to embrace tobacco control policies. In 2000 it adopted a set of ‘National Tobacco Control Provisions’ which consisted of a ban on tobacco advertising on television, radio, the printed media and billboards; public information campaigns on the dangers of tobacco use; health warnings and the disclosure of tobacco product ingredients; and restrictions on smoking in public places such as educational and healthcare facilities, government buildings and public transport. The government signed in 2004 and ratified in 2006 the Framework Convention for Tobacco Control (FCTC). However, advertising on billboards and at the point of sale and other promotional activities were still allowed. In 2006, Albania increased cigarette taxes, and in May 2007 banned all outdoor tobacco advertisements including billboards, prohibited smoking in all public places including restaurant and bars, and banned sales of tobacco products to those under 18 years of age. At that time, the smoke-free regulations were among the strongest in Europe. In order to assess the impact of the 2007 policies, the American Cancer Society funded two waves of a population-level survey. The first survey, the Albanian Adult Tobacco Survey (AATS-1), was conducted in April 2007, prior to the implementation of the May 2007 law, and established a baseline for measuring its impact. The second survey (AATS-2) was conducted 2 years later, in April 2009. This paper evaluates the impact of the policy change on smoking behaviour, exposure to tobacco advertising and second-hand smoke. It also assesses the trend in cigarette illicit trade based on additional questions included in the AATS-2, which were not included in AATS-1. ## Data and methods ### Sample Both waves of the AATS survey collected data from a representative sample of 4000 adults (age 18 years and older) living in private households in Albania. For the AATS-1, the population was stratified into urban and rural areas. Within these two strata, the sample was selected through a two-stage process. In the first stage, the population of each stratum was divided into 36 districts and each district was subdivided into 400-inhabitant segments, or primary sampling units (PSUs). There were a total of 7823 PSUs, of which 3518 were from urban areas. These PSUs were sorted by strata and district using systematic sampling, and 500 PSUs were chosen, 250 of which were in urban areas. In the second stage, eight households were randomly selected for each PSU. All household members 18 years and over present at the time of the visit were eligible to participate and each respondent individually answered the questions. The minimum response rate to the face-to-face interviews in AATS-1 was 82.3%. The minimum response rate, as defined by the American Association for Public Opinion Research,6 was calculated as the number of complete interviews divided by the number of interviews (complete plus partial) plus the number of non-interviews (refusal and break-off plus non-contacts plus others) plus all cases of unknown eligibility (unknown if housing unit, plus unknown, other). For the AATS-2, the interviewers attempted to contact the same households which participated in the AATS-1. They were able to re-interview 80.8% of AATS-1 participants. Using the sampling design developed for the AATS-1, some members of the AATS-1 households were newly included in AATS-2 since they had become adults and some new households were also included to reach the 4000 quota. The response rate for the new participants was 80.5%. We used a two-sided z test for each demographic group in AATS-1 and AATS-2 samples to test for differences in their demographic composition. All p values were <0.01. As table 1 indicates, both samples represent the Albanian adult population well, with the exception of a significant over-sampling of males and females in the 45–54-year-old age group and a significant under-sampling of females over 65 years of age. This was corrected by applying the weighing techniques developed for the AATS-1.5 Table 1 Sample and population demographics ### Data collection instruments The questionnaire used in both surveys was based on a shorter version of the Global Adult Tobacco Survey prototype5 and collected data on smoking prevalence, cessation, exposure to second-hand smoke, and socio-economic variables relevant to smoking behaviour.5 The AATS-1 and the AATS-2 questionnaires were similar, although AATS-2 included additional questions on illicit cigarettes. In the prevalence section of the survey, individuals were first asked if they were current smokers (daily or occasional). Occasional smokers reported how many days per week they typically smoked. All smokers provided the number of cigarettes they smoked during a typical day (smoking intensity), while non-smokers were asked if they were former smokers. Current smokers reported if they had made an attempt to quit in the last year, and if they had been advised by a doctor to quit smoking. Former smokers estimated how long they had abstained from cigarette smoking. All survey participants were asked about their exposure to second-hand smoke and tobacco advertising (see tables 2 and 3 for details on the questions). Table 2 Exposure to second-hand smoke, 2007 and 2009 Table 3 ### Illicit cigarettes In 2009, approximately 19% of smokers in urban areas and 27% in rural areas suspected that some of the cigarettes that they had purchased in the last year were illicit. Half of these respondents cited a missing tax stamp and/or a missing Albanian health warning and/or not having nicotine/tar information in Albanian as features of an illicit cigarette pack. Another 29% cited tax stamps and health warnings written in a foreign language, and 27% cited the taste of the cigarettes. Meanwhile, a cigarette pack with a tax stamp and health warning in Albanian was recorded for 93% of the most recent cigarette purchases. The share of cigarettes with a tax stamp and health warning in Albanian was independent of whether the information was self-reported or came from interviewer's inspection of a cigarette pack. Excluding cigarettes purchased in duty-free shops and abroad, cigarettes purchased from street vendors had the highest percentage of missing tax stamps and/or health warnings in Albanian (16%). The majority (70%) of the most recent cigarette purchases occurred in convenience stores, while only a small percentage of recent cigarette transactions (8.5%) involved street vendors. ## Discussion Despite the implementation of new tobacco control policies in May 2007, the survey results indicate that smoking prevalence among Albanian males did not decrease, and that smoking rates among females in general and males aged 18–29 years continue to grow. The results did provide some indications that adopting stricter tobacco control laws in 2007 was a positive step. Self-reported exposure to cigarette advertising and exposure to second-hand smoke in all public spaces have both declined. The data also indicate some reduction in smoking intensity, a small increase in quit attempts, and an increase in quit ratios among 18–24 years olds. In evaluating tobacco control policies, a limitation of this study is the lack of data to sufficiently gauge what trends in smoking rates might have been in the absence of recent policies. Trends in former communist Russia9 indicate that Albanian smoking rates, especially among females, may have increased more in the absence of the policies. Spurred by tobacco industry marketing and distribution practices, the failure to reduce smoking prevalence in Albania may be due to the social acceptability of smoking among males,10 growing female economic independence, increasing social acceptability of female smoking5 11 and the ongoing appeal of western products in Albania.5 11 The higher rates of female smoking among urban than rural dwellers is indicative of the above factors' influence. The impact of the 2007 tobacco control policies on smoking prevalence should also be understood in the context of their inadequate enforcement and the increasing affordability of cigarettes in Albania. The 2009 survey revealed that exposure to second-hand smoke is still extremely high, particularly in private workplaces, restaurants and bars. In addition, more than half the population reported exposure to some form of cigarette advertising. The high smoking rates found among younger smokers suggest that smoking prevalence may increase in the future in the absence of stronger tobacco control policies. The quit rate in Albania remains low compared to countries with advanced tobacco control. Among adults, only 13.7% of ever smokers were former smokers in 2009, while in the United States, for example, 51.8% of the ever smokers in 2008 were former smokers.12 The introduction of cessation services, which are not currently available in Albania, could help increase the number of former smokers, especially among females, whose quit rates remain low despite increasing quit attempts. In addition, quit rates might be increased through better enforcement of advertising bans and smoke-free laws, as well as increasing the tax on cigarettes. Emerging literature on tax policy points to the importance of taking inflation and income growth into account.13 While real cigarette prices increased by 3.4% between the two surveys, real GDP increased by 12% in the same period.14 In addition, the official unemployment rate declined from 13.7% (first quarter of 2007) to 12.7% (last quarter of 2008). Economic growth and lower unemployment increase purchasing power and thereby the affordability of cigarettes. The July 2009 tobacco tax increase from 40 Lek to 50 Lek per pack is a step in the right direction. If the tax is fully passed on to consumers, cigarette prices will increase, on average, by 7.3%. Opponents of higher cigarette taxes argue that higher tobacco taxes will lead to illicit cigarette trade. Historically, the share of illicit cigarettes on the market in Albania has been high, as it has been in other Balkan states such as Bosnia-Herzegovina or Macedonia.4 This share, however, does not seem to be related to tobacco taxes/prices. Illicit cigarettes occupied about 72% of the total market in 2001 when a pack of cigarettes cost about US$0.30,3 but in 2007, when a pack of cigarettes cost approximately US$1.30 (AATS-1), WHO estimated that 40–50% of cigarettes consumed in Albania were illicit.4 In addition, the higher average price paid for illicit cigarettes suggests that attributes other than the price could play a role in their market penetration. Anecdotal evidence from the survey participants revealed that illicit cigarettes were perceived as being of higher quality, similar to the situation in Vietnam.15 Our 2009 estimate of cigarette consumption based on the survey is 21.2% higher than taxed consumption based on the official statistical records on production, imports and exports.2 This would suggest that the illicit cigarettes occupied a little over 20% of the market in 2009, again a decline since 2007. Our estimate is likely to be conservative since our survey does not capture cigarettes consumed by youth and there may be under-reporting of cigarette use. However, the Albanian Customs Directorate also believes that illicit cigarette trade in Albania is on the decline as the quantity of cigarettes clearing customs has been substantially increasing in recent years. Between the first 7 months of 2007 and the first 7 months of 2009 the total number of cigarettes that cleared customs increased by 22.5%.2 Since 95% of legally consumed cigarettes are imported (conversation between Vice Minister of Finance Mima Florion and E Zaloshnja, Tirana, August 2009), the total consumption would need to increase by 21.4% to absorb this increase in cigarette imports. Even though consumption of cigarettes increased during this period, our surveys indicate that total consumption increased by only 8% between April 2007 and April 2009. Therefore, some of the legal imports must have substituted for illegal cigarettes during a period when the average nominal price of a cigarette pack increased from US$1.30 to US$1.40. The inspection of cigarette packs revealed that about 7% were suspected of being illegal due to missing tax stamps/health warnings in Albanian. However, 23% of all smokers believed that some of the cigarettes that they had purchased in the last year were illicit. The discrepancy between the micro-level estimates based on our survey and the macro-level estimate using trade and consumption data may be due to under-reporting of illicit cigarette purchases by smokers. The seasonality of illicit cigarette flows and higher smoking intensity among those consuming illicit cigarettes may also contribute to this discrepancy. A limitation of this study is the failure to inspect cigarette packs in the first wave of the survey, since that would have allowed us to assess the trend in illicit cigarette consumption based on micro-level data. In addition, attrition in the sample required replacement of some of those originally interviewed in the 2007 sample. To lower smoking prevalence and improve public health, the government of Albania should enforce existing tobacco control policies, and adopt further policies as recommended by the WHO's Framework Convention on Tobacco Control, which Albania ratified in April 2006. Experience from other countries indicates that a comprehensive set of tobacco control policies that are simultaneously implemented can achieve large reductions in smoking prevalence.16–20 • This study provides the first assessment of the impact of the May 2007 Tobacco Control Law in Albania. • This study demonstrates that adopting stricter tobacco control laws, but inadequately enforcing them, does not curb smoking prevalence. ## Acknowledgments The authors would like to thank Silva Bala from the Lung Disease Hospital in Tirana, Albania for reviewing the study plan and the results of the data collection, and Elizabeth Ward and Evan Blecher from the American Cancer Society for their valuable comments on the manuscript. View Abstract ## Footnotes • Funding The American Cancer Society provided funding for this study. • Competing interests None. • Ethics approval This study was conducted with the approval of The National Committee of Ethics, Ministry of Health of Albania. • Provenance and peer review Not commissioned; externally peer reviewed. ## Request permissions If you wish to reuse any or all of this article please use the link below which will take you to the Copyright Clearance Center’s RightsLink service. You will be able to get a quick price and instant permission to reuse the content in many different ways.
### Fifteen chips numbered from 1 to 15 are placed in a sack. If a chip is drawn at random, what is the probability of drawing the chip numbered 11? a) 1/5 b) 1/11 c)1/15 d) 11/15 Fifteen chips numbered from 1 to 15 are placed in a sack. If a chip is drawn at random, what is the probability of drawing the chip numbered 11? a) 1/5 b) 1/11 c)1/15 d) 11/15... ### Standard form of line that passes thru (-3,5) and (-2,-6) standard form of line that passes thru (-3,5) and (-2,-6)... ### Word that has been formed to associate with a sound Word that has been formed to associate with a sound... ### Need help with this math problem Need help with this math problem... ### Solve for x: -3(x+3)=-3(x+1)-5 Solve for x: -3(x+3)=-3(x+1)-5... ### A DUI conviction remains on a driver's record for ___ years. A. 10 B. 25 C. 50 D. 75 A DUI conviction remains on a driver's record for ___ years. A. 10 B. 25 C. 50 D. 75... ### Why is Elizabeth so worthless in Seven deadly sins? Why is Elizabeth so worthless in Seven deadly sins?... ### Consider the function f(x) = 2x - 3. a. What is the independent variable? What is the dependent variable? Consider the function f(x) = 2x - 3. a. What is the independent variable? What is the dependent variable?... ### You have found the following ages in years of all 5 gorillas at your local zoo: 8,4,14,16,8 what is average age of the gorillas at your zooo? What is variance You have found the following ages in years of all 5 gorillas at your local zoo: 8,4,14,16,8 what is average age of the gorillas at your zooo? What is variance... ### How many fixed points are there for the function f(x) = x^5? How many fixed points are there for the function f(x) = x^5?... ### Help me find the Measure of FQD Help me find the Measure of FQD... ### The total cost of renting a movie for different numbers of days is shown in the table. Which equation was used to create this table? look at this table The total cost of renting a movie for different numbers of days is shown in the table. Which equation was used to create this table? look at this table... ### Juan ordered 4 CDs for $48.96, which includes a$5.00 shipping charge. If each CD was the same price, what was the cost of each CD? Worth 20 pls answer ASAP Juan ordered 4 CDs for $48.96, which includes a$5.00 shipping charge. If each CD was the same price, what was the cost of each CD? Worth 20 pls answer ASAP... ### 61% of 33.8 is what? 61% of 33.8 is what?... ### In a population of goats, both beige-coated and brown-coated goats are better able to blend with the rocky environment than white-coated goats. In this case, the beige and brown coat colors are favored by natural selection over the white color. Which type of pattern of natural selection would occur in this scenario In a population of goats, both beige-coated and brown-coated goats are better able to blend with the rocky environment than white-coated goats. In this case, the beige and brown coat colors are favored by natural selection over the white color. Which type of pattern of natural selection would occur ... ### The employment sector with the largest number of uninsured is The employment sector with the largest number of uninsured is...
• S S Desai Articles written in Pramana – Journal of Physics • Two-dimensional position sensitive neutron detector A two-dimensional position sensitive neutron detector has been developed. The detector is a3He + Kr filled multiwire proportional counter with charge division position readout and has a sensitive area of 345 mm × 345 mm, pixel size 5 mm × 5 mm, active depth 25 mm and is designed for efficiency of 70% for 4 Å neutrons. The detector is tested with 0.5 bar3He + 1.5 bar krypton gas mixture in active chamber and 2 bar4He in compensating chamber. The pulse height spectrum recorded at an anode potential of 2000 V shows energy resolution of ∼25% for the 764 keV peak. A spatial resolution of 8 mm × 6 mm is achieved. The detector is suitable for SANS studies in theQ range of 0.02-0.25 Å−1. • Development of a microstrip-based neutron detector A gas-filled microstrip detector for thermal neutrons has been built and successfully tested in our laboratory. The detector has an active area of 20 mm × 15 mm and consists of alternate anodes and cathodes of widths 12 μm and 300 μm respectively. The anode to cathode gap is 150 μm and the pitch is 612 μm. A high resistance, meandering type horizontal strip connects the anodes at one end and aids in position sensing by charge division method. The detector is tested with gas mixtures3He+Kr (1: 2) and3He+CF4 (2:1) at pressure of 3 atmospheres and using a Pu-Be neutron source. The pulse height spectrum shows energy resolution of ∼8% (FWHM) for the 764 keV peak at anode voltage of 525 V for3He+Kr and ∼15% at anode voltage of 800 V for3He+CF4. Gas gains up to 6.3 × 103 and 3.6 × 103 are obtained respectively with these gas mixtures. The overall efficiency of the detector along the sensitive length is tested by exposing the active area to neutrons and recording the position spectrum. The detector shows fairly uniform efficiency (∼45%) over the active length. • Performance studies on high pressure 1-D position sensitive neutron detectors The powder diffractometer and Hi-Q diffractometer at Dhruva reactor make use of five identical 1-D position sensitive detectors (PSDs) to scan scattering angles in the range 3° to 140°. In order to improve the overall throughput of these spectrometers, it is planned to install a bank of 15 high-efficiency and high-resolution PSDs arranged in three layers with five PSDs in each layer. With each high pressure PSD (3He 10 bar + Kr 2 bar) showing the efficiency gain of 1.8 at 1.2 Å, detector bank is expected to show overall gain of 5.5 times the present detection efficiency and reduction in data collection time by equivalent factor. The 1-D PSDs are developed in batches of five, and are characterized so that all PSDs operate at uniform parameters such as position resolution, uniformity of efficiency and linearity of response. Position spectrum indicates the differential position resolution to be $\sim 1$ mm and integral position resolution to be 3–4 mm. Broadening of position spectrum at the extreme end of sensitive length of PSD is analysed using fine shift of the beam. Dependence of position resolution and dynamic range of output pulse on the input impedance of pre-amplifier is also presented. • # Pramana – Journal of Physics Current Issue Volume 93 | Issue 6 December 2019 • # Editorial Note on Continuous Article Publication Posted on July 25, 2019
# word problem with distance #### Dr.Peterson ##### Elite Member "shortest" relative to the other 5 choices? or shortest within the choice A? If it's shortest distance within choice A, there could be infinite number of layouts in 2D space with 4 loci's to consider? how can i do this without a map? i'm more confused than ever before. I, too, have not taken the time to fully solve it yet. But I beg you to answer my question about context, which I've been wishing for since I first saw the problem. Where did it come from, and why did you expect to be able to solve it? I'm looking for indications of what methods might be expected, other than raw intelligence. (My guess is still that it is essentially an intelligence test, looking for people who can invent their own methods for solving a non-standard problem. If so, then you are free to give up, and perhaps most of us will!) #### JeffM ##### Elite Member "shortest" relative to the other 5 choices? or shortest within the choice A? If it's shortest distance within choice A, there could be infinite number of layouts in 2D space with 4 loci's to consider? how can i do this without a map? i'm more confused than ever before. Yes, you need to think about choice A as its own problem, which makes it quite different from the normal multiple choice problem. As we have said, it is possible to “solve” A, and therefore A is not the correct answer. Weird. I am 90% sure that this is a basic problem in topology,, but virtually no one who is not a trained mathematician studies topology. #### lev888 ##### Senior Member i give up. can someone just plainly show how they got the answer? i don't even know what branch of math this would be under other than just word problems. Where did get this problem? What class/book? Is there a layout where this is the shortest route? No. Why? Because for any layout going back to B instead of returning directly to X makes the route longer. This is the type of reasoning you need to use to conclude that one of the provided choices can't be the shortest route. You'll probably need to use geometry (maybe the fact that in any triangle the sum of 2 sides is always greater than the 3rd). #### lev888 ##### Senior Member Where did get this problem? What class/book? Is there a layout where this is the shortest route? No. Why? Because for any layout going back to B instead of returning directly to X makes the route longer. This is the type of reasoning you need to use to conclude that one of the provided choices can't be the shortest route. You'll probably need to use geometry (maybe the fact that in any triangle the sum of 2 sides is always greater than the 3rd). Correction: Because for any layout looping back to B before returning to X from C makes the route longer. #### eric beans ##### Junior Member this is so poorly worded problem. this is why i hate tests. they get overly convoluted in order to try to trip up students. #### lev888 ##### Senior Member this is so poorly worded problem. this is why i hate tests. they get overly convoluted in order to try to trip up students. The only problem I see is "depending on" vs "independent of". Look at E: XABCBAX. Let's try to figure out the layout. XABC does not tell us much. After C we are done and can go back to X. But before X we visit B and A. Why? The shortest way from C to X is the straight road the problem tells us must exist. And yet we visit B and A. The reason is the B and A lie on the straight road from C to X. So, the layout suggested by the answer is X----A----B----C. Now, is the proposed answer in fact the shortest route? Yes: we need to get to C, then back to X and we do it in a shortest way possible (straight line). We visit A and B along the way, without adding anything to the final distance. That's it. This proves that E _can_ be the shortest route. Therefore, we need to look at another answer to either prove that it can serve as the shortest route for some layout, or that it can't. #### eric beans ##### Junior Member i think i sort of figured it out. let me reiterate, i think this is freaking poorly worded problem. i don't think i even still understand what it's asking. there's no way they're asking me to think through all the permutations. even if i were to just look at simple line (24 permutations) and a simple square alone (24 permutations) map/layout or whatever the heck they are calling this and then try the 5 choices against all the possible permutations of maps that would be 240 permutations. here's the thing, choice c doesn't come out to be "not shortest" aka longest. choices A, D and E tie for longest path. at 6. but choice c has that odd diagonal path from c to x that can't be avoided unlike other answer choices. I have no idea how choice B could not be the shortest when the distance is 4 the shortest in this scenario. #### lev888 ##### Senior Member i think i sort of figured it out. let me reiterate, i think this is freaking poorly worded problem. i don't think i even still understand what it's asking. there's no way they're asking me to think through all the permutations. even if i were to just look at simple line (24 permutations) and a simple square alone (24 permutations) map/layout or whatever the heck they are calling this and then try the 5 choices against all the possible permutations of maps that would be 240 permutations. here's the thing, choice c doesn't come out to be "not shortest" aka longest. choices A, D and E tie for longest path. at 6. but choice c has that odd diagonal path from c to x that can't be avoided unlike other answer choices. I have no idea how choice B could not be the shortest when the distance is 4 the shortest in this scenario. View attachment 28312 Did you read and did you understand the explanation for E in my post #26? #### Dr.Peterson ##### Elite Member this is so poorly worded problem. this is why i hate tests. they get overly convoluted in order to try to trip up students. Once again I need to ask you: Where did this question come from? If it is a test for a class, that is one thing; if it is something like a contest or admission test, that is entirely different. It may well, in that case, be precisely intended to separate the best thinkers from the ordinary, and therefore to trip up the unwary. But if it is for a course, then it should use ideas that were taught, even though they may be hidden. #### eric beans ##### Junior Member Once again I need to ask you: Where did this question come from? If it is a test for a class, that is one thing; if it is something like a contest or admission test, that is entirely different. It may well, in that case, be precisely intended to separate the best thinkers from the ordinary, and therefore to trip up the unwary. But if it is for a course, then it should use ideas that were taught, even though they may be hidden. it would be the latter situation in this case. they're just being devilishly tricky. #### JeffM ##### Elite Member it would be the latter situation in this case. they're just being devilishly tricky. You have been asked now quite a few times about context. Why are you so rude as not to answer? #### Dr.Peterson ##### Elite Member it would be the latter situation in this case. they're just being devilishly tricky. It bothers me when people stubbornly refuse to answer direct questions about the source of a problem. I searched for the problem and found that it's #48 in the "TSA Oxford 2009 Section 1 - Thinking Skills Assessment". Clearly it is more or less the sort of thing I suspected. Of course it's tricky, and of course it isn't a routine problem. And clearly you aren't ready to take it. But that's not shameful; so why hide it? I also found the answer key, which says the answer is C. Now, at one point I had almost convinced myself that all of them could in fact be the shortest; but that one was the most subtle. The layout that almost solves it looks like this: B / | A --- X | \ | C or with B or C inline with A and X. Can you see the shorter route than XAXBCX? And can you see how knowledge of the triangle inequality helps in the proof? It's also worth noting that rather than actually proving that this can't be the shortest route for any layout, you can use counterexamples to eliminate all the other answers, and go with that. Of course, I'm not happy doing that (and perhaps others whom they should want to give good scores to would feel the same); that's my main concern about this problem. While we're getting this out in the open, let's make it easier for others to find this discussion by searching. Here is the problem, in text rather than image form: 48 Starting from its depot in town X, a delivery lorry is to make deliveries to three towns A, Band C, in any order which the driver chooses and finally to return to X.​ Straight roads connect each town to every other town.​ Depending on the layout of the towns, which of the following could NOT be the shortest journey for him to take?​ A XAXBCBX​ B XACBX​ C XAXBCX​ D XBABXCX​ E XABCBAX​ #### eric beans ##### Junior Member i understand triangle inequality but how that can be applied to this, i still don't get. how did you know to put the x in the middle and not say a,b, or c? is that layout the same to be used against all 5 choices? so the objective is to prove that c can't be the shortest possible path of the 5 choices isn't it? #### lev888 ##### Senior Member i understand triangle inequality but how that can be applied to this, i still don't get. how did you know to put the x in the middle and not say a,b, or c? is that layout the same to be used against all 5 choices? so the objective is to prove that c can't be the shortest possible path of the 5 choices isn't it? Did you read any of my posts??? Each answer corresponds to a different layout. Please reread my posts if you missed them. Especially the one going over "E". The 5 choices are independent, the objective is to find the one (yes, it's C) that can't be the shortest route for any of infinitely many layouts. #### Cubist ##### Senior Member I searched for the problem and found that it's #48 in the "TSA Oxford 2009 Section 1 - Thinking Skills Assessment". ... I also found the answer key, which says the answer is C. Great research! I think I just proved that A is also a good answer. In all dimensions (linear, 2d, 3d,...) AND in all possible layouts, route B ≤ A. So the people at Oxford may be turning away good candidates (unless I'm wrong in the following logic ) First, split the routes into individual legs... A) xa ax xb bc cb bx B) xa ac cb bx Put each leg into alphabetical order (eg. write "xa" as "ax"). This doesn't change the distance of each separate leg of the journey. A) ax ax bx bc bc bx B) ax ac bc bx Now "cancel" any pairs that A and B have in common. If A contains "ab" and B also contains "ab" then remove them both. This will reduce the length of both routes by exactly the same amount. A) (ax) ax bx (bc) bc (bx) B) (ax) ac (bc) (bx) A) ax bx bc B) ac Clearly, route B which goes direct "ac" is always less than or equal to route A "ax xb bc". (Yes, I just did the "clearly" thing ) #### lev888 ##### Senior Member Great research! I think I just proved that A is also a good answer. In all dimensions (linear, 2d, 3d,...) AND in all possible layouts, route B ≤ A. So the people at Oxford may be turning away good candidates (unless I'm wrong in the following logic ) First, split the routes into individual legs... A) xa ax xb bc cb bx B) xa ac cb bx Put each leg into alphabetical order (eg. write "xa" as "ax"). This doesn't change the distance of each separate leg of the journey. A) ax ax bx bc bc bx B) ax ac bc bx Now "cancel" any pairs that A and B have in common. If A contains "ab" and B also contains "ab" then remove them both. This will reduce the length of both routes by exactly the same amount. A) (ax) ax bx (bc) bc (bx) B) (ax) ac (bc) (bx) A) ax bx bc B) ac Clearly, route B which goes direct "ac" is always less than or equal to route A "ax xb bc". (Yes, I just did the "clearly" thing ) Why does it matter how the 5 answers relate to each other? #### Cubist ##### Senior Member Why does it matter how the 5 answers relate to each other? I don't understand. Maybe there's a flaw in my post that you've spotted? Isn't A a valid answer because it "could NOT be the shortest journey". #### lev888 ##### Senior Member I don't understand. Maybe there's a flaw in my post that you've spotted? Isn't A a valid answer because it "could NOT be the shortest journey". I haven't reviewed your post, it's most likely a valid proof, that given a particular layout, route A is not shorter than B. However, in my understanding, this is not what the problem is asking us to do. The layout is not the same for all choices. We need to consider them independently. Is there a layout for which A is the shortest route? Yes. Next. Is there a layout for which B is the shortest route? Yes. Next. Is there a layout for which C is the shortest route? No. C is the correct answer. #### Cubist ##### Senior Member I haven't reviewed your post, it's most likely a valid proof, that given a particular layout, route A is not shorter than B. However, in my understanding, this is not what the problem is asking us to do. The layout is not the same for all choices. We need to consider them independently. Is there a layout for which A is the shortest route? Yes. Next. Is there a layout for which B is the shortest route? Yes. Next. Is there a layout for which C is the shortest route? No. C is the correct answer. Ahh, very interesting! I understand your interpretation now, and you're probably correct because it means that the question could be solved in much less time (without, potentially, doing LOTS of comparisons between the options). However, I still can't see why C could not be a shortest route if this is the layout in 2d... A----X----B----C C is XAXBCX, however there are some equivalent length routes, like XAXBCBX, XACBX. Perhaps another part of this puzzle is that if a direct route passes through another location then you HAVE to state that location? So, for the above layout, you couldn't write "CX" since it would have to be written as "CBX" because the lorry passes through B en-route. I was thinking that each letter in the route would just be a delivery stop. #### lev888 ##### Senior Member Perhaps another part of this puzzle is that if a direct route passes through another location then you HAVE to state that location? So, for the above layout, you couldn't write "CX" since it would have to be written as "CBX" because the lorry passes through B en-route. I was thinking that each letter in the route would just be a delivery stop. Yes, it should've been CBX, not CX. If we record this route as XAXB... then we are recording any stops along the way, not just deliveries - the second X is not a delivery.
# Linear Interpolation/Extrapolation I have the following grid of data. The first row represents a value called $m$ that ranges between 0.8 and 1.2, and the first column represents days that can be anywhere between 0 and $\infty$ (but usually no more than 1080). \begin{matrix} &0.8 &0.9 &0.95 &0.975 &1 &1.025 &1.05 &1.1 &1.2 \\\hline 30 &36.499 &33.035 &30.583 &29.22 &27.753 &26.214 &24.699 &22.244 &21.376 \\ 60 &36.347 &32.382 &29.923 &28.594 &27.238 &25.899 &24.612 &22.271 &19.141 \\ 90 &35.446 &31.059 &28.836 &27.712 &26.591 &25.492 &24.428 &22.405 &18.886 \\ 180 &29.444 &29.143 &27.566 &26.692 &25.823 &24.961 &24.107 &22.614 &22.5 \\ 260 &29.999 &27.402 &26.083 &25.448 &24.823 &24.208 &23.608 &22.424 &20.231 \\ 540 &28.775 &26.552 &25.42 &24.878 &24.351 &23.84 &23.346 &22.405 &20.865 \\ 720 &27.868 &26.283 &25.273 &24.79 &24.319 &23.861 &23.414 &22.561 &21.295 \end{matrix} I have $7 \times 9 = 63$ data points, that creates some sort of 3D surface. what I want to do is somehow interpolate across the rows, but be able to extrapolate the columns so that I could consider a value for $(0.99, 12)$ which I imagine would be about $28.1$ or for $(1.08, 900)$ which I reckon gives $23.2$. I am not entirely certain how to perform this kind of procedure in either R or Matlab and hope someone can help explain this to me. • Are these truly 'data' (based on observations randomly selected from a population)? Or were they computed by a mathematical algorithm? – BruceET Mar 15 '17 at 16:36 • @BruceET I believe the latter, which I am trying to reproduce. However, I imagine that the algorithm was far more complex than the simple linear relationship that I am looking for. – User101 Mar 15 '17 at 16:50 Speculations on possible methods. The last two columns seem to involve a hint of randomness (or computational instability). Some printed tables of probability distributions are amenable to various kinds of simple interpolation (linear for normal, harmonic for F, none at all between degrees of freedom for chi-squared). ('Harmonic' means to do linear interpolation on reciprocals and take the reciprocal of the result.) You might try leaving out a row or column and see how well various kinds of interpolation can be used to reconstruct it. You might start with simple linear regressions on a few individual rows and (separately) on a few columns. At least, that would give a clue as to linearity. By whatever scheme, extrapolation (say to 1080) will be almost entirely speculative, and hence risky. Addendum: Crude start. Here is one of your rows plotted against the top header (using R). This one doesn't look alarmingly nonlinear. x = c(.8,.9,.95,.975,1,1.025,1.05, 1.1, 1.2) y.90 = c(35.446,31.059,28.836,27.712,26.591,25.492,24.428,22.405,18.886) plot(x,y.90,pch=20)
# the step weights 3 Step 1: Design weights. Ideally, muscle failure will occur immediately following your last intended rep. For some recipe inspiration, check out our blog or speak to your Consultant who might have plenty of ideas up their sleeve! No-equipment power workout: Strength and stability with Knuckle Pushups, Smash it like Sindhu: 4 easy home exercises for badminton beginners, Busting Fitness Myths With Shwetha Bhatia – Part 2. You will want to use weights which are still comfortable to use, but heavy enough to 'only' let you do three or four sets of 8-12 reps each. To lift weights properly, start by picking an appropriate weight for your skills. Registered in England and Wales No.1673704. Should I use whey protein when lifting weights? By using this service, some information may be shared with YouTube. To perform the squat, bend your knees and hips, taking your thighs parallel to the ground. It’s a great, flexible workout when you’re strapped for time, but also relatively simple for beginners to pick up at their own pace. If you're active (with a busy life, hectic job or you're a gym bunny) then a few more calories might be just what you need. We've got a tasty snack range you can try. The full explanation of the sampling procedure is given in page 163 of The data documentation report (Edition 3.1). Even though it’s seen as a feminine exercise, the benefits also apply to men. We see that our weights scaled (base.weigth.scaled) are almost equal to those computed in the ESS dataset (dweigth). For legs, try weighted squats, weighted lunges, and jumps. The small differences are probably due to rounding error. Therefore, the design weight (d0) of a respondent (i) will be equal to: $$d_{0i} = 1/\pi_{i}$$ where $$pi_{i}$$ is the probability of that unit of being included in the sampling. Your Consultant will continue to support you, to help you keep on track. The more you lift, the more familiar you'll become with your muscle failure point, and the more you'll be able to push it. As we mentioned before, design weights should sum up to the entire population from which the sample is drawn or to the total number of respondents if scaled as they did in the ESS. You can either alternate arms or you can do several reps with each arm before switching. Grab the bar firmly, shoulder width apart. You can plan this meal yourself or with the help of your Consultant. This Step will help you lose weight quickly and effectively. Approved. To learn more from our Personal Trainer co-author, like how to develop a regular routine for weightlifting, keep reading! VAT No: 550 6021 81. When you’re lifting, go slowly and steadily to ensure your safety, working out for at least an hour. To work a slightly different muscle group, also consider doing both bench and dumbbell presses on an inclined bench. (including the bar). To perform the squat, bend your knees and hips, taking your thighs parallel to … By using our site, you agree to our, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/3\/35\/Lift-Weights-Step-1-Version-4.jpg\/v4-460px-Lift-Weights-Step-1-Version-4.jpg","bigUrl":"\/images\/thumb\/3\/35\/Lift-Weights-Step-1-Version-4.jpg\/aid1546149-v4-728px-Lift-Weights-Step-1-Version-4.jpg","smallWidth":460,"smallHeight":306,"bigWidth":"728","bigHeight":"485","licensing":"
## Lagrange Points in Binary Star Systems This work was done by LaGuardia students Daniel Gallego and Layla Xholi as a part of the Honors “General Physics I” class, Fall 2021. The project studies binary star systems and derives the corresponding Lagrange points. The project was conducted under the supervision of Dr. Roman Senkov. Other research projects done by students in the Physics Honors courses: “Orbital Decay of a Massive Black Hole”, “Computer Modelling of Physical Systems”, and “Atomic Nuclei and Pairing Correlations”. ### Abstract We studied Lagrange points and tried to locate them in any given binary star system. The obtained equations were applied to both a Sun-Earth-Moon scenario as well as a binary star system. Using Python we mapped the potential energy of various binary systems with different mass ratios and identified their respective Lagrange points. Today the Lagrange points of our Earth-Sun system are of special interests as the point furthest from the Sun, also known as $$L_2$$, hosts NASA's newest and most powerful James Webb Telescope. ### 1  Introduction The planets in our solar system revolve around a single star, the Sun. The universe, however, is filled with stars that are orbiting other stars. We refer to these as binary star systems [1]. The technological advances made over the last century have enabled us to send rovers, telescopes and spaceships to places unimaginable before. Predicting the motions of all these objects in space requires a good understanding of complicated environments where multiple gravitational forces act. In a two-body system, Kepler’s 3rd Law is sufficient to predict the motion of both objects. When a third body is introduced, the motion becomes more complicated since the objects are constantly pulled and pushed by multiple forces. In this project we analyze and describe motion in this intricate three-body problem. To analyze a three-body system we present it as a binary system (for example, two stars orbiting the common center of mass or a star-planet system) and a third celestial body (for example, a planet or a moon). If we assume a third body of negligible mass, we can imagine that it will be of little to no consequence on the binary system's motion. Such examples exist and we can look at an Earth-Sun-satellite scenario. Another simplification can be achieved by choosing a non-inertial frame of reference that is rotating together with the binary system. In this rotating frame the binary system will be stationary, so the third body will experience the gravitational forces from two stationary masses. Having a stationary binary system is very convenient, but the non-inertiality of the reference frame introduces an additional fictitious force that will contribute to the net force on the third body and to the potential energy of the entire system. Using Python to create contour maps of the potential energy of our three-body system, we are able to locate its Lagrange Points often referred to as the “parking spots of space”. Those points, named after the mathematician of the same name, are interesting positions in space; any object placed at those points will experience the same orbital period as that of the binary-system. It is possible to identify five Lagrange points in a given system of which two should be stable and three are unstable. Spacecraft and satellites positioned there need very little to no fuel to maintain their position. Today there are probes present at some of the Lagrange points of our Earth-Sun system and the point furthest from the Sun, also known as $$L_2$$, is the home of NASA's newest and most powerful James Webb Telescope that was launched from French Guyana in December of 2021. ### 2  Theory We will start by considering a two-body problem which corresponds to the motion of two stars about a common center of mass or motion of a planet in the gravitational field of a star. According to the universal law of gravity, the gravitational force between two point-like masses is given by the following equation $$\tag{1} \vec{F}= - G\frac{m_1 m_2}{r^2} \vec{n},$$ where $$m_1$$ and $$m_2$$ are the interacting masses, $$r$$ is the distance between the masses, $$\vec{n}$$ is the unit vector defining the direction of the force, and $$G=6.67\times10^{-11}\,Nm^2/kg^2$$ is the universal gravitational constant. It is also useful to define the potential energy of interaction of two point-like masses: $$\tag{2} U(r)=-\int \vec{F}(r)\cdot d\vec{r} = -G\frac{m_1m_2}{r}.$$ These two equations are common knowledge and have been used to analyze the two-body problem. If we introduce a third body, the motion of the binary system will not be affected assuming that we are considering a third body of negligible mass. This is often the case when looking at the relative mass of a planet compared to two much heavier stars, or a moon relative to a planet and a star. We can thus use the same equations. Let us look at such system. We know that the two bodies, $$m_1$$ and $$m_2$$, will orbit the center of mass with a certain orbital speed. If we begin rotating with the system then $$m_1$$ and $$m_2$$ appear to become stationary. This “freezing” of the frame allows us to analyze more conveniently the motion and relationship between this binary system and the third body. This approach renders the frame non-inertial. Traditionally, an inertial frame is required to apply Newton's laws of motion but for the sake of ease, we decide to use a rotating frame of reference. To preserve the laws of motion in this non-inertial frame we must introduce fictitious forces such as $$\vec{F} \rightarrow \vec{F} + \vec{F}_{NI}$$. Such a fictitious force acting on the third body can be written as $$\tag{3} \vec{F}_{NI} = m \omega^2 \vec{r},$$ where $$m$$ is the mass of the third body, $$\omega$$ is the angular velocity of the binary system, and $$\vec{r}$$ is the position of the third body relative to the center of the binary system [2]. The corresponding potential energy that can provide this fictitious force is given by $$\tag{4} U_{NI} = -\int \vec{F}_{NI}(r)\cdot d\vec{r} = - \frac{1}{2} m \omega^2 r^2.$$ Now let's consider a three body system and write the equation for the corresponding Lagrange points. In the rotating frame, at any Lagrange point all the forces acting on the third-body balance out each other, so the third body is stationary relative to the binary system. The corresponding equation can be written as $$\tag{5} \vec{F}_{1}+\vec{F}_{2}+\vec{F}_{NI}=0,$$ where $$\vec{F}_{1}$$ is the force between one component of the binary system and the third body, $$\vec{F}_{2}$$ is the force between the second component of the binary system and the third body, and $$\vec{F}_{NI}$$ is the fictitious force on the third body due to non-inertiality of the frame. Another way to determine Lagrange points is to find local extrema of the potential energy of the third body in the binary system field $$\tag{6} \delta U(r) = 0,$$ where $$U(r) = U_{1}(r) + U_2(r) + U_{NI}(r)$$ is the energy of interaction of the third body with $$m_1$$, $$m_2$$, and the fictitious (so called centrifugal) potential energy. Equations (5) and (6) are equivalent. #### 2.1  LPs for Sun-Earth system In this section we apply the above equations to the Sun-Earth system and analytically solve for the simplest Lagrange Points located near the Earth. We consider the situation represented on Fig. 1. Figure 1: Graphical representation of the forces present in a three-body system. Using universal law of gravity (1) and the non-inertial force (3) we can rewrite Eq.(5) as $$\tag{7} -G\frac{m_1 m}{r_1^2}-G\frac{m_2 m}{r_2^2}+ m \omega^2 r_3 = 0,$$ where $$r_1$$ is the distance from the Sun to the mass $$m$$, $$r_2$$ is the distance from the Earth to the mass $$m$$, $$r_3 \approx r_1$$ is the distance from mass $$m$$ to the center of the Sun-Earth system, and $$\omega$$ it's angular velocity of the Sun-Earth system. Here we assumed that the Sun is much more massive than the Earth, $$m_2 \gg m_1$$. Using Kepler's third law we can find the angular velocity $$\omega$$ as $$\tag{8} \omega^2 \approx G\frac{m_1}{a^3},$$ where $$m_1$$ is the solar mass and $$a$$ is the average radius of Earth's orbit, so called Astronomical Unit or AU. Now we can rewrite the balance of forces (7) as $$\tag{9} G\frac{m_1 m}{r_1^2} +G\frac{m_2 m}{r_2^2} = G\frac{m_1}{a^3} m r_1.$$ It is convenient to divide by $$G m_1 m$$ on both sides of Eq. (9) and introducing the ratio $$\tag{10} \mu = \frac{m_2}{m_1},$$ we finally get $$\tag{11} \frac{1}{r_1^2}+\frac{\mu}{r_2^2}= \frac{r_1}{a^3}.$$ We can measure all the distances in AU so that $$a = 1$$ and $$\tag{12} \frac{1}{r_1^2}+\frac{\mu}{r_2^2}= r_1.$$ To solve Eq.(12) we will substitute $$\tag{13} r_1 = 1 + \delta r\, \mbox{ and }\, r_2 = \delta r,$$ where $$\delta r \ll 1$$ is the deviation of $$r_1$$ from 1 AU. Using the smallness of $$\delta r$$ and applying Taylor expansion [3], $$\tag{14} \frac{1}{(1+\delta r)^2} \approx 1 - 2 \delta r,$$ we finally arrive at $$\tag{15} 1 -2\delta r + \frac{\mu}{\delta r^2} \approx 1 + \delta r.$$ The method works best by choosing a point far enough into the series to grant a good approximation and then “cutting of” the tail of the polynomial chain there. Following this principle we obtain: $$\tag{16} \delta r = \left(\frac{\mu}{3} \right)^{1/3}.$$ This allowed us to find the $$L_2$$ point for our Earth-Sun system. For the Sun-Earth system $$\mu = 1/330000$$ and Eq.(16) gives $$\delta r =0.01$$ AU. We were then able to calculate for the other point $$L_1$$ located on the other side of the Earth also at 0.01 AU. To do so we simply had to subtract $$\delta r$$ instead of adding it an change the corresponding sign in Eq.(7) because of the different direction of the force. #### 2.2  LPs for Arbitrary Binary Systems Now let us consider an arbitrary three-body system. Instead of using forces to look for the precise location of each Lagrange point, we use potential energy, denoted as $$U$$, to visualize the extrema. Those extrema would represent our Lagrange points. Using potential energy is much easier to deal with than forces because it's not a vector. Finding the potential energy extrema is equivalent to what is done in Eq (5) where we set the forces equal to zero. Figure 2: Chart of binary star system showing center of mass, as used in mapping potential energies of different binary systems based on different masses, in BSU. Figure 2 can then be utilized to introduce the center of mass for any arbitrary binary system with different distances from a mass of interest. With this we can derive the parameters of this three-body system that we wish to use later. If the coordinates of mass $$m$$ are $$(x,y)$$, then $$\tag{17} r_1= \sqrt{x^2+y^2}, r_2= \sqrt{(x-a)^2+y^2}, r_3=\sqrt{(x-l)^2+y^2},$$ and center of mass position $$l$$ and the angular velocity $$\omega$$ are $$\tag{18} l=\frac{m_2}{m_1+m_2}a ,\; \omega^2 = \frac{G(m_1+m_2)}{a^3},$$ where $$a$$ is the size of the binary system and the angular velocity $$\omega$$ is expressed in terms of $$G$$, the total mass $$m_1+m_2$$, and the size $$a$$. Using the above parameters we can piece together an equation for potential energy of the system as follows: $$\tag{19} U(x,y) = - \frac{Gm_1 m}{r_1} - \frac{Gm_2 m}{r_2} - \frac{m\omega^2 r_3^2}{2},$$ which corresponds to the following after substituting all the appropriate parameters: $$\tag{20} U(x,y) = - \frac{Gm_1m}{\sqrt{x^2 + y^2}} - \frac{Gm_2m}{\sqrt{(x-a)^2 + y^2}} -\frac{G(m_1+m_2)m}{2a^3} \left((x-l)^2+y^2\right).$$ To make the equation more manageable we try to simplify components of the equation. It is convenient to divide Eq.(20) by the 'typical' potential energy $$G(m_1+m_2)m/a$$ and introduce ratio of each mass to the total mass as $$\tag{21} \mu_1 = \frac{m_1}{m_1+m_2},\; \mu_2 = \frac{m_2}{m_1+m_2},\; \mbox{ and } \mu_1 + \mu_2 = 1,$$ and measure all the distances in the size of the binary system $$a$$ $$\tag{22} r_1 \rightarrow a r_1,\; r_2 \rightarrow a r_2,\; r_3 \rightarrow a r_3.$$ Now the 'reduced' potential energy $$u = U/[G(m_1+m_2)m/a]$$ looks like: $$\tag{23} u(x,y) = - \frac{\mu_1}{r_1} - \frac{\mu_2}{r_2}-\frac{ r_3^2 }{2},$$ where $$r_1 = \sqrt{x^2+y^2}$$, $$r_2 = \sqrt{(x-1)^2+y^2}$$, and $${r_3} = \sqrt{(x-\mu_2)^2+y^2}$$. Using the end result, Eq (23) allows us to change the parameters $$(\mu_1, \mu_2)$$ quite easily in a program we wrote in Python to show the results for very different types of binary systems. We were able to use the same equation for our Sun-Earth-Moon system, and for binary system with different mass distribution ratios. Potential energy diagrams were mapped for binary star systems of nearly equal mass as well as systems with a ratio of 80:20. ### 3  Conclusion Though motion in three-body systems are complicated it is possible to analyze them under certain assumptions. Computational tools can help us map the potential energy of such systems and locate Lagrange points. Figure 3: Top left: PE diagram depicting the five Lagrange Points in our Earth-Sun-system. Top right: PE diagram for a system with a smaller difference in masses between the two bodies. The mass difference here is 80 to 20. Bottom left: PE diagram for a recently discovered binary system in the NGC 1850 cluster [4]. The binary system is composed of a main sequence turn-off star and a black hole with a mass ratio of 5 to 11. Bottom right: PE diagram for a system composed of three stars of equal mass. Figure 4: A closer look at a Lagrange point on a potential energy diagram. Here a stable point is depicted, which corresponds to a minimum peak. The resulting potential energy contour maps, Figures 3, 4 and 5, show that a binary system's Lagrange points are affected by the mass distribution of the two bodies $$m_1$$ and $$m_2$$, as predicted. Interestingly the $$L_1$$ point, the point between both masses, appears to be the same between most types of binary systems. The stable Lagrange points, $$L_4$$ and $$L_5$$, appear to decrease in size as the disparity between $$m_1$$ and $$m_2$$ becomes more significant. A system with a mass ratio of about 80:20 shows these stable points to be larger, meaning there could be a wide deviation in the movement of an object there before it leaves equilibrium. Figure 5: An animation demonstrating evolution of the potential energy field and the corresponding Lagrange points of a binary system. The binary system mass distribution changes from $$\mu_1 = 0.9, \mu_2 = 0.1$$ to $$\mu_1 = 0.1, \mu_2=0.9$$. While human space exploration has its limits, it is not unreasonable to imagine sending satellites, telescopes and probes to occupy these points in space. The authors would like to thank Dr. Roman Senkov for his help and guidance in this research project. The research was done as a part of the Honors General Physics I course at LaGuardia Community College. ### References [1] S. Naimi et al., Phys. Rev. C 86, 014325 (2012).
# New Constraints on Methane Fluxes and Rates of Anaerobic Methane Oxidation in a Gulf of Mexico Brine Pool via In Situ Mass Spectrometry Title: New Constraints on Methane Fluxes and Rates of Anaerobic Methane Oxidation in a Gulf of Mexico Brine Pool via In Situ Mass Spectrometry Author: Wankel, Scott D.; Joye, Samantha B.; Samarkin, Vladimir A.; Friederich, Gernot; Melas-Kyriazi, John; Girguis, Peter R.; Shah, Sunita Rajesh Note: Order does not necessarily reflect citation order of authors. Citation: Wankel, Scott D., Samantha B. Joye, Vladimir A. Samarkin, Sunita Rajesh Shah, Gernot Friederich, John Melas-Kyriazi, and Peter R. Girguis. 2010. New constraints on methane fluxes and rates of anaerobic methane oxidation in a Gulf of Mexico brine pool via in situ mass spectrometry. Deep Sea Research Part II: Topical Studies in Oceanography 57(21-23): 2022-2029. Full Text & Related Files: Wankel_NewConstraints.pdf (4.223Mb; PDF) Abstract: Deep-sea biogeochemical cycles are, in general, poorly understood owing to the difficulties of making measurements in situ, recovering samples with minimal perturbation, and, in many cases, coping with high spatial and temporal heterogeneity. In particular, biogeochemical fluxes of volatiles such as methane remain largely unconstrained because of the difficulties with accurate quantification in situ and the patchiness of point sources such as seeps and brine pools. To better constrain biogeochemical fluxes and cycling, we have developed a deep-sea in situ mass spectrometer (ISMS) to enable high-resolution quantification of volatiles in situ. Here we report direct measurements of methane concentrations made in a Gulf of Mexico brine pool located at a depth of over 2300 m. Concentrations of up to 33 mM methane were observed within the brine pool, whereas concentrations in the water directly above were three orders of magnitude lower. These direct measurements enabled us to make the first accurate estimates of the diffusive flux from a brine pool, calculated to be $$1.1\pm0.2 mol m^{-2} yr^{-1}$$. Integrated rate measurements of aerobic methane oxidation in the water column overlying the brine pool were $$~320 \mu mol m^{-2} yr^{-1}$$, accounting at most for just 0.03% of the diffusive methane flux from the brine pool. Calculated rates of anaerobic methane oxidation were $$600-1200 \mu M yr^{-1}$$, one to two orders of magnitude higher than previously published values of AOM in anoxic fluids. These findings suggest that brine pools are enormous point sources of methane in the deep sea, and may, in aggregate, have a pronounced impact on the global marine methane cycle. Published Version: doi:10.1016/j.dsr2.2010.05.009 Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:10136320 Downloads of this work:
• 14 • 12 • 9 • 10 • 13 # Planetary Gravity. This topic is 4584 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic. ## Recommended Posts Well, googling "planetary gravity formula" didn't get me anywhere... I'm tring to figure out how to make a program that simulates gravity of bodyies in space like planets and moons and such. The bodies would probably have a certain mass and density and such. Now how would I go about doing this? I'm guessing there is some crazy complicated formular out there that I can just input a bunch of values to get the velocities/locations on the bodies. See, I think it would be fun to set moons in orbit around planets and such. And once I get this working I'll probably make some extreme pong game with planets in the arena that effect the ball. Thanks for any info! ##### Share on other sites Well the classical Newtonian formula for gravity is: F = GMm/r^2 G - gravitational constant M and m - mass of two (point) bodies r - separation of two bodies The reason I write (point) is because is also applies to perfectly spherical bodies and is a good enough approximation if the two things are far enough apart. I don't know how much this is going to help a simulator though, from what I've heard you're likely to suffer stability problems. I'd look up a good numerical integration method (can't remember the name of the one I last used at the moment). ##### Share on other sites Thanks! I'll attempt to write out a demo. If it explodes.... I'll know it's unstable. ##### Share on other sites FROM: http://hyperphysics.phy-astr.gsu.edu/hbase/grav.html#grav X1, X2 are the x-coordinates of body 1 and 2 repectfully Y1, Y2 are the y-coordinates of body 1 and 2 repectfully M1, M2 are the masses of body 1 and 2 repectfully RXsquared = (X1-X2)^2 RYsquared = (Y1-Y2)^2 Rsquared = RXsquared + RYsquared Fgrav = (M1*M2) / Rsquared BTW Fgrav is simplified From newton: Force = Mass * Acceleration We need to find the change in velocity AKA acceleration So Acceleration = Force / Mass A1 = (Fgrav/M1) You'll need to split the acceleration into X and Y components If X1< ##### Share on other sites Awww... Anonymous Poster(first one), thanks for the straigt forwardness.... I thought I had it in the bag. My only trouble was being caused by the "splitting of the acceleration into the X and Y"... Can you finish that last little part you were about to say? "You'll need to split the acceleration into X and Y components If X1<" I'm guessing I need to find the angle at which the second body is located with respect to the first(the one I'm calculating this for)... and then doing something like xvel = xvel + A1*cos(angle) and the same for yvel. Is that right? If so, then how do I acquire the angle mathmaticly. ##### Share on other sites Nevermind about that... I just did arc tan of the slope. I think that's how it's done. And then I did the: cur1\xvel = cur1\xvel + A1#*Sin(SlopeAngle#) cur1\yvel = cur1\yvel + A1#*Cos(SlopeAngle#) So I guess that's all right. Now when I run the program, I see the two bodies for an instant then they disappear. I'm not sure what's up there. What value should I use for the mass of the bodies? A large number say 300 or something super small like 0.003? I tried both and it still disappears in an instant. Here is the code for updating the bodies (if it's any help): ;Cycle through and update all existing bodies For cur1.Body = Each Body For cur2.Body = Each Body ;Calculate gravitational force RXsquared# = (cur1\x-cur2\x)*(cur1\x-cur2\x) RYsquared# = (cur1\y-cur2\y)*(cur1\y-cur2\y) Rsquared# = RXsquared + RYsquared Fgrav# = (cur1\mass*cur2\mass)/Rsquared ;Calculate the slope angle Slope# = (cur2\y-cur1\y)/(cur2\x-cur1\x) SlopeAngle# = ATan(Slope) Next ;Calculate acceleration based on (Force = Mass * Acceleration) A1# = (Fgrav/cur1\mass) ;Adjust the velocities of this body based on the force calculated cur1\xvel = cur1\xvel + A1#*Sin(SlopeAngle#) cur1\yvel = cur1\yvel + A1#*Cos(SlopeAngle#) ;Adjust the position of the bodies based on their velocity cur1\x = cur1\x + cur1\xvel cur1\y = cur1\y + cur1\yvel ;Draw the body Color 255,255,255 Oval cur1\x-cur1\radius,cur1\y-cur1\radius,cur1\radius*2,cur1\radius*2,1 Color 0,0,255 Text cur1\x-cur1\radius,cur1\y-cur1\radius-20,"Force: "+A1# Next What could be causing my planets to just explode out of view? ##### Share on other sites Vel = Vel + Acc * t Position = Position + Vel * t Lower values of t will result in more accuracy but a slower simulation. It's nice to be able to control it. This is a basic explicit integration scheme, and it should work fine for what you're doing for now. The errors will tend to make the bodies gain energy as the simulation runs, so if you get bodies orbiting each other, the orbits may slowly get larger and larger. More sophisticated integration schemes have less error; some integration schemes will tend to reduce the energy in the system instead of increase it. But for getting planets to orbit each other this simple scheme is good enough. Also it looks like you might be trying to make a planet apply its gravitational force to itself. The distance between a planet and itself is 0, so you end up dividing by 0 and getting infinite force. ##### Share on other sites Thanks Anonymous Poster, I didn't realize I was calculating the bodies by them selves. That fixed the exploding out of view problem. But before I add a time step, can someone tell me how to correctly split that acceleration into the X and Y components? I did this: ;Calculate the slope angle Slope# = (cur2\y-cur1\y)/(cur2\x-cur1\x) SlopeAngle# = ATan(Slope) ;Calculate acceleration based on (Force = Mass * Acceleration) A1# = (Fgrav/cur1\mass) ;Adjust the velocities of this body based on the force calculated cur1\xvel = cur1\xvel + A1#*Sin(SlopeAngle#) cur1\yvel = cur1\yvel + A1#*Cos(SlopeAngle#) But I don't think that works perfectly. What happens when I run the program is the two bodies move in the same direction instead of towards each other. I think it has something to do with the fact that slope doesn't account for direction... so I need to somehow get a negative sometimes or something. ##### Share on other sites For one thing, I think you might have the sine and cosine parts mixed up. I'm not entirely sure about that though. More importantly, yeah, the atan function has a period of 180 degrees. It returns the same angle for a vector as it would for a vector pointing in exactly the oposite direction. There's usually an atan2 function that takes the x and y components separately and works in any direction, or you can check if the x component is negative and if so add 180 degrees or pi radians or whatever units it is in to the angle returned by atan. Or you can avoid trigonometric functions altogether. The sine of an angle of a vector can be interpreted as the ratio of the y component to the magnitude. You already can calculate this ratio without using any angles. If the distance between the bodies in the x direction is dx and the distance in the y direction is dy, the ratio is just dy/sqrt(dx^2 + dy^2). This will also give the correct sign. And if you really wanted to for some reason, there are a few simple optimizations. One of them is if you use the formula above, it includes what you are already calculating and calling RSquared. Another is that the force A is applying to B is equal in magnitude and opposite in direction to the force B is applying to A (equal and opposite reaction...). This allows you to perform almost half as many calculations when calculating the gravitational forces between n bodies.
New Titles  |  FAQ  |  Keep Informed  |  Review Cart  |  Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Mathematical Physics Math Education Iwanami Series in Modern Mathematics Variational Problems in Geometry Seiki Nishikawa, Mathematical Institute, Tohoku University, Sendai, Japan SEARCH THIS BOOK: Translations of Mathematical Monographs Iwanami Series in Modern Mathematics 2002; 209 pp; softcover Volume: 205 ISBN-10: 0-8218-1356-0 ISBN-13: 978-0-8218-1356-0 List Price: US$55 Member Price: US$44 Order Code: MMONO/205 A minimal length curve joining two points in a surface is called a geodesic. One may trace the origin of the problem of finding geodesics back to the birth of calculus. Many contemporary mathematical problems, as in the case of geodesics, may be formulated as variational problems in surfaces or in a more generalized form on manifolds. One may characterize geometric variational problems as a field of mathematics that studies global aspects of variational problems relevant in the geometry and topology of manifolds. For example, the problem of finding a surface of minimal area spanning a given frame of wire originally appeared as a mathematical model for soap films. It has also been actively investigated as a geometric variational problem. With recent developments in computer graphics, totally new aspects of the study on the subject have begun to emerge. This book is intended to be an introduction to some of the fundamental questions and results in geometric variational problems, studying variational problems on the length of curves and the energy of maps. The first two chapters treat variational problems of the length and energy of curves in Riemannian manifolds, with an in-depth discussion of the existence and properties of geodesics viewed as solutions to variational problems. In addition, a special emphasis is placed on the facts that concepts of connection and covariant differentiation are naturally induced from the formula for the first variation in this problem, and that the notion of curvature is obtained from the formula for the second variation. The last two chapters treat the variational problem on the energy of maps between two Riemannian manifolds and its solution, harmonic maps. The concept of a harmonic map includes geodesics and minimal submanifolds as examples. Its existence and properties have successfully been applied to various problems in geometry and topology. The author discusses in detail the existence theorem of Eells-Sampson, which is considered to be the most fundamental among existence theorems for harmonic maps. The proof uses the inverse function theorem for Banach spaces. It is presented to be as self-contained as possible for easy reading. Each chapter may be read independently, with minimal preparation for covariant differentiation and curvature on manifolds. The first two chapters provide readers with basic knowledge of Riemannian manifolds. Prerequisites for reading this book include elementary facts in the theory of manifolds and functional analysis, which are included in the form of appendices. Exercises are given at the end of each chapter. This is the English translation of a book originally published in Japanese. It is an outgrowth of lectures delivered at Tohoku University and at the Summer Graduate Program held at the Institute for Mathematics and its Applications at the University of Minnesota. It would make a suitable textbook for advanced undergraduates and graduate students. This item will also be of interest to those working in analysis. Advanced undergraduates, graduate students, and research mathematicians interested in differential geometry, global analysis, and analysis on manifolds. Reviews "A welcome contribution to and survey of some of the fundamental questions and results in geometric variational problems on the length of curves and the energy of maps." -- Mathematical Reviews • Arc-length of curves and geodesics • First and second variation formulas • Energy of maps and harmonic maps • Existence of harmonic maps • Fundamentals of theory of manifolds and functional analysis • Prospects for contemporary mathematics • Solutions to exercise problems • Bibliography • Books • Index • Copying and reprinting notice • Other titles in this series
# 统计代写|时间序列分析代写Time-Series Analysis代考|STA457H1 ## 统计代写|时间序列分析代写Time-Series Analysis代考|Are Shocks to British GDP Temporary or Permanent? Fig. $5.5$ shows the logarithms of British real GDP per capita annually over the period of 1822-1913, i.e., from just after the end of the Napoleonic wars to the beginning of World War I, a period which covers the whole of the Victorian era. A linear trend line has been superimposed on the plot, calculated from a model of the form of (5.8): $$\begin{gathered} x_t=\underset{(0.019)}{0.329}+\underset{(0.0004)}{0.0103 t} t+\varepsilon_t \ \varepsilon_t=\underset{(0.076)}{0.696} \varepsilon_{t-1}+\hat{a}_t \end{gathered}$$ This TS model implies that, since we are dealing with logarithms, trend growth in real GDP per capita was $1.03 \%$ per annum, with there being stationary deviations about the trend line. Consequently, all shocks that push real GDP per capita away from its long-run trend path have only short-run, “transitory” impacts, with the series always returning to this trend path. Since the error component is modeled by an AR(1) process with a parameter of around $0.7$, such shocks die away geometrically and rather quickly; being reduced by over $90 \%$ in size after 7 years $\left(0.7^7=0.082\right)$. Note that the error component displays no evidence of a “business cycle,” for this would require $\varepsilon_t$ to follow (at least) an $\mathrm{AR}(2)$ process with complex roots, for which there is no evidence, since the inclusion of a second autoregressive term produces an insignificant coefficient. This TS representation may be contrasted with the DS representation $$\nabla x_t=\underset{(0.0003)}{0.0104}+\hat{a}_t$$ obtained by replacing the autoregressive coefficient of $0.7$ with one of unity. This model is a drifting random walk with the drift parameter estimated as $1.04 \%$ per annum. The interpretation of this model, however, is one in which all shocks are permanent; remaining in the series for all time with no dissipation. ## 统计代写|时间序列分析代写Time-Series Analysis代考|OTHER APPROACHES TO TESTING FOR A UNIT ROOT 5.12 An alternative unit root test to the ADF for dealing with autocorrelation in $a_t$, which also allows for heterogeneity of variance, has been proposed by Phillips and Perron (1988). Rather than including extra lags of $\nabla x_t$ to ensure that the errors of $(5.4)$ are indeed white noise, the idea here is to estimate an “unaugmented” model-(5.3), say-and to modify the test statistics so that the effects of any autocorrelation are accounted for. This will enable the same DF limiting distributions and, hence, critical values to be used. Under a specific set of conditions placed upon $a_t$, known as weak dependency, which are described in detail by Phillips (1987), the $\tau_\mu$ statistic obtained from the estimation of $(5.3)$ is modified to $$Z\left(\tau_\mu\right)=\tau_\mu\left(\hat{\sigma}0 / \hat{\sigma}{\ell}\right)-\frac{1}{2}\left(\hat{\sigma}{\ell}^2-\hat{\sigma}_0^2\right) / \Sigma{\ell}$$ in which \begin{aligned} &\hat{\sigma}0^2=T^{-1} \sum{t=1}^T \hat{a}t^2 \ &\hat{\sigma}{\ell}^2=\hat{\sigma}0^2+2 T^{-1} \sum{j=1}^{\ell} w_j(\ell)\left(\sum_{t=j+1}^T \hat{a}t \hat{a}{t-j}\right) \ &\Sigma_{\ell}^2=T^{-2} \hat{\sigma}{\ell}^2 \sum{t=2}^T\left(x_{t-1}-\bar{x}{-1}\right)^2 \quad \bar{x}{-1}=(T-1)^{-1} \sum_{t=1}^{T-1} x_t \end{aligned} $\hat{\sigma}{\ell}^2$ is a consistent estimator of the long-run variance and employs a window or kernel function $w_j(\ell)$ to weight the sample autocovariances appearing in the formula. This ensures that the estimator remains positive, with $\ell$ acting as a truncation lag, much like $k$ in the ADF regression. A range of kernel functions are available, such as the “triangular” set of lag weights $w_j(\ell)=\ell-j /(\ell+1) . Z\left(\tau\mu\right)$ is often referred to as the Phillips-Perron (PP) non-parametric unit root test. $Z\left(\tau_\mu\right)$ has the same limiting distribution as $\tau_\mu$, so that the latter’s critical values may again be used. If $x_t$ has zero mean, the adjusted statistic, $Z(\tau)$, is as in (5.10) with $\bar{x}{-1}$ removed and has the same limiting distribution as $\tau$. If a time trend is included then a further adjustment is required to enable the statistic, now denoted $Z\left(\tau\tau\right)$, to have the limiting $\tau_\tau$ distribution (Mills and Markellos, 2008, page 87, for example, provide details). 5.13 Many alternative unit root tests have been developed since the initial ADF and PP tests were introduced. A recurring theme of unit root testing is the low power and severe size distortion inherent in many tests: see, especially, the review by Haldrup and Jansson (2006). For example, the PP tests suffer severe size distortions when there are moving average errors with a large negative root and, although their ADF counterparts are better behaved in this respect, the problem is not negligible even here. Moreover, many tests have low power when the largest autoregressive root is close to, but nevertheless less than, unity. A related issue is that unlike many hypothesis testing situations, the power of tests of the unit root hypothesis against stationary alternatives depends less on the number of observations per se and more on the span of the data (i.e., the length of the observation period). For a given number of observations, power has been found to be highest when the span is longest; conversely, for a given span, additional observations obtained using data sampled more frequently lead to only a marginal increase in power, the increase becoming negligible as the sampling interval is decreased. Hence, a series containing fewer annual observations over an extended time period will often lead to unit root tests having higher power than those computed from a series containing more observations over a shorter period. # 时间序列分析代考 ## 统计代写|时间序列分析代写时间序列分析代考|对英国GDP的冲击是暂时的还是永久性的? $5.5$显示了1822-1913年期间英国人均实际GDP的年对数,即从拿破仑战争刚刚结束后到第一次世界大战开始,这一时期涵盖了整个维多利亚时代。在图上叠加了一条线性趋势线,根据(5.8)形式的模型计算: $$\begin{gathered} x_t=\underset{(0.019)}{0.329}+\underset{(0.0004)}{0.0103 t} t+\varepsilon_t \ \varepsilon_t=\underset{(0.076)}{0.696} \varepsilon_{t-1}+\hat{a}_t \end{gathered}$$ $$\nabla x_t=\underset{(0.0003)}{0.0104}+\hat{a}_t$$ )相比,DS表示是通过将$0.7$的自回归系数替换为单位系数得到的。该模型是一个漂移随机游走,其漂移参数估计为每年$1.04 \%$。然而,对这个模型的解释是,所有的冲击都是永久性的; ## 统计代写|时间序列分析代写时间序列分析代考|测试单位根的其他方法 5.12 Phillips和Perron(1988)提出了一种替代ADF的单位根检验来处理$a_t$中的自相关,该单位根检验也考虑到了方差的异质性。这里的想法不是包括$\nabla x_t$的额外滞后以确保$(5.4)$的错误确实是白噪声,而是估计一个“未增强的”模型(5.3),并修改测试统计数据,以便考虑到任何自相关的影响。这将启用相同的DF限制分布,因此,使用临界值 $$Z\left(\tau_\mu\right)=\tau_\mu\left(\hat{\sigma}0 / \hat{\sigma}{\ell}\right)-\frac{1}{2}\left(\hat{\sigma}{\ell}^2-\hat{\sigma}0^2\right) / \Sigma{\ell}$$ ,其中 \begin{aligned} &\hat{\sigma}0^2=T^{-1} \sum{t=1}^T \hat{a}t^2 \ &\hat{\sigma}{\ell}^2=\hat{\sigma}0^2+2 T^{-1} \sum{j=1}^{\ell} w_j(\ell)\left(\sum{t=j+1}^T \hat{a}t \hat{a}{t-j}\right) \ &\Sigma_{\ell}^2=T^{-2} \hat{\sigma}{\ell}^2 \sum{t=2}^T\left(x_{t-1}-\bar{x}{-1}\right)^2 \quad \bar{x}{-1}=(T-1)^{-1} \sum_{t=1}^{T-1} x_t \end{aligned} $\hat{\sigma}{\ell}^2$是长期方差的一致估计量,并使用窗口或核函数$w_j(\ell)$对公式中出现的样本自协方差进行加权。这确保了估计器保持为正,$\ell$充当截断延迟,很像ADF回归中的$k$。可以使用一系列的核函数,例如滞后权重的“三角”集$w_j(\ell)=\ell-j /(\ell+1) . Z\left(\tau\mu\right)$通常被称为Phillips-Perron (PP)非参数单位根检验。 $Z\left(\tau_\mu\right)$与$\tau_\mu$具有相同的极限分布,因此后者的临界值可能再次被使用。如果$x_t$的均值为零,则调整后的统计量$Z(\tau)$如(5.10)中删除了$\bar{x}{-1}$,具有与$\tau$相同的极限分布。如果包含时间趋势,则需要进一步调整以使统计量(现在标记为$Z\left(\tau\tau\right)$)具有有限的$\tau_\tau$分布(例如,Mills和Markellos, 2008年,第87页提供详细信息)。 myassignments-help数学代考价格说明 1、客户需提供物理代考的网址,相关账户,以及课程名称,Textbook等相关资料~客服会根据作业数量和持续时间给您定价~使收费透明,让您清楚的知道您的钱花在什么地方。 2、数学代写一般每篇报价约为600—1000rmb,费用根据持续时间、周作业量、成绩要求有所浮动(持续时间越长约便宜、周作业量越多约贵、成绩要求越高越贵),报价后价格觉得合适,可以先付一周的款,我们帮你试做,满意后再继续,遇到Fail全额退款。 3、myassignments-help公司所有MATH作业代写服务支持付半款,全款,周付款,周付款一方面方便大家查阅自己的分数,一方面也方便大家资金周转,注意:每周固定周一时先预付下周的定金,不付定金不予继续做。物理代写一次性付清打9.5折。 Math作业代写、数学代写常见问题 myassignments-help擅长领域包含但不是全部:
# Difference between revisions of "LaTeX" LaTeX is a system for preparing documents to be printed or displayed. It is built on top of the Donald Knuth's TeX typesetting system. You can learn more about LaTeX on TeX Users Group FAQ, WikiPedia, CTAN (Comprehensive TeX Archive Network). The rest of this article focus on getting Inkscape to work with LaTex. ## How to embed a LaTeX equation inside Inkscape Recent versions of Inkscape (since 0.48?) have built-in support for including a LaTeX formula inside a drawing. It is on the menu bar: Extensions->Render->LaTeX Formula. This menu might be hidden if Inkscape cannot find these helper programs: latex, dvips, pstoedit. On Ubuntu, you can install these programs with the command, sudo apt-get install texlive pstoedit Alternatively, you can use the textext extension. It is similar to the build-in LaTeX support, but has a slightly more polished input interface. ## How to embed an Inkscape drawing inside a LaTeX document From the menu : File -> Save a Copy. On the lower right corner, choose file type "Encapsulated PostScript (*.eps)" In your LaTeX file, use "\includegraphics{filename.eps}". For a tutorial on how to use the EPS file inside LaTeX, search on Google: latex import graphics. ## How to turn an Inkscape drawing into an editable LaTeX document From version 0.48, Inkscape has a special PDF+LaTeX output option. All lines and shapes are saved into a PDF file, while all texts are saved into a LaTeX file. Compiling this LaTeX will give you back the whole drawing. This method allows you to use LaTeX equations. You can also export EPS+LaTeX or PS+LaTeX. More details is here: SVG in LaTeX (CTAN). ### Lyx LyX provides a GUI frontend for creating and editing a LaTeX document. If you want to use PDF+LaTeX from Lyx, you have to put this in your Latex preable (in Lyx, menu "document" -> "preferences" -> "latex preamble"): \usepackage{graphicx} \usepackage{xcolor} \definecolor{darkblue}{rgb}{0,0,0.5} \usepackage{transparent} \centering
# Galvanic reaction between aluminum and carbon fiber composite I understand that there is a galvanic reaction between aluminum and carbon fiber composite. Structural aluminum parts in contact with carbon fiber composites should be insulated by something like fiberglass. But what exactly is it that happens, chemically? I know that aluminum has a tendency to be oxidized; aluminum oxidizes readily by itself in air. I also know that carbon fiber itself is a conductor due to delocalized electrons. So assuming that aluminum is oxidized then the carbon fiber composite must be reduced. What exactly is reduced? The carbon fiber, or the epoxy? What is the role of the epoxy in all of this? Wouldn't the epoxy be electrically insulating? How exactly does this redox reaction take place across the epoxy? The reason is that aluminium carbide, $\ce{Al4C3}$ is formed. The reaction occurs at around 500°C on the interface. The problem with this substance is that it is brittle, and it also reacts with water: $\ce{Al4C3 + 12H2O -> 4Al(OH)3 + 3CH4}$.
Share Books Shortlist # The Equation of Motion of a Particle is S = 2t2 + Sin 2t, Where S is in Metres and T is in Seconds. the Velocity of the Particle When Its Acceleration is 2 M/Sec2, is (A) π + √ 3 M / Sec - CBSE (Science) Class 12 - Mathematics ConceptRate of Change of Bodies Or Quantities #### Question The equation of motion of a particle is s = 2t2 + sin 2t, where s is in metres and is in seconds. The velocity of the particle when its acceleration is 2 m/sec2, is • $\pi + \sqrt{3} m\ /\sec$ • $\frac{\pi}{3} + \sqrt{3} m/\sec$ • $\frac{2\pi}{3} + \sqrt{3} m/\sec$ • $\frac{\pi}{3} + \frac{1}{\sqrt{3}} m/\sec$ #### Solution $\frac{\pi}{3} + \sqrt{3} \ m/\sec$ $\text { According to the question },$ $s = 2 t^2 + \sin 2t$ $\Rightarrow \frac{ds}{dt} = 4t + 2 \cos 2t$ $\Rightarrow \frac{d^2 s}{d t^2} = 4 - 4 \sin 2t$ $\Rightarrow 4 - 4 \sin 2t = 2$ $\Rightarrow 4 \sin 2t = 2$ $\Rightarrow \sin 2t = \frac{1}{2}$ $\Rightarrow 2t = \frac{\pi}{6}$ $\text { Now,}$ $\frac{ds}{dt} = 4\left( \frac{\pi}{12} \right) + 2 \cos\left( \frac{\pi}{6} \right)$ $\Rightarrow \frac{ds}{dt} = \frac{\pi}{3} + \sqrt{3} m/\sec$ Is there an error in this question or solution? #### Video TutorialsVIEW ALL [3] Solution The Equation of Motion of a Particle is S = 2t2 + Sin 2t, Where S is in Metres and T is in Seconds. the Velocity of the Particle When Its Acceleration is 2 M/Sec2, is (A) π + √ 3 M / Sec Concept: Rate of Change of Bodies Or Quantities. S
qscqesze Published on 2017-09-02 11:31 in 暂未分类 with qscqesze Codeforces Round #596 (Div. 2, based on Technocup 2020 Elimination Round 2) A. Forgetting Things 水题 A. Forgetting Things Kolya is very absent-minded. Today his math teacher asked him to solve a simple problem with the equation 𝑎+1=𝑏 with positive integers 𝑎 and 𝑏, but Kolya forgot the numbers 𝑎 and 𝑏. He does, however, remember that the first (leftmost) digit of 𝑎 was 𝑑𝑎, and the first (leftmost) digit of 𝑏 was 𝑑𝑏. Can you reconstruct any equation 𝑎+1=𝑏 that satisfies this property? It may be possible that Kolya misremembers the digits, and there is no suitable equation, in which case report so. Input The only line contains two space-separated digits 𝑑𝑎 and 𝑑𝑏 (1≤𝑑𝑎,𝑑𝑏≤9). Output If there is no equation 𝑎+1=𝑏 with positive integers 𝑎 and 𝑏 such that the first digit of 𝑎 is 𝑑𝑎, and the first digit of 𝑏 is 𝑑𝑏, print a single number −1. Otherwise, print any suitable 𝑎 and 𝑏 that both are positive and do not exceed 109. It is guaranteed that if a solution exists, there also exists a solution with both numbers not exceeding 109. input 1 2 output 199 200 代码 #include<iostream> using namespace std; int main(){ int a,b; cin>>a>>b; if(b==1&&a==9){ cout<<"9 10"<<endl; }else if(b-a==1){ cout<<a<<" "<<b<<endl; }else if(a==b){ cout<<a<<"1 "<<b<<"2"<<endl; }else{ cout<<"-1"<<endl; } } posted @ 2019-11-01 14:36  qscqesze  阅读(115)  评论(0编辑  收藏
## burhan101 Group Title Factor x²+4x-4 one year ago one year ago 1. burhan101 Group Title is it a quadratic equation question ? 2. micahwood50 Group Title Do you mean x²+4x+4? 3. burhan101 Group Title no it's -4 i've been working on it, but it's no factoring :/ 4. micahwood50 Group Title Because factoring x²+4x-4 is pretty difficult. 5. micahwood50 Group Title Well, It's safe to say that it cannot be factored. 6. Copythat Group Title Using the quadratic formula would be the easiest method 7. micahwood50 Group Title @Copythat How can quadratic formula help us to factor it? 8. burhan101 Group Title yeah, i dont think the formula's working 9. burhan101 Group Title $\lim_{x \rightarrow -3} \frac{ x^2+4x-4 }{ x-3 }$ 10. Copythat Group Title You could try factoring out the x. x(x+4)-4 11. micahwood50 Group Title I don't see why you have to factor the numerator. All you have to do is plug -3 into x. 12. burhan101 Group Title but the i get a number over x 13. micahwood50 Group Title What do you mean? Ave to do is plug -3, like this:$\frac{ (-3)^2 + 4(-3) - 4 }{ (-3) - 3 }$ 14. burhan101 Group Title yes you're right i got 7/6 15. micahwood50 Group Title
# Python - strange behaviour This topic is 1928 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic. ## Recommended Posts Hello everyone, Yesterday I got my homework from my math teacher. We are studing graphs ( f(x) = x^2 for example ) and how to visualize them( yeah I know, easy ) So she gave me the task to write a programm that will print the graph on the screen. I've chosen python because its high lvl language and I do't have exp with it. (I''m using pygame) I came to the part where I need to grab the mouse coordinates, substract them from the last mouse coords so I can get a vector represention my movement. elif event.type == MOUSEMOTION: print('--------------------') self.mousepos1 = self.mousepos2 self.mousepos1.Print() self.mousepos2.x, self.mousepos2.y = event.pos self.mousepos2.Print() self.mousemotion.Print() self.mousemotion.x = self.mousepos2.x - self.mousepos1.x self.mousemotion.y = self.mousepos2.y - self.mousepos1.y self.mousemotion.Print() Sorry for the possibly dumb question but why the hell this prints something like: -------------------- [ 614 , 258 ] [ 625 , 212 ] [ 0 , 0 ] [ 0 , 0 ] NOTE: I was using functions for +, -, * , /, however I put everything here because I have no idea why it is behaving this way(I assumed the functions may be the problem, but it isn't) EDIT: I'll post the whole code if requiredq just ask - its only 100 lines. I'm using python ver 3.2.2 Edited by Nickie ##### Share on other sites NEVERMIND! I've been using something like C's references. Fixed!
Tag Info Refers to the conversion of electric power by using solid state components such as semiconductors. Can also generally apply to the field of electrical engineering which works with power electronics. Power Electronics deals with the transformation of power to suit a needed purpose. Applications include switch-mode power supply design and motor drives. Some assorted books on the subject: Power Electronics: Converters, Applications, and Design Mohan et al. (Considered a standard undergrad power electronics textbook in the US.) Transformer and Inductor Design Handbook McLyman Switching Power Supply Design Pressman Switchmode Power Supply Handbook Billings Switching Power Supply Design and Optimization Maniktala
#### MATH 1711 ##### Midterm 2 - Practice | Fall '15| Barone True or False questions. (a) The matrix $\left[ \begin{array}{c c c | c} 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 0 \end{array} \right]$ corresponds to a system of linear equations with unique soln $x=y=z=0$. (b) Given two mutually exclusive events $E$ and $F$, we have $P(E \; \text{or} \; F)$=$P(E)+P(F)$. (c) If $E$ and $F$ are independent, events then $P(E \; \text{and} \; F)=P(E)\cdot P(F/E)$ T (d) If $I$ is the $3 \times 3$ identify matrix and $A$ is any $3*3$ matrix, then $AI=IA$. (e) Roll a die and record the number and let $E$ and $F$ be the following events $E={ 2,4,6 }$ and $F={ 1,3,5 }$. Then the events $E$ and $F$ are independent. 2. Find the matrix product of $AB$and $BA$ if 3. Solve the system of linear equations with augmented matrix $A$ given below. Use elementary row operations to obtain the rref(reduced row echelon from)of $A$ and be precise in your answer. you should assume that the column that the column variables are $x,y,z$ in the usual order. 4. Consider an experiment where two fair dice are rolled and the sum of the two numbers are recorded. Let $X$ be the sum of the two nembers which appear face up on the dice. Find the expected calue and variance of $X$. 5. Suppose four fair die are rolled. What is the probability that at least one of the die shows either a 1 or a 2? 7. Let $X$ be a normally distributed continous random variable withand
# Quadratic equation in a graph The question is why does the line with equation ax+by+c=0 has a negative slop is wrong? I get a and b<0 by -b/2a , is it correct to proof the values in this way? However, when I try to calculate its slope by -a/b, it is a negative slope. I have no idea why the above statement is wrong. Can anyone please teach me? Thank you]1 • I get a and b<0 by -b/2a Could you explain that step by step. Think you've got a sign wrong. – dxiv Dec 4 '16 at 4:12 • If you have a and b smaller than 0, when calculating slope by -a/b the slope will definitely be negative. This is my idea – Estudiantekriss Dec 4 '16 at 4:30 • Question was how did you get a and b smaller than 0 in the first place. – dxiv Dec 4 '16 at 4:32 $a<0$ because of downward parabola. $\frac{-2b}{2a}>0 \implies b>0$ by the $X$ co-ordinate of vertex. Now figure out the sign of slope of the straight line. P.S. : You don't actually need sign of $a$ to figure out the sign of slope.
Mobile QR Code 1. (Department of Electronics Engineering and Department of BIT Medical Convergence, Kangwon National University, Chuncheon 24341, Korea ) Bluetooth low energy, current-bleeding circuit, current-reuse, IoT, I/Q mixer, gain and phase mismatch, low-IF receiver, low-voltage, quadrature generator, quadrature transconductor ## I. INTRODUCTION Bluetooth low energy (BLE) is a representative communication standard, that is widely utilized in Internet of Things (IoT) sensor devices. Ultra-low-power BLE transceivers for IoT applications have been actively studied and developed (1-19). Most BLE receivers (RXs) employ a low-intermediate frequency (IF) single-quadrature architecture to achieve low 1/$\textit{f}$ noise with a channel bandwidth of 1 MHz. However, low-IF RXs suffer from a so-called image problem. When the sensitivity degradation, caused by the image signal, is less than 0.3 dB, an image rejection ratio (IRR) greater than 21 dB is required from a carrier-to-image interference ratio ($\textit{C}$/$\textit{I}$$_{\mathrm{Image}}) of {-}9 dB (17,20). In general, quadrature signals for single-quadrature mixing are generated by a quadrature voltage-controlled oscillator or divide-by-two circuit in the local oscillator (LO) path (1-12). Recently, owing to less restrictive IRR requirements, numerous studies on BLE RXs, whose quadrature signals are provided by a quadrature low-noise amplifier (LNA) or a quadrature mixer in the RF path or quadrature LO buffer in the LO path, have been published (15-18,21). In these studies, the quadrature LNA and mixer have a lower voltage gain and degraded noise figure (NF) instead of providing quadrature signals without additional power consumption. Moreover, in terms of the RX sensitivity, it is more advantageous that the quadrature mixer provides the quadrature signals rather than the quadrature LNA. Kwon \textit{et al.} introduced the in-phase/quadrature (I/Q) down-conversion active mixer to generate quadrature signals (21). The quadrature mixer employs a common-source (CS) amplifier with capacitive degeneration and a compensating resistor. In addition, a current-bleeding circuit is used to reduce the 1/\textit{f} noise of the switching stage. If the current consumed by the current-bleeding circuit can be reused to boost the overall transconductance (\textit{g}$$_{\mathrm{m}}$) and generate quadrature signals, the performances of the I/Q mixer can be improved. Fig. 1. (a) Conventional I/Q mixer architecture with quadrature transconductor (21), (b) proposed I/Q mixer architecture with current-reused quadrature transconductor. ##### (6) $\omega_{c}=\frac{1}{\sqrt{\left(2 L_{g}+L_{S}\right) C_{T}}}$ and $\textit{Z}$$_{\mathrm{IN}} = \textit{g}$$_{\mathrm{m}}$$\textit{L}$$_{\mathrm{S}}$/2$\textit{C}$$_{\mathrm{T}} = 50 Ω. The voltage gain of the proposed push-pull LNA from the voltage source \textit{V}$$_{\mathrm{S}}$ with source resistance $\textit{r}$$_{\mathrm{S}} to \textit{V}$$_{\mathrm{OUT}}$ can be expressed as ##### (7) $A_{V L N A}=\frac{V_{O U T}}{V_{S}}=2 Q_{I N} g_{m} Z_{O U T}$ Fig. 5. Schematic of the I/Q down-conversion active mixer using the proposed current-reused quadrature transconductor. Fig. 6. Simulated gain and phase mismatches of the I/Q mixer. Here, $\textit{Q}$$_{\mathrm{IN}} is the \textit{Q}-factor of the input impedance network, and \textit{Z}$$_{\mathrm{OUT}}$ denotes the output impedance of the LNA, whose values are given approximately as ##### (8) $Q_{I N}=\frac{1}{4 R_{S} \omega C_{T}}$ ##### (9) $Z_{\text {OUT }} \approx \frac{1}{s C_{N, M \text { ixer }}}\left\|\frac{r_{O}}{2}\right\| R_{B 3}$ ##### (10) $F_{L N A}=1+\frac{V_{M N 1}^{2}+V_{M P 1}^{2}}{4 k T R_{S} A_{V L M A}^{2}}=1+\frac{\gamma}{8 Q_{N N}^{2} g_{m} R_{S}}$ where $\textit{V}$$^{2}$$_{\mathrm{MN1}}$ and $\textit{V}$$^{2}$$_{\mathrm{MP1}}$ represent the output-referred noise voltages generated by $\textit{M}$$_{\mathrm{N1}} and \textit{M}$$_{\mathrm{P1}}$, and ${\gamma}$ denotes the noise parameter of the transistor. The proposed LNA halves the excess noise factor because its total output-referred noise power is the sum of the noise powers generated by $\textit{M}$$_{\mathrm{N1}} and \textit{M}$$_{\mathrm{P1}}$, and its total voltage gain is the sum of the voltage gains provided by $\textit{M}$$_{\mathrm{N1}} and \textit{M}$$_{\mathrm{P1}}$. Therefore, compared to a conventional CS LNA with inductive source degeneration and additional $\textit{C}$$_{\mathrm{EX}}, the proposed current-reused push-pull LNA with inductive source degeneration can achieve a larger voltage gain and lower noise performance. Fig. 5 shows the I/Q down-conversion active mixer using the proposed current-reused quadrature transconductor. The current-bleeding circuit reduces the 1/\textit{f} noise of the switching stage, performs voltage-to-current conversion, and generates quadrature signals. Therefore, it can enhance the conversion gain and NF. In high frequencies, the parasitic capacitances of main transistors in the current-reused quadrature transconductor (\textit{M}$$_{\mathrm{N1}}$, $\textit{M}$$_{\mathrm{N2}}, \textit{M}$$_{\mathrm{P1}}$, and $\textit{M}$$_{P2}) can cause gain and phase mismatches. To compensate for both mismatches and increase the design degree of freedom, compensating resistors of \textit{r}$$_{\mathrm{N}}$ and \textit{r}_{\mathrm{P}} are added (21). Fig. 6 shows the simulated gain and phase mismatches of the proposed I/Q mixer. As shown in Fig. 6, there is little difference in the BLE band. The proposed I/Q mixer can provide quadrature signals with gain and phase mismatches of less than 0.15 dB and 0.65^{\circ} in the BLE band, respectively. These values are sufficient to provide an IRR of more than 21 dB. The I-path conversion gain of the proposed I/Q mixer can be expressed as ##### (11) A_{V M \text { axer }}=\frac{V_{\text {OUTI }}}{V_{I N}}=\frac{\sqrt{2}}{\pi} g_{m T}\left(R_{L} \| \frac{1}{s C_{L}}\right) The I-path noise factor of the proposed I/Q mixer can be expressed as ##### (12) \begin{aligned} F_{\text {Mxxer }} &=1+\frac{V_{M N}^{2}+V_{M P 1}^{2}+2 V_{M N 3}^{2}+2 V_{M P 3}^{2}+2 V_{R L}^{2}}{4 k T R_{S} A_{V M \times e r}^{2}} \\ & \approx 1+\frac{\pi^{2}}{R_{S}}\left(\frac{\gamma}{4 g_{m T}}+\frac{2 \gamma I_{B}}{g_{m T}^{2} \pi A}+\frac{2 \gamma g_{m P 3}}{g_{m T}^{2}}+\frac{1}{g_{m T}^{2} R_{L}}\right) \end{aligned} where \textit{V}^{2}$$_{\mathrm{MN1}}, \textit{V}$$^{2}$$_{\mathrm{MP1}}, \textit{V}$$^{2}$$_{\mathrm{MN3}}, \textit{V}$$^{2}$$_{\mathrm{MP3}} and \textit{V}$$_{RL} represent the output-referred noise voltages generated by $\textit{M}$$_{\mathrm{N1}}, \textit{M}$$_{\mathrm{P1}}$, $\textit{M}$$_{\mathrm{N3}}, \textit{M}$$_{\mathrm{P3}}$, and $\textit{r}$$_{\mathrm{L}}, respectively, \textit{I}$$_{\mathrm{B}}$ denotes the dc current flowing into $\textit{M}$$_{\mathrm{N3,4}} of the switching stage, and \textit{A} denotes the amplitude of the LO signal. In \textit{f}$$_{\mathrm{Mixer}}$, the switching noises of $\textit{M}$$_{\mathrm{N3}} and \textit{M}$$_{\mathrm{N4}}$ are the dominant noise contributions. Because the proposed I/Q mixer with the current-reused quadrature transconductor enhances the overall transconductance, it has a smaller noise factor compared to that of the conventional quadrature transconductor. Table 1. Power breakdown of the BLE RX front-end Block Current Power LNA 0.4 mA 0.4 mW I/Q mixer 0.6 mA 0.6 mW Total 1 mA 1 mW Fig. 7. Layout of the proposed BLE RX front-end. ## IV. CONCLUSIONS In this study, a 2.4 GHz low-power low-IF BLE RX front-end employing the new I/Q down-conversion active mixer with the current-reused quadrature transconductor was designed in a 65 nm CMOS technology. The quadrature signals required for single-quadrature mixing were generated at the transcondcutor of the I/Q mixer to reduce the power consumption and NF. The proposed current-reused current-bleeding circuit of the I/Q mixer improved the overall transconductance of the mixer, provided quadrature signals, and reduced the 1/$\textit{f}$ noise of the switching stage. The designed BLE RX front-end obtained a conversion gain of 37.6 dB, NF of 3.3 dB, and IIP3 of -22.73 dBm. ### ACKNOWLEDGMENTS This work was supported in part by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education under Grant NRF-2018R1D1A1B07042804 and in part by the Ministry of Science and ICT, Korea, under the Information Technology Research Center Support Program supervised by the Institute for Information and Communications Technology Promotion (IITP) under Grant IITP-2021-2018-0-01433. The chip fabrication and EDA tool were supported by the IC Design Education Center (IDEC), Korea. ### REFERENCES 1 Lin Z., Mak P., Martins R. P., June 2014, A 2.4 GHz ZigBee receiver exploiting an RF-to-BB-current-reuse blixer + hybrid filter topology in 65 nm CMOS, IEEE J. Solid-State Circuits, Vol. 49, No. 6, pp. 1333-1344 2 Lin Z., Mak P., Martins R. P., Dec 2014, A Sub-GHz multi-ISM-band ZigBee receiver using function-reuse and gain-boosted N-path techniques for IoT applications, IEEE J. Solid-State Circuits, Vol. 49, No. 12, pp. 2990-3004 3 Ramella M., Fabiano I., Manstretta D., Castello R., Sep 2017, A SAW-Less 2.4-GHz receiver front-end with 2.4-mA battery current for SoC coexistence, IEEE J. of Solid-State Circuits, Vol. 52, pp. 2292-2305 4 Kim S., Kwon K., Sep 2019, A low-power RF-to-BB-current-reuse receiver employing simultaneous noise and input matching and 1/f noise reduction for IoT applications, IEEE Microw. Wireless Compon. Lett., Vol. 29, No. 9, pp. 614-616 5 Lee S., Jeong D., Kim B., May 2018, Ultralow-power 2.4-GHz receiver with all passive sliding-IF mixer, IEEE Trans. Microw. Theory Tech., Vol. 66, No. 5, pp. 2356-2362 6 Thijssen B. J., Klumperink E. A. M., Quinlan P., Nauta B., pp 466-468, A 370 µW 5.5dB-NF BLE/BT5.0/IEEE 802.15.4-compliant receiver with > 63dB adjacent channel rejection at >2 channels offset in 22nm FDSOI, in IEEE Int. Solid-State Circuits Conf. Tech. Dig., San Francisco, CA 7 Wang K., Qiu L., Koo J., Ruby R., Otis B., June 2018, Design of 1.8-mW PLL-free 2.4-GHz receiver utilizing temperature-compensated FBAR resonator, IEEE J. Solid-State Circuits, Vol. 53, No. 6, pp. 1628-1639 8 Kargaran E., Bryant C., Manstretta D., Strange J., Castello R., 2019, A Sub-0.6V, 330 µW, 0.15 mm$^{2}$ Receiver Front-End for Bluetooth Low Energy (BLE) in 22 nm FD-SOI with Zero External Components, in 2019 IEEE Asian Solid-State Circuits Conference (A-SSCC), Vol. macau, No. macao, pp. 169-172 9 Shirazi A. H. M., Lavasani H. M., Sharifzadeh M., Rajavi Y., Mirabbasi S., Taghivand M., TX, A 980μW 5.2dB-NF current-reused direct-conversion bluetooth-low-energy receiver in 40nm CMOS, in 2017 IEEE Custom Integrated Circuits Conference (CICC), Austin, pp. 1-4 10 Zhang F., Miyahara Y., Otis B. P., Dec 2013, Design of a 300-mV 2.4-GHz receiver using transformer-coupled techniques, IEEE J. Solid-State Circuits, Vol. 48, No. 12, pp. 3190-3205 11 Kargaran E., Guo B., Manstretta D., Castello R., April 2019, A sub-1V, 350-µW, 6.5-dB integrated NF low-IF receiver front-end for IoT in 28-nm CMOS, IEEE Solid-State Circuits Lett., Vol. 2, No. 4, pp. 29-32 12 Liu Y., Purushothaman V. K., Bachmann C., Staszewski R. B., March 2019, Design and analysis of a DCO-based phase-tracking RF receiver for IoT applications, IEEE J. Solid-State Circuits, Vol. 54, No. 3, pp. 785-795 13 Song E., Park B., Kwon K., July 2021., 2.4 GHz low-power low-IF receiver with a quadrature local oscillator buffer for Bluetooth low energy applications, IEEE Trans. Circuits Syst. II, Express Briefs, Vol. 68, No. 7, pp. 2369-2373 14 Silva-Pereira M., de Sousa J. T., Costa Freire J., Caldinhas Vaz J., Jan 2019, A 1.7-mW −92-dBm sensitivity low-IF receiver in 0.13-μm CMOS for Bluetooth LE applications, IEEE Trans. Microw. Theory Tech., Vol. 67, No. 1, pp. 332-346 15 Tedeschi M., Liscidini A., Castello R., Sep 2010, Low-power quadrature receivers for ZigBee (IEEE 802.15.4) applications, IEEE J. Solid-State Circuits, Vol. 45, No. 9, pp. 1710-1719 16 Selvakumar A., Zargham M., Liscidini A., Dec 2015, Sub-mW current re-use receiver front-end for wireless sensor network applications, IEEE J. Solid-State Circuits, Vol. 50, No. 12, pp. 2965-2974 17 Park B., Kwon K., March 2021, 2.4-GHz Bluetooth low energy receiver employing new quadrature low-noise amplifier for low-power low-voltage IoT applications, IEEE Trans. Microw. Theory Tech., Vol. 69, No. 3, pp. 1887-1895 18 Park B., Kwon K., April 2021, 2.4 GHz BLE receiver with power-efficient quadrature RF-to-baseband-current-reuse architecture for low-power IoT applications, IEEE ACCESS, Vol. 9, No. 4, pp. 62734-62744 19 Park , Kwon K., Oct 2020, A 2.4-GHz low-power Low-IF receiver employing a quadrature low-noise amplifier for Bluetooth low energy applications, J. Semicond. Technol. Sci., Vol. 20, No. 5, pp. 415-422 20 Dec. 2016, Bluetooth Specification; version 5.0; vol.6 (Low Energy Controller); Part A, Bluetooth SIG 21 Kwon K., Nov 2010, A 5.8 GHz integrated CMOS dedicated short range communication transceiver for the Korea/Japan electronic toll collection system, IEEE Trans. Microw. Theory Tech., Vol. 58, No. 11, pp. 2751-2763 ## Author ##### Yoonji Park Sengjun Jo is currently studying integrated B. S. and M. S. program in Department of Electronics Engi-neering, Kangwon National Univer-sity, Chuncheon, Korea. His research interests include CMOS mmWave/ RF/analog integrated circuits and RF system design for wireless communications. ##### Ji-Hoon Kim Hyeonjun Kim is currently studying integrated B. S. and M. S. program in Department of Electronics Engi-neering, Kangwon National Univer-sity, Chuncheon, Korea. His research interests include CMOS mmWave/ RF/analog integrated circuits and RF system design for wireless communications. ##### Ji-Hoon Kim Kuduck Kwon received the B.S. and Ph.D. degrees in Electrical Engi-neering and Computer Science from Korea Advanced Institute of Science and Technology (KAIST), in Daejeon, Korea, in 2004 and 2009, respectively. His doctoral research concerned digital TV tuners and dedicated short-range communication (DSRC) systems. From 2009 to 2010, he was a Post-Doctoral Researcher with KAIST, where he studied a surface acoustic wave (SAW)-less receiver and developed RF transceivers for DSRC applications. From 2010 to 2014, he was a Senior Engineer with Samsung Electronics Co. LTD., Suwon, Korea, where he was involved in studying software-defined receiver and developing silicon tuner and cellular RFICs. In 2014, he joined the Department of Electronics Engineering, Kangwon National University, Chuncheon, Korea, where he is currently an Associate Professor. His research interests include CMOS mmWave/RF/analog integrated circuits and RF system design for wireless communications.
Fault Calculation - Per Unit System By on Symbol   Definition - per unit method current base - per unit method power base - per unit method voltage base - per unit method admittance base - per unit method impedance base - percentage impedance - per unit impedance - actual impedance - per unit base impedance Per unit fault calculations is a method whereby system impedances and quantities are normalised across different voltage levels to a common base.  By removing the impact of varying voltages, the necessary calculations are simplified. To use the per unit method, we normalise all the system impedances (and admittances) within the network under consideration to a common base.  These normalised impedances are know as per unit impedances.  Any per unit impedance will have the same value on both the primary and secondary of a transformer and is independent of voltage level. A network of per unit impedances can then be solved using standard network analysis (see the example).  From this fault level can be readily determined. In applying the per unit method, the first step is to select an arbitrary voltage (Vbase) and power (Pbase) base. Tip: while the base power and voltage be any value, typically it would make sense to select values related to the system under construction (for example 11 kV and 20 MVA may be appropriate for a distribution type system) Per Unit Method Having selected a base power and voltage, the base per unit values of impedance, admittance and current can be calculated from: Per Unit Single Phase Three Phase Dividing a system element by it’s per-unit base value gives the per-unit value of the element, for example Some times per-unit values are available for a given base kV, but the problem being solved is using a different base.  In this instance it is possible to convert the unit: Fault calculation problems typically deal wit power sources, generators, transformers and system impedances.  Per-unit values for these elements can be quickly derived from: Element Per-Unit Value Source impedance Generators Transformers Impedances , where V is in kV Example - calculating per unit values Consider a system of source impedance 4.48 Ω connected to a 20 MVA transformer (11/0.4 kV) at 6% impedance.  We want to find the fault level at the transformer secondary. Selecting Pbase as 20 MVA and Vbase as 11 kV and using the above equations: and the Line-Neutral voltage on the secondary of the transformer is 0.4/√3 = 0.230 kV, giving: Three Phase Fault Example Three Phase Fault Example Per unit analysis can be used to calculate system three phase fault levels and the current distributions.  To gain a better understanding, it is worth running through the typical steps required to solve a fault calculation problem. Given the system single line diagram, construct and simplify the per unit impedance diagram. The fault level at the point under consideration is given by: Where Zpu, is the total impedance between the source and the fault. Fault flow through parallel branches is given by the ratio of impedances. As illustrated this can enable fault flows to be found through each branch. Having calculated the fault flow in each branch, it is then relatively simple to find the current distribution using: where: Related Notes More interesting Notes: Steven has over twenty five years experience working on some of the largest construction projects. He has a deep technical understanding of electrical engineering and is keen to share this knowledge. About the author myElectrical Engineering 1. FELIX JR. says: 5/21/2013 7:52 AM greetings !, hello ! this article which you have shared is a good explanation for short circuit current calculations using the P.U. Method based on a given kVA base, as this is the old school way (i.e. during my college days and my early prof. work with my employer). But how do you find and comment on the IEC-60909 way of using the ohmic method and also that of the MVA method, alternative ? So, which of the three (3) are more easy to use and accurate ? felix jr. 2. gilly1 says: 5/29/2013 6:41 PM Just wondering which method do you think the most accurate for calculating single phase-earth faults, the Ohmic Method or Symmetrical Component Method. The Symm. Comp. method is quite complex and while a lot of people use it to solve complex types of unbalanced faults it is not real in the sense that there aren't really 3 currents flowing at once : Pos, Neg and Zero sequence currents, whereas the Ohmic Method is based in reality with real impedances??? 3. Steven says: 5/30/2013 3:03 AM My opinion is that symmetrical components would be more accurate (especially for any unbalanced faults like phase to earth). If your looking for more practical guidance on using symmetrical components, then I would reefer to IEC 60909. This standard is also implemented in many software programs. 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# Thread: Image set of a function? 1. ## Image set of a function? How do u find the image set for a function with no domain? 2. ## Re: Image set of a function? you don't. a function without a domain is an empty function, with a "blank" graph. put it this way, how many pairs (x,f(x)) can occur in such a function, when there is no possible "first coordinate"? 3. ## Re: Image set of a function? I thought it was the lowest possible value for y and the highest possible vaule foe y?? 4. ## Re: Image set of a function? Originally Posted by Orlando How do u find the image set for a function with no domain? Please show us what you mean by "a function with no domain". At least, describe it in detail. 5. ## Re: Image set of a function? Sorry I am tring to find the image set of : f(x)=1/4(x-1)^2 -9 In interval notation. There is no domain given so I persume the answear would be [-9, to infinity) Sorry don`t know how to us the symbol for infinity Or am I completly of the mark 6. ## Re: Image set of a function? Originally Posted by Orlando f(x)={1/4(x-1)^2} -9 In interval notation. Assuming that the function is $f(x)=\frac{1}{4(x-1)^2}-9$ then the domain is all $x\ne 1$. The range is $(-9,\infty)$. Because $f(x)\ne -9$ for any $x$. 7. ## Re: Image set of a function? sorry the function is 1/4*(x-1)^2-9 sorry for how I have presented it still trying to get use to typing maths in a computer 8. ## Re: Image set of a function? Then that has "natural domain" of all real numbers. It's graph is a parabola with vertex at (1, 9), vertical axis, opening upward. If a function is given without an explicit domain, unless stated to the contrary, the domain is taken to be the "natural domain"- the set of all real numbers for which it is possible to calculate the value. The natural domain of a polynomial is all real numbers. The natural domain of [1/(4(x-1)^2]- 9] is all real number except x= 1. That is because x= 1 would make the denominator of that fraction 0. 9. ## Re: Image set of a function? Originally Posted by Orlando sorry the function is [TEX]f(x)=\frac{1/4}(x-1)^2-9[TEX] Is the function $f(x)=\frac{1}{4}(x-1)^2-9~???$ 10. ## Re: Image set of a function? yes it is. Sorry for messing everyone about still getting my head round La Tex 11. ## Re: Image set of a function? Originally Posted by Orlando yes it is. Sorry for messing everyone about still getting my head round La Tex Then the domain is $\mathbb{R}$ and range $[-9,\infty)$ 12. ## Re: Image set of a function? Thanks for everyones help. Going to learn how to use La Tex looks a great bit of software.
# Tag Info 4 The master theorem isn't a good theorem to apply in this case, it's power comes from situations where the input size is reduced by a constant fraction (not decreased by a constant amount). In this case, $$T(n)=T(n-10)+n.$$ Then, $$T(n-10)=T(n-20)+(n-10)$$ Similarly, $$T(n-20)=T(n-30)+(n-20).$$ Therefore, $$... 2 You have proved that the limit exists, so let's set$$b:=\lim_{n\to\infty}b_n.$$Given the recurrence relation b_{n+1}^2=2+b_n we can take limits on both sides to find$$\lim_{n\to\infty}b_{n+1}^2=\lim_{n\to\infty}(2+b_n)=2+\lim_{n\to\infty}b_n=2+b.$$Now on the left-hand side we have ... 2 Michael Burr's answer was first and is correct. Here is another way of explaining it using the technique of telescoping series. For every n \in \{0, 1, 2, 3, \ldots\} we have:$$ T(n) - T(n-10) = n Fix an integer k \geq 1. Writing this equation for n\in\{10, 20, 30, ..., 10k\} gives: \begin{align} &\underbrace{T(10)}-T(0) &= 10\\ ... 2 Of course, no deterministic algorithm can generate truly random numbers. The goal is to find an algorithm that gives output values that 'behave as if' they are independent and identically distributed according to some distribution--usually Unif(0, 1). By 'behave as if' one means that the pseudo-random numbers pass a large battery of benchmark tests for ... 1 Shift indices to get: b_{n + 2} = 2 b_{n + 1} + b_n $$Define the generating function:$$ B(z) = \sum_{n \ge 0} b_n z^n $$Multiply the recurrence by z^n, sum over n \ge 0 and recognize the resulting sums:$$ \frac{B(z) - b_0 - b_1 z}{z^2} = 2 \frac{B(z) - b_0}{z} + B(z) As partial fractions: \begin{align} B(z) &= \frac{2z}{1 - 2 z ... 1 Let us assume WLOG thatn\equiv 1 \pmod{10}$, i.e.$n=10k+1$for some nonnegative integer$k$. Then if$k\geqslant 1, \begin{align} T(n) &= \sum_{j=0}^k T(10(k-j)+1) + 10(k-j)\\ &= T(1) + \sum_{j=0}^k 10(k-j)\\ &= T(1) + 10\sum_{j=1}^k j\\ &= T(1) + 5k(k+1)\\ &= T(1) + 5\left(\frac{n-1}{10}\right)\left(\frac{n}{10}\right)\\ &= T(1) ... 1 Let me explain why it is impossible to inscribe a regular pentagon into a regular hexagon in the way you want. Let's suppose that the sideAB$of the hexagon contaning no pentagon vertex is parallel to side$GH$of the pentagon (see picture). I'll take hexagon sides of unit length and set$x=AH$so that$GH=1+x$and$FH=1-x$. We can determine$x$so that ... 1 A proof goes by using generating functions. Define$A(z) = \sum_{n \ge 0} a_n z^n$, and take your recurrence with initial values$a_0$through$a_{k - 1}$. Shift indices to get:$\begin{align} a_{n + k} = c_1 a_{n + k - 1} + \dotsb + c_k a_n \end{align}$Multiply by$z^n$, sum over$n \ge 0$and get:$\begin{align} \sum_{n \ge 0} a_{n + k} z^n = c_1 ... 1 You aren't doing the induction correctly it should be T(n+1)=n+1 +2kn/2=(k+1)n+1 which is not less than kn Correct proof T(2) = 1 T(n) = n + 2T(n/2) T(n) <= k n lg(n) T(n+1) = n+ 2 (kn/2 lg(n/2)) = n + kn lg(n/2) < kn lg(n) 1 Denote $A(n)=\sqrt{T(n)}$ and solve for A formula. For example try to find in $A(n) = \lambda^{n}$ form. 1 You first prove that the right-shift operator $R$ is a linear operator on (doubly infinite) sequences. Then you define addition and scalar multiplication on operators so that you can given a sequence $f$ obeys a recurrence relation rewrite the recurrence relation as $(P(R))(f) = 0$ for some polynomial $P$, which is the characteristic polynomial. Now $P(R)$ ... 1 For the record, generating functions solve this type of problems in uniform way. Define $A(z) = \sum_{n \ge 0} a_n z^n$; take your recurrence, multiply by $z^n$ and add over $n \ge 0$: \$\begin{align} \sum_{n \ge 0} a_{n + 2} z^n + 2 \sum_{n \ge 0} a_{n + 1} z^n - 3 \sum_{n \ge 0} a_n z^n &= \sum_{n \ge 0} n z^n + \sum_{n \ge 0} (-1)^n n 3^n ... Only top voted, non community-wiki answers of a minimum length are eligible
# COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS ### What is the Coefficient of Thermal Expansion? - Matmatch The coefficient of thermal expansion (CTE) refers to the rate at which a material expands with increase in temperature.More specifically,this coefficient is determined at constant pressure and without a phase change,i.e.the material is expected to still be in its solid or fluid form..Different materials have different CTEs,which make them suited for the particular use they are selected for.What is the Coefficient of Thermal Expansion? - MatmatchThe coefficient of thermal expansion (CTE) refers to the rate at which a material expands with increase in temperature.More specifically,this coefficient is determined at constant pressure and without a phase change,i.e.the material is expected to still be in its solid or fluid form..Different materials have different CTEs,which make them suited for the particular use they are selected for.Tungsten - Thermal Expansion CoefficientFor these materials,the area and volumetric thermal expansion coefficient are,respectively,approximately twice and three times larger than the linear thermal expansion coefficient ( V = 3 L).If it is not isometric,there may be different expansion coefficients for different crystallographic directions,and the crystal will change shape ### Thermal expansion physics Britannica Thermal expansion,the general increase in the volume of a material as its temperature is increased.It is usually expressed as a fractional change in length or volume per unit temperature change; a linear expansion coefficient is usually employed in describing the expansion of a solid,while a volume expansion coefficient is more useful for a liquid or a gas.Thermal expansion behavior of various aromatic polyimides The thermal expansion behavior for various aromatic polymides was investigated.Usally polymers,including polyimides,have high thermal expansion coefficients (36 COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#215; 10 5 K 1),compared with metals and ceramics.However,there are some polyimides which have very low thermal expansion coefficients below 1 COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#215; 10 5 K 1.This property was observed for the polymides obtained from Thermal Expansion of Stainless Steels Part One : Total The coefficient of linear thermal expansion (CTE,CLTE,,or 1) is a material property that is indicative of the extent to which a material expands upon heating.Different substances expand by different amounts.Over small temperature ranges,the thermal expansion of uniform linear objects is proportional to temperature change. ### Thermal Expansion of Solids and Liquids Physics Linear thermal expansion is L = LT,where L is the change in length L,T is the change in temperature,and is the coefficient of linear expansion,which varies slightly with temperature.The change in area due to thermal expansion is A = 2 A T ,where A is the change in area.Thermal Expansion of Solids and Liquids PhysicsLinear thermal expansion is L = LT,where L is the change in length L,T is the change in temperature,and is the coefficient of linear expansion,which varies slightly with temperature.The change in area due to thermal expansion is A = 2 A T ,where A is the change in area.Thermal Expansion of Metals - Engineering ToolBoxThe linear thermal expansion coefficient is the ratio c hange in length per degree temperature to length.Linear thermal expansion for some common metals T (oC) = 5/9 [T (oF) - 32] 1 in (inch) = 25.4 mm ### Thermal Expansion and the Coefficient of Thermal Expansion sess different coefficients of thermal expansion,due to which their expansion with a rise in temperature is different.The strips bend since the expansion or contraction of the materials used is not similar.This concept is utilized in measurement of temperature.Automobile Engine Coolant.Thermal Expansion Examples and ApplicationsJun 22,2020 COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#0183;Applications of Thermal Expansion in everyday life.Thermal expansion is used in our daily life.Thermometers.In thermometers,thermal expansion is used in temperature measurements.Removing tight lids.To open the cap of a bottle that is tight enough,immerse in it hot water for a minute or so.Metal cap expands and becomes loose.Thermal Expansion Calculator - calculate linear or The formula for volumetric thermal expansion of a solid object used in the calculator is where V is the change in volume,cV is the coefficient of volumetric thermal expansion of the material in K -1 (3 times the coefficient of linear thermal expansion),Vinit is the initial volume and T is ### Thermal Expansion Calculator - Good Calculators Thermal expansion refers to the way in which any given substance (either gas,liquid,or solid) will undergo modifications of shape (either volume,area,or length) as temperatures vary.Thermal expansion is caused by particles expanding or contracting within particular substances according to different temperatures.There are three forms of Thermal Expansion Calculator - Good CalculatorsThermal expansion refers to the way in which any given substance (either gas,liquid,or solid) will undergo modifications of shape (either volume,area,or length) as temperatures vary.Thermal expansion is caused by particles expanding or contracting within particular substances according to different temperatures.There are three forms of THERMAL EXPANSION OF COMPOSITE LAMINATESThermal expansion coefficients [1] Thermal expansion [1/ COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#176;C] Steel Carbon fibre Epoxy resin 1 16E-6 -0.6E-6 55E-6 2 16E-6 8.5E-6 55E-6 As it can be noticed from Table 1,the steel has a larger thermal expansion coefficient than the fibre but lower than the matrix.Moreover,the fibre is actually contracts at high temperature,having a ### People also askHow to calculate thermal expansion?How to calculate thermal expansion?How to calculate thermal expansion Linear thermal expansion.Linear thermal expansion applies mostly to solids. The change in length is directly Areal thermal expansion.Thermal expansion also applies to surfaces.Imagine a sheet of metal with a defined area.If Volumetric thermal expansion.Thermal expansion causes variations in volume for solids and liquids More How to calculate thermal expansion - x-engineerPRODUCTLINEAR TEMPERATURE EXPANSION COEFFICABS (Acrylonitrile butadiene styrene) thermoplastic72 - 108ABS -glass fiber-reinforced31Acetal - glass fiber-reinforced39Acetals85 - 110 196 rows on engineeringtoolboxCoefficient of Thermal Expansion - Repair Engineering 69 rows COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#0183;A Coefficient of Thermal Expansion,typically represented by the symbol,is a measure ofMETAL OR ALLOY GMATERIAL DESIGNACOEFFICIENT OF EXCOEFFICIENT OF EXPure MetalsTungsten4.52.5Pure MetalsMolybdenum4.82.7Pure MetalsChromium4.92.7Pure MetalsZirconium5.73.2 69 rows on repairengineeringList of Thermal Expansion Coefficients (CTE) for Natural 211 rows COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#0183;Choose professional Dilatometry and Thermal Expansion Coefficient (CTE) Testing ### MATERIALSLINEAR THERMAL EXPANSION COEFFICIENT ABS (Acrylonitrile butadiene styrene) thermoplastic73.8ABS -glass fiber-reinforced30.4Acetals106.5Acetal - glass fiber-reinforced39.4 211 rows on msesuppliesLinear Thermal Expansion Coefficient for Metals Linear thermal expansion coefficient is defined as material's fractional change in length divided by the change in temperature.Coefficient of linear thermal expansion is designated by the symbol (alpha).The SI unit of thermal expansion coefficient is ( COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#176;C)-1and U.S.customary unit is ( COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#176;F)-1.Linear Thermal Expansion Coefficient of SteelLinear thermal expansion coefficients of various steels are given in the following chart.Room Temperature Linear Thermal Expansion Coefficient Values for Steels Material Temp.Coef.of Thermal Expansion (CTE) 10-6 ( COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#176;C)-1 10-6 ( COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#176;F)-1 Plain Carbon and Low Alloy Steels AISI 1010,Annealed 0-100 COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#176;C / 32-212 COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#176;F:Linear Coefficient of Thermal Expansion - nde-edThe phenomena of thermal expansion can be challenging when designing bridges,buildings,aircraft and spacecraft,but it can be put to beneficial uses.For example,thermostats and other heat-sensitive sensors make use of the property of linear expansion.Linear Coefficient of Thermal Expansion for a Few Common Materials ### How to calculate thermal expansion x-engineer Linear thermal expansion applies mostly to solids.Knowing the initial length L 0 [m] of a given solid (e.g.metal rod),the temperature difference T [ COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#186;C] and the coefficient of linear expansion of the solid [1/ COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#186;C],the change in length T [m] of the solid can be calculated as $\Delta L = \alpha \cdot L_0 \cdot \Delta T \tag{1}$ The change in length is directly proportional with the How to Calculate Thermal Expansion of Steel Sciencing COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#0183;Each material has a different response to the heat,which is characterized by its thermal expansion coefficient.The thermal expansion coefficient represents the amount that the material expands per each degree increase.Use a thermometer to measure the change in temperature in degrees Fahrenheit.For example,if the original temperature was 70 Heat - Thermal expansion Characteristics of Fine Expansion values vary depending on the material being heated.The coefficient ratio of thermal expansion indicates how much a material expands per 1 (2.2) rise in temperature.Fine Ceramics (also known as advanced ceramics) have low coefficients of thermal expansion less than half those of stainless steels. ### Heat - Thermal expansion Characteristics of Fine Expansion values vary depending on the material being heated.The coefficient ratio of thermal expansion indicates how much a material expands per 1 (2.2) rise in temperature.Fine Ceramics (also known as advanced ceramics) have low coefficients of thermal expansion less than half those of stainless steels.File Size 326KBPage Count 6Thermal Expansion Table of Coefficient of Thermal The coefficient of thermal expansion or CLTE,Coefficient of Linear Thermal Expansion The linear expansion of a heated solid (or liquid) is measured by = the coefficient of linear expansion,The coefficient of thermal expansion is defined such that measures the percentage change in the length of the material per degree of temperature change.Coefficients of Linear Thermal Expansion196 rows COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#0183;Thermal expansion coefficients for some common materials 10-6 m/moC = 1 m/moC ### Coefficient of Thermal Expansion Converter The coefficient of thermal expansion describes how the size of an object changes with a change in its temperature.The coefficient of thermal expansion measures the fractional change in size per degree change in temperature at a constant pressure and is expressed in 1/K or K COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#185; (reciprocal kelvin) .There are several types of coefficients of Coefficient of Thermal Expansion - an overview The coefficient of thermal expansion of an FRP composite depends upon both the fibre used and its lay-up in the matrix.The manufacturer should supply the values of the coefficient of thermal expansion for their specific composite products.Table 2.6 gives typical coefficient of thermal expansion values for certain fibre arrangements in composites.Coefficient of Thermal Expansion - an overview The coefficient of thermal expansion of an FRP composite depends upon both the fibre used and its lay-up in the matrix.The manufacturer should supply the values of the coefficient of thermal expansion for their specific composite products.Table 2.6 gives typical coefficient of thermal expansion values for certain fibre arrangements in composites. ### Coefficient of Thermal Expansion (CTE) The coefficient of thermal expansion for a material is usually specified over a temperature range because it varies depending on the temperature.The following values are given for a temperature around 20 COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#176;C.CTE is usually given in units of um/m/ COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#176;C or ppm/ COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#176;C.Coefficient of Thermal Expansion (CTE)The coefficient of thermal expansion for a material is usually specified over a temperature range because it varies depending on the temperature.The following values are given for a temperature around 20 COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#176;C.CTE is usually given in units of um/m/ COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#176;C or ppm/ COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#176;C.Coefficient of Linear Thermal Expansion (CLTE) Formula Linear Coefficient of Thermal Expansion Values of Several Plastics The Coefficient of Linear Thermal Expansion (Or Linear Coefficient of Thermal Expansion) lies between (in the service temperature range for each case) Ca.0.6 x 10-4 to 2.3 x 10-4 K-1 for most of the thermoplastics; Ca.0.2 x 10-4 to 0.6 x 10-4 K-1 for thermosets ### Coefficient of Expansion (COE) - Santa's Bling Cullet,billets,patties,and dalle - various sizes and shapes of glass chunks used primarily for casting.For the scientific world COE,or coefficient of expansion,doesn't really have to do with atomic vibrations - it's the amount that a material expands with a change in temperature relative to a standard.COEFFICIENT OF THERMAL EXPANSION FOR VARIOUSThe coefficient of thermal expansion is used to determine the rate at which a material expands as a function of temperature.CTE is used for design purposes to determine if failure by thermal stress may occur.Understanding the relative expansion/contraction characteristics of materials is important for application success.Bonding Substrates with Different Thermal Expansion One of the most difficult of all adhesive applications is the bonding of substrates with different coefficients of thermal expansion (CTE).Common examples include bonding aluminum to glass,glass to plastics,ceramic to plastics and rubbers to metals. ### results for this questionWhat is the meaning of thermal expansion?What is the meaning of thermal expansion?Thermal expansion is the tendency of matter to change its shape,area,and volume in response to a change in temperature.Thermal expansion - Wikipedia results for this questionWhat factors affect thermal expansion?What factors affect thermal expansion?Factors affecting thermal expansion.Imagine that a long,thin metal wire is heated.The wire expands.The amount by which it expands depends on three factors its original length,the temperature change,and the thermal (heat) properties of the metal itself.Some substances simply expand more easily than others.Expansion,Thermal - body,used,water,substance,change results for this questionHow do you calculate linear thermal expansion?How do you calculate linear thermal expansion?Linear Thermal Expansion is calculated using the following formula Where L = Initial Length.L = The change in Length.L = Coefficient of Linear Thermal Expansion.T = Change in temperature.Linear thermal expansion is the most common calculation used to estimate the expansion caused by a change in temperature.Reference epsilonengineer/thermal-expansion-calculator results for this questionFeedbackCoefficients of Thermal Expansion - an overview Coefficients of Thermal Expansion Coefficients of thermal expansion are reported as cm/cm/ COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#176;C or,more generally,as unit/unit/ COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#176;C or ppm/ COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS#176;C.CTEs vary with temperature and are usually reported for a temperature range.From Adhesives Technology for Electronic Applications,2005 ### Send us a Message #### Shipbuilding Steel Plate ABS/A steel,ABS AH32,LR AH36,RINA EH36. #### Alloy Steel Plate 50CrMo4,42CrMo4,12Cr1MoV,25MnTi.
# 1 1/3 • 5 3/4 pls helppp ###### Question: 1 1/3 • 5 3/4 pls helppp ### At Brown Elementary School, 80% of all fifth graders ride the bus to school. If 124 fifth graders ride the bus to school, how many fifth graders are there at the school? At Brown Elementary School, 80% of all fifth graders ride the bus to school. If 124 fifth graders ride the bus to school, how many fifth graders are there at the school?... ### Which of the following are examples of physical properties A corrosion B compressibility Cfluidity D flammability E density Freactivity Geffusion Which of the following are examples of physical properties A corrosion B compressibility Cfluidity D flammability E density Freactivity Geffusion... ### The amount of work done to produce a sound determines which property of sound waves? A. amplitude B. frequency C. pitch D. wavelength The amount of work done to produce a sound determines which property of sound waves? A. amplitude B. frequency C. pitch D. wavelength... ### PLEASE HELP!!! ILL MARK BRAINLIEST!! Match each form of IPR to the protection it affords. patent trademark copyright protects the specific expression of a creation protects signs, symbols, names, or short phrases that reveal the origin of a product or service protects the idea underlying a creation PLEASE HELP!!! ILL MARK BRAINLIEST!! Match each form of IPR to the protection it affords. patent trademark copyright protects the specific expression of a creation protects signs, symbols, names, or short phrases that reveal the origin of a product or service protects the idea underlying a creation... ### 3. A force F = 30N, east. Find 3.1. 5F 3.2. - 6F 3.3. 0.5 F​ 3. A force F = 30N, east. Find 3.1. 5F 3.2. - 6F 3.3. 0.5 F​... ### What is a similarity between the Abbasid and Umayyad islamic empires?​ what is a similarity between the Abbasid and Umayyad islamic empires?​... ### F(x)=-3x+2 PORFAVORRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR F(x)=-3x+2 PORFAVORRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR... ### Please solve 1 through 6, thanks! Please solve 1 through 6, thanks!... ### After the Battle of Gettysburg, the South ____. never again fought on Union soil. mounted one last march into the North. surrendered immediately. refused to retreat. After the Battle of Gettysburg, the South ____. never again fought on Union soil. mounted one last march into the North. surrendered immediately. refused to retreat.... ### In which stage of the energy flow does carbon move from the non living to the living environment In which stage of the energy flow does carbon move from the non living to the living environment... ### You compress 0.5 moles of a gas at constant pressure from 4 liters to 1 liter while 2625 J of heat is removed, the temperature drops by 180.4 K, and Eth drops by 1875 J. How much work energy is added to the gas? You compress 0.5 moles of a gas at constant pressure from 4 liters to 1 liter while 2625 J of heat is removed, the temperature drops by 180.4 K, and Eth drops by 1875 J. How much work energy is added to the gas?... ### ILL GIVE U BRAINLYIST ILL GIVE U BRAINLYIST... ### Vocabulary Words: El doctor te examina Complete the vocabulary chart. They are divided per vocabulary presentation with the page title in the lesson. They also include the cognates, which are also a part of your vocabulary. Optional: To help you remember, you can draw or add a picture. You may copy and paste the accented and special characters from this list if needed: Á, á, É, é, Í, í, Ó, ó, Ú, ú, ü, Ñ, ñ, ¡, ¿ English Spanish Drawing/Image (optional) seat belt to feel; feeling skin arm knee ba Vocabulary Words: El doctor te examina Complete the vocabulary chart. They are divided per vocabulary presentation with the page title in the lesson. They also include the cognates, which are also a part of your vocabulary. Optional: To help you remember, you can draw or add a picture. You may copy ... ### How many solutions does the following equation has? 5 (m - 3) + 6 = 4m + 3 A-No Solution B-Infinitely Many Solutions C-One Solution How many solutions does the following equation has? 5 (m - 3) + 6 = 4m + 3 A-No Solution B-Infinitely Many Solutions C-One Solution... ### What is the solution to the y = 4x – 10 y = 2 O (3, 2) O (2, 3) O (-2, 2) O (2,-2) What is the solution to the y = 4x – 10 y = 2 O (3, 2) O (2, 3) O (-2, 2) O (2,-2)... ### Joshua built a fence that is 3 feet by 5 feet. What is the area of the rectangular fence? Joshua built a fence that is 3 feet by 5 feet. What is the area of the rectangular fence?...
# Gradient & Directional Derivative Question (multi var) 1. Nov 2, 2013 ### Alex Bard $\partial$This is my first post, so I apologize for all my mistakes. Thank you for the help, in advance. These are test review questions for Multi Variable Calculus. 1. The problem statement, all variables and given/known data Let f(x,y) = tan-1(y2 / x) a) Find fx($\sqrt{5}$, -2) and fy($\sqrt{5}$, -2). b) Find the rate of change of f at the point ($\sqrt{5}$, -2) in the direction toward the point (0,0). c) Find the directional derivative in the direction of fastest increase at the point ($\sqrt{5}$, -2). 2. Relevant equations So from my understanding, part a, I would just have to do partial derivatives to x then y and then plug in the coordinates afterwards that are given. Part b is the gradient vector. Part c is just the largest value when getting the derivative. 3. The attempt at a solution a. $\frac{∂f}{∂x}$ = [1 / 1 + (y^2/x)^2] * y^2 = (y^2 * x^2)/1+y^4 when subbing in the points given, I get 20/17 $\frac{∂f}{∂y}$ = 1 / [1 + (y^2/x)^2] * 2y/x = (2y * x^2) / x(1 + y^4) when subbing in the points given, I get 20/17√5 b. So here I would first make a vector from (√5, -2) going to (0,0), which is <-√5, 2> Then unit vector is 1/√[(√5)2 + 22] = 1 / √9 = 1/3 Then 1/3(-√5, 2) is the unit vector To get the Gradient, I use ∂ in respect to x and y AND using the calculations from part a, I get: ∇f(x,y) = <(y^2 * x^2)/1+y^4, (2y * x^2) / x(1 + y^4)> now I'm a bit stuck. Do I just do the DOT product of ∇f and u? as in: 1/3(-√5, 2) ° <(y^2 * x^2)/1+y^4, (2y * x^2) / x(1 + y^4)> or should I sub the points given of (√5, -2) into the ∇f and then dot them? I haven't really gotten to part c yes since I believe I need the answer from b to do c. 2. Nov 2, 2013 ### LCKurtz It's hard to read your work with lots of missing parentheses and, I think, some mistakes. But to answer your last question, I would say to evaluate both partials at the point and your gradient at the point. Then dot that simple vector with your unit vector in whatever direction you need. Again, I think you need to check your arithmetic in spots. 3. Nov 2, 2013 ### Ray Vickson Your $f_x$ and $f_y$ are incorrect; go back and *very carefully* use the chain rule. In particular, you should not have (1+y^4) in the denominators; something else needs to replace that. $$\frac{y^2 x^2}{1} + y^4 = x^2 y^2 + y^4$$ when read using standard rules for parsing mathematical expressions. If you mean $$\frac{y^2 x^2}{1+y^4}$$ then use parentheses, like this: y^2 * x^2/(1 + y^4). 4. Nov 2, 2013 ### Alex Bard Reworking Part A Okay, thank you for your help, let me do this all over again. Also, I apologize for my sloppy writing, will do my best to be neat and organized. Lets have a crack at this. a. ∂f∂x = $\frac{1}{1+[\frac{y^2}{x}]^2} * y^2 * \frac{-1}{x^2}$ so : $\frac{y^2 x^2} {(-x)^2 - y^4 x^2}$ Simplifying, I get : $\frac{1} {-x^2 - y^2}$ Subbing in my values: $\frac{1}{(-√5)^2 - 2^2}$ = 1 ∂f∂y = $\frac{1}{1+[\frac{y^2}{x}]^2} * \frac{2y}{x}$ so : $\frac{2yx^2} {x (1 + y^4)}$ Simplifying, I get : $\frac{2yx^2} {x + xy^4}$ Now with substitution, I would get $\frac{20}{17√5}$ 5. Nov 2, 2013 ### LCKurtz Check your simplification. Only the first line is correct. Not wrong, but why not finish simplifying? Woops, yes it is wrong. Your algebra needs some work. 6. Nov 3, 2013 ### Alex Bard Finished? Thank you for the help LCKurtz, I'm going to go through the entire problem again, with feeling this time. $Let f(x,y) = tan^-1(\frac{y^2}{x})$ A) Find fx(√5, -2) and fy(√5, -2). $\frac{∂f}{∂x} = \frac{1}{1 + [\frac{y^2}{x}]^2} * y^2 * \frac{-1}{x^2}$ Since I suck at simplification, I will plug my numbers in right away to avoid confusion: $\frac{∂f}{∂x} = \frac{1}{1 + [\frac{(-2)^2}{√5}]^2} * (-2)^2 * \frac{-1}{(√5)^2}$ Solving: $\frac{∂f}{∂x} = \frac{1}{\frac{5}{5} + [\frac{16}{5}]} * 4 * \frac{-1}{5}$ → $\frac{∂f}{∂x} = \frac{-4}{21}$ Now for $\frac{∂f}{∂y}$ $\frac{∂f}{∂y} = \frac{1}{1 + [\frac{y^2}{x}]^2} * \frac{2y}{x}$ Once again, subbing in values; $\frac{∂f}{∂y} = \frac{1}{1 + [\frac{4}{√5}]^2} * \frac{-4}{√5} → \frac{-4}{√5( \frac{21}{5}) }$ → $\frac{∂f}{∂y} = \frac{-4}{√5(4\frac{1}{5}) }$ Pain in the butt, but that's fx, fy ---------------------------------------------------------------------------------------------------- Now, part B) Find the rate of change of ∫ at the point (√5, -2) in the direction toward the point (0,0). For directional vector I get (0 - √5, - (-2)) → (-√5, 2) Then $\frac{1} {√[(√5)^2 + (-2)^2]} → \frac {1}{√(5 + 4)} → \frac {1}{3}$ The unit vector is $→ \frac{1}{3}<-√5, 2>$ Now to get the Gradient, I, once again, take, $\frac{∂f}{∂x} and \frac{∂f}{∂y}$ This will be : $\frac{∂f}{∂x} = \frac{- y^2}{x^2 + y^2}$ $\frac{∂f}{∂y} = \frac{- 2y}{x(1 + \frac{y^4}{x^2})}$ $∇∫ = <\frac{- y^2}{x^2 + y^2} , \frac{- 2y}{x(1 + \frac{y^4}{x^2})} >$ Thus $∇∫(√5, -2) = <\frac{- (-2)^2}{(√5)^2 + (-2)^2} , \frac{- 2(-2)}{√5(1 + \frac{(-2)^4}{(√5)^2})} >$ → $∇∫(√5, -2) = <\frac{-4}{5 + 4} , \frac{4}{√5(1 + \frac{16}{5})} >$ → $∇∫(√5, -2) = <\frac{-4}{9} , \frac{4}{√5(4\frac{1}{5})} >$ Since we have the unit vector and gradient, we use : Du∫(√5, -2) = $∇∫(√5, -2) \bullet u = <\frac{-4}{9} , \frac{4}{√5(4\frac{1}{5})} > \bullet \frac{1}{3}<-√5, 2>$ ---------------------------------------------------------------------------------------------------- Now, since we have all that, onto part C. Find the directional derivative in the direction of fastest increase at the point (√5, -2). In reality this has already been solved by the above equation, as it will give us the rate of change as well. We just have to evaluate the equation and get. Du∫(√5, -2) = $∇∫(√5, -2) \bullet u = <\frac{-4}{9} , \frac{4}{√5(4\frac{1}{5})} > \bullet \frac{1}{3}<-√5, 2>$ $\frac{1}{3} (\frac{4√5}{9}, \frac{8}{√5(4\frac{1}{5})})$ That should do it....what say you? EDIT: Algebra fix...agaain Last edited: Nov 3, 2013 7. Nov 3, 2013 ### LCKurtz Perhaps, if you plan to pass calculus, you should learn how to simplify algebraic expressions. Correct. If you can simplify it with numbers, you should be able to simplify it with variables. Surely your teacher would dock points for an answer like that, right or wrong. And it is wrong. : Perhaps not wrong, just poorly presented. See my next post Doesn't it bother you that you don't have the same value for $f_x$ that you have earlier. And surely you wouldn't leave the answer like that. And what's with the integral signs? I say that last part is wrong. A directional derivative is a scalar and you have an answer that is a vector. Also there is something in your text about the direction of the max rate of change and its magnitude. Last edited: Nov 3, 2013 8. Nov 3, 2013 ### LCKurtz I just realized that you apparently attempted to use a mixed fraction in that expression. I don't think they are ever used in printed material. In usual notation $4\frac 1 5$ is the same as $4\cdot \frac 1 5 =\frac 4 5$. If you must use that notation, you would have to write it as $4 + \frac 1 5$. And in any case you should simplify the expression. 9. Nov 3, 2013 ### Ray Vickson You may "suck" at simplification, but that just means that your elementary algebra skills are deficient. That is not a good sign if you plan to continue in mathematics, physics, operations research, engineering, etc. NOW is the time to improve your algebraic skills; perhaps working through one of the "College Outline" books, or using some other tutorial packages on- or off-line is what you need to do. Life will get increasingly difficult for you if you don't address this issue. 10. Nov 3, 2013 ### Alex Bard Thank you for your input, I will work in variables more to get that buttoned up. Would you please give me a hint? I'm not exactly sure where my mistake is. Looking at it again I can see it this way. tan^-1(y^2/x) ∂z/∂y = $\frac{1}{1 + (\frac{y^2}{x})^2} * \frac{2y}{x}$ → $\frac{2y}{1 + \frac{y^4}{x^2}} * \frac{1}{x}$ $\frac{2y}{x(1 + y^2x^{-2})}$ Here I can distribute x but that's about it as far as I can tell and when I solve, I will get $\frac{-4}{√5(1 + 4(5^{-1}))} → \frac{-4√5}{9}$. That was an absent minded mistake, it should have been a y^4 in the denominator, giving me the same answer. $∂z/∂x = \frac {-4}{21}$ $∂z/∂y = \frac {-4√5}{9}$ My unit vector is $\frac{1}{3}<-√5, 2>$ Dotting the vectors then adding I get: Duf = $(\frac {-4}{21})(\frac{-√5}{3}) + (\frac {-4√5}{9})(\frac{2}{3}) → \frac{4√5}{63} - \frac{8√5}{27} → -\frac{44√5}{189}$ Rate of change of f in the direction from (√5, -2) to (0, 0) is $-\frac{44√5}{189}$ **We are not allowed to use calculators in my school so this answer should be fine** I'm a little lost really. I know that the direction of the fastest increase is the gradient vector. I also know that the directional derivative formula is Duf = ∇f°u but I really don't know how to apply it. 11. Nov 3, 2013 ### Alex Bard Thank you for the input - as I understand how important it is, I will surely be working on it. 12. Nov 3, 2013 ### LCKurtz As long as you have negative exponents in there like that, it isn't simplified. Fix the red typo and multiply both the numerator and denominator by $x$, then distribute the $x^2$ in the denominator. You should get$$\frac {2xy}{x^2+y^4}$$ Try again with the simplified expression. Simplifying makes things easier. Again, do it with the correct numbers. Yes. And what about the gradient gives the max rate of change? 13. Nov 3, 2013 ### Alex Bard Where should I send the cake? LCKurtz, I believe I owe you a cup of coffee or something. Thank you for your input and gentle guidance. $Let f(x, y) = tan^{-1} \frac{y^2}{x}$ A. $fx(√5, -2) = \frac{1}{1 + \frac{y^4}{x^2}} * \frac{y^2}{-x^2} → \frac{-y^2}{1 + y^4x^{-2}} * \frac{1}{x^2} → \frac{-y^2}{x^2 + y^4} → \frac{-4}{21}$ $fy(√5, -2) = \frac{1}{1 + \frac{y^4}{x^2}} * \frac{2y}{x} → \frac{2y}{1 + y^4x^{-2}} * \frac{1}{x} *\frac{x}{x} → \frac{2yx}{x^2 + y^4} → \frac{-4√5}{21}$ B. P = (√5, -2) O = (0, 0) → PO = <-√5, 2> u = √[(-√5)^2 + 2^2] → √(5 + 4) = 3 → $\frac{1}{3}<-√5, 2> → <\frac{-√5}{3}, \frac{2}{3}>$ ∇f(x, y) = <fx, fy> = $<\frac{-y^2}{x^2 + y^4}, \frac{2yx}{x^2 + y^4}>$ ∇f(√5, -2) = $<\frac{-4}{21}, \frac{-4√5}{21}>$ The rate of Change of f in the Direction P to Q is: Duf(√5, -2) = $<\frac{-4}{21}, \frac{-4√5}{21}> \bullet <\frac{-√5}{3}, \frac{2}{3}> = (\frac{4√5}{63} - \frac{8√5}{63}) = \frac{-4√5}{63}$ C. The Directional Derivative is ∇f(x, y) $\bullet$ u and since θ = 0 because u is pointing in the same direction as the gradient vector, it is the maximum rate of increase. ∇f(x, y) $\bullet$ u = $<\frac{-4}{21}, \frac{-4√5}{21}> \bullet <\frac{-√5}{3}, \frac{2}{3}>cosθ = (\frac{4√5}{63} - \frac{8√5}{63}) (1) = \frac{-4√5}{63}$ Last edited: Nov 3, 2013 14. Nov 3, 2013 ### LCKurtz Better check those denominators. I don't get $25$. The vector u doesn't have anything to do with the last part. What does your book say about the gradient vs. max rate of change. Look it up. 15. Nov 3, 2013 ### Alex Bard I fixed the 25 to 21. This is the theorem from the book. I actually didn't feel too comfortable with the answer myself and have been searching the internet for a better explanation. I understand that the gradient is the direction of the maximum increase, and is orthogonal to the level curve/surface. I also understand that it measures just one maximum and not all. Now as far as a directional derivative, I've been reading here and trying to understand as I go. Its frustrating to think you almost have it but there is a little bit of information I'm just not getting. Thankfully with persistence I know I will, the AHA is just around the corner. #### Attached Files: • ###### Screen Shot 2013-11-03 at 8.25.18 PM.png File size: 8.2 KB Views: 68 16. Nov 3, 2013 ### LCKurtz 17. Nov 3, 2013 ### Alex Bard Okay sir, I'm stumped. Find the Directional derivative in the direction of fastest increase at the point (√5, -2) The Direction of the FASTEST increase is Gradient, which I've found is ∇f(√5, -2) = $<\frac{-4}{21}, \frac{-4√5}{21}>$ The magnitude of the gradient is the maximal directional derivative. The directional derivative is maximal in the direction of $<\frac{-4}{21}, \frac{-4√5}{21}>$ So that means I would have to put $\frac{-4}{21}, \frac{-4√5}{21} over √{(\frac{-4}{21})^2 + (\frac{-4√5}{21})^2$, correct? and wouldn't that just return my unit vector from before? or am I taking the wrong point here? 18. Nov 3, 2013 ### haruspex Yes, but that's not just the direction. It is ∇f, and according to the theorem you just want the magnitude of that. 19. Nov 3, 2013 ### Alex Bard So then it's simply square both and add under a square root? 20. Nov 3, 2013 ### haruspex That's my understanding
# So the amphibious seaplane thing is pretty much dead in the water so to speak ?? ### Help Support HomeBuiltAirplanes.com: #### TFF ##### Well-Known Member Here is a practical problem. Insurance. The stranger it is, the less chance you will get insurance on it. You will have to self insure. Self insuring a $20,000 airplane is not that big a loss. Hurts, but it better not be changing your life stile loosing the money; you are not suppose to be spending rent money on a toy.$200,000 airplane and even a multi millionaire will say bad investment. A friend of a friend just got a Seawind; thumbs up all around. No one will insure him in it. Airline captain maybe, but no 500 hr Cessna Piper driver. Now he has a plane he can't fly because of money risk. A friend putting his VK30 together probably will not have insurance except liability. He is a retired airline captain but has not flown in eight years. Its a 200K project that may or may not be worth something in the end. There was another VK30 at the airport that was a total loss when the engine quit on takeoff; no one hurt but it was self insured because not insurable and a turbine. By by a couple of hundred grand. #### FritzW ##### Well-Known Member Log Member ...Bring back the Libelle! ;-) They kind of did: At only $20k for the kit I don't know why there wern't more Avid Catalina's. General characteristics Crew: one Capacity: two passengers Length: 19.40 ft (5.91 m) Wingspan: 36 ft 0 in (10.97 m) Wing area: 150 sq ft (14 m2) Empty weight: 600 lb (272 kg) Gross weight: 1,200 lb (544 kg) Fuel capacity: 17.5 U.S. gallons (66 L; 14.6 imp gal) Powerplant: 1 × Rotax 582 twin cylinder, liquid-cooled, two stroke aircraft engine, 65 hp (48 kW) Propellers: 2-bladed wooden Performance Maximum speed: 90 mph (145 km/h; 78 kn) Cruise speed: 75 mph (121 km/h; 65 kn) Stall speed: 32 mph (51 km/h; 28 kn) Range: 364 mi (316 nmi; 586 km) Service ceiling: 12,500 ft (3,800 m) Rate of climb: 1,000 ft/min (5.1 m/s) while operated solo Wing loading: 8.0 lb/sq ft (39 kg/m2) #### BBerson ##### Well-Known Member HBA Supporter The Avid Amphibian wasn't heavily advertised. No major articles in Sport Aviation at that time. #### Topaz ##### Super Moderator Staff member Log Member They kind of did:... At only$20k for the kit I don't know why there wern't more Avid Catalina's.... And where would they be able to justify the water hull? Excepting areas like the Pacific Northwest or Florida, approved or even allowed areas for an amphibian or seaplane to land on the water are not exactly commonplace. #### Hot Wings ##### Grumpy Cynic HBA Supporter Log Member And where would they be able to justify the water hull? Interesting chicken and egg kind of thing: It was mentioned above about a side by side water 'runway' for water landing. It's much easier to scrape out a trough, line it with bentonite and then fill it with water than it is to build a nice flat runway - especially if the land isn't already pretty flat. Lower maintenance than a grass strip as well. Even around here where it gets down to -20F in the winter it will remain ice free for a surprising number of days in the winter. No one will build such a water runway without demand and there will be little demand unless there are already a number of aircraft that can land on water. Being able to land on water, even if it is illegal to do so, should open up a lot more emergency landing places? #### Topaz ##### Super Moderator Staff member Log Member ... Being able to land on water, even if it is illegal to do so, should open up a lot more emergency landing places? Would it? Enough to justify the drag, weight, and fuel-expenditure penalty the rest of the time? Or would a fraction of that money be better spent learning more about off-airport landings in a landplane than the 3-5 "pull the throttle on you" examples you get in the course of regular flight instruction, to almost never be practiced again? I'll be the first to admit that I'm totally biased about this because of what I fly. It's not that I dislike amphibians - I'm just as interested as everyone else - but when it comes down to it, unless you happen to live in one of the relatively few areas with lots of open, unregulated bodies of water, there's nothing but "cost" associated with having the hull or floats. Which, I think, is why these kinds of airplanes don't sell well, in all those places with few open, unregulated bodies of water. Last edited: #### BJC ##### Well-Known Member HBA Supporter And where would they be able to justify the water hull? Excepting areas like the Pacific Northwest or Florida, approved or even allowed areas for an amphibian or seaplane to land on the water are not exactly commonplace. I will confess that I had the opportunity to loosen restrictions on several privately owned lakes. I elected to retain the “no seaplane operations” restriction to minimize the PITA factor as well as to minimize the risk of becoming a deep pockets liability target. The liability issue has nothing to do with right and wrong; it has everything to do with public image and the cost of mounting a defense of frivolous law suits. BJC #### ScaleBirdsScott ##### Well-Known Member In addition to pylon-mounted engine configuration like the Thurston Teal and other designs, the parasol wing with a wing-mounted engine and sponsons like the Dornier Libellule (or auxiliary floats like the bigger Shavrov Sh-2) is also very appealing in a small flying boat or amphibian. I think that latter configuration works better for a very light amphibian in terms of weight and balance issues because it puts the heavy engine forward and the pilot and passenger very close to the center of gravity. View attachment 74124 View attachment 74125 As a matter of fact, other than having a limited payload because of the rather heavy empty weight, the Dornier Libelle I was pretty much spot on as an LSA for water operations...back in 1921! With a modern engine producing more power with less weight and modern understanding of how to build light but strong all-metal structures, it would be just great. Bring back the Libelle! ;-) DORNIER LIBELLE Specifications (Libelle I) General characteristics Crew: one Capacity: two passengers Length: 7.18 m (23 ft 7 in) Wingspan: 8.5 m (27 ft 11 in) Height: 2.27 m (7 ft 5 in) Wing area: 14 m2 (150 sq ft) Empty weight: 420 kg (926 lb) Gross weight: 640 kg (1,411 lb) Fuel capacity: fuel 42 kg (93 lb)fuel + oil 10 kg (22 lb) Powerplant: 1 × Siemens-Halske Sh 4 5-cyl. air-cooled radial piston engine, 45 kW (60 hp) Performance Maximum speed: 120 km/h (75 mph; 65 kn) Cruise speed: 100 km/h (62 mph; 54 kn) Range: 300 km (186 mi; 162 nmi) Service ceiling: 1,600 m (5,200 ft) Ugh I want one so bad. Or at least plans. If I knew the airfoils and sizing I could do the rest. Even have the perfect engine for it! #### Riggerrob ##### Well-Known Member How minutes to fold wings on an Avid Catalina? How long (feet) grass runway does it need for takeoff? How long a lake (feet) does it need for takeoff? #### FritzW ##### Well-Known Member Log Member And where would they be able to justify the water hull? Surprisingly there are a lot more places than I thought. According to the Seaplane Pilots Association there are a dozen or so places within an easy day trip of where I live, and I live in the worst part of the country for finding a place to fly an amphib out of. #### BBerson ##### Well-Known Member HBA Supporter I have an Avid Amphibian kit to finish. But I don't have any need for actual water landing. My thinking is just flying low above the water is enough for what I want to do. And the hull (kind of like antique glider skid) is great for landing in an emergency in a plowed or grass field. I never liked the idea of fixed gear to flip over in an emergency landing. #### Tiger Tim ##### Well-Known Member unless you happen to live in one of the relatively few areas with lots of open, unregulated bodies of water, there's nothing but "cost" associated with having the hull or floats. I happen to live in one of those areas and I see floatplanes mostly for two very things in two very different areas: outdoorsmen and rich folks. The outdoorsmen charter planes on straight floats to take them way out from civilization to go hunting and fishing. There’s some neat stuff too. Beavers and Otters, Caravans, all manner of Cessnas, Beech 18s and even a couple Norsemen still. The wealthy folks charter Cessna Caravans and Turbo Beavers on amphibs to fly them from a couple airports in Toronto up to their lakeside cottages on the weekends. Note that with the exception of the Beeches all of those floatplanes are high-wings (made even higher with the plane all the way up on floats). This allows them to use the existing docks that may or may not have been built with airplanes in mind. A Lake amphibian needs an incredibly low dock and I’m not sure something like a Taylor Coot can be docked at all. You’ll never find a seaplane ramp up out of the water around here (or at least they’re pretty rare) so you have to work with the docks that there are. Note also that most floatplanes are flying in places where the lakes are seasonal. In the winter they often operate on skis or wheels, with the resulting bump in useful load you get when the heavy floats come off. Even the Caravans out of Toronto go back on wheels for the winter so they can help move the mail around Christmas time. From where I’m sitting, this is why you don’t see a lot of flying boats. #### Topaz ##### Super Moderator Staff member Log Member I will confess that I had the opportunity to loosen restrictions on several privately owned lakes. I elected to retain the “no seaplane operations” restriction to minimize the PITA factor as well as to minimize the risk of becoming a deep pockets liability target. The liability issue has nothing to do with right and wrong; it has everything to do with public image and the cost of mounting a defense of frivolous law suits. BJC Exactly. And I know you're hardly an anomaly in that regard. #### Hot Wings ##### Grumpy Cynic HBA Supporter Log Member there's nothing but "cost" associated with having the hull or floats. That is what I have thought, and how I'm still leaning but, maybe I/we am/are just being biased - like some pilots are toward flying wings? #### davidb ##### Well-Known Member I will confess that I had the opportunity to loosen restrictions on several privately owned lakes. I elected to retain the “no seaplane operations” restriction to minimize the PITA factor as well as to minimize the risk of becoming a deep pockets liability target. The liability issue has nothing to do with right and wrong; it has everything to do with public image and the cost of mounting a defense of frivolous law suits. BJC I’m not getting something. How does no seaplane operations affect liability and whose liability? I can see reasons why some entity would not want motorized vehicles on a lake but if motorboats and jet skis are permitted, what is the justification for prohibiting seaplanes? #### blane.c ##### Well-Known Member HBA Supporter I’m not getting something. How does no seaplane operations affect liability and whose liability? I can see reasons why some entity would not want motorized vehicles on a lake but if motorboats and jet skis are permitted, what is the justification for prohibiting seaplanes? Ignorance, mostly perpetuated by the press. #### BJC ##### Well-Known Member HBA Supporter I will confess that I had the opportunity to loosen restrictions on several privately owned lakes. I elected to retain the “no seaplane operations” restriction to minimize the PITA factor as well as to minimize the risk of becoming a deep pockets liability target. The liability issue has nothing to do with right and wrong; it has everything to do with public image and the cost of mounting a defense of frivolous law suits. BJC I’m not getting something. How does no seaplane operations affect liability and whose liability? I can see reasons why some entity would not want motorized vehicles on a lake but if motorboats and jet skis are permitted, what is the justification for prohibiting seaplanes? Do you understand how liability law suits work? Anyone who can find a lawyer willing to take a contingency fee case can file a law suit. It has nothing to do with the target having done something wrong. It has to do with the target perceived to have lots of insurance and or lots of assets. In my post, the potential target was (is) a Fortune 200 corportion. Once the law suit has been filed, there will be news coverage, and even if it is fairly and accurately reported, large public corporations try to avoid it. And the case will need to be defended in court, which is a PITA for everyone involved, and a big distraction from one’s primary business. And then the jury may ignore the law (Are you familiar with the concept of jury nullification? Then there are juries in injury or loss of life cases that act on sympathy rther than legal liability.) and make an award, and the cycle repeats through the appeal. All it takes to start the mess is an airplane running aground and getting damaged. Boaters are enough of a pain; pilots are a special class of pain. Imagine the mess when a boat hits an airplane, or vice versa, and someone gets killed. The PITA factor could be as simple an event as having a resident near the lake complaining about an airplane flying too low over their house. Ignorance, mostly perpetuated by the press. As noted above, even accurate reporting of the facts often leades to adverse publicity. BJC #### Topaz ##### Super Moderator Staff member Log Member That is what I have thought, and how I'm still leaning but, maybe I/we am/are just being biased - like some pilots are toward flying wings? The drag of the hull, the weight of the extra material to prevent penetration by floating debris during high-speed operation on water, the weight and drag of the sponsons or tip floats, retractable gear, the extra maintenance of a structure you're dunking in water on a regular basis... None of those seem like "bias" to me. YMMV, of course. #### blane.c ##### Well-Known Member HBA Supporter With the perception that the size of the average pilot is increasing, and therefore increasing the cabin size is prudent, incorporating the increased cabin size to accommodate a portion of the hull could amortize the weight and drag of a flying boat. I like the S-38 best. It would be cool to design a floatplane that incorporated the floats into twin-booms reminiscent of the S-38 but smaller and put the occupants some in each float. #### cluttonfred ##### Well-Known Member HBA Supporter Ugh I want one so bad. Or at least plans. If I knew the airfoils and sizing I could do the rest. Even have the perfect engine for it! Shavrov Sh-2 plans can be found...but they are in Russian. Knowing that the Volmer Sportsman and Anderson Kingfisher both used what were basically Cub or Champ wings, I don't think the airfoil is very critical. Piper J-3 Cub specs with 80-100 hp ought to be a pretty good conceptual start, you want the big wing area to get up off the water fast. Personally, I'd try to channel the spirit of those designs rather than build an exact replica, though the Shavrov has always appealed to me. See also:
Ask question # Find the x-and y-intercepts of the graph of the equation algebraically. y=-\frac{1}{2}x+\frac{2}{3} Question Upper level algebra asked 2020-11-22 Find the x-and y-intercepts of the graph of the equation algebraically. $$\displaystyle{y}=-{\frac{{{1}}}{{{2}}}}{x}+{\frac{{{2}}}{{{3}}}}$$ ## Answers (1) 2020-11-23 Calculation: Consider, the equation, $$\displaystyle{y}=-{\frac{{{1}}}{{{2}}}}{x}+{\frac{{{2}}}{{{3}}}}$$ To determine x -intercept, substitute $$\displaystyle{y}={0}$$ in the above equation, $$\displaystyle{0}=-{\frac{{{1}}}{{{2}}}}{x}+{\frac{{{2}}}{{{3}}}}$$ $$\displaystyle{\frac{{{1}}}{{{2}}}}{x}={\frac{{{2}}}{{{3}}}}$$ $$\displaystyle{x}={\frac{{{2}}}{{{3}}}}\times{2}$$ $$\displaystyle={\frac{{{4}}}{{{3}}}}$$ Therefore, the x -intercept is $$\displaystyle{\left({\frac{{{4}}}{{{3}}}},{0}\right)}$$. To determine y -intercept, substitute $$\displaystyle{x}={0}$$ in the equation, $$\displaystyle{y}=-{\frac{{{1}}}{{{2}}}}{x}+{\frac{{{2}}}{{{3}}}}$$, $$\displaystyle{y}=-{\frac{{{1}}}{{{2}}}}\times{0}+{\frac{{{2}}}{{{3}}}}$$ $$\displaystyle={\frac{{{2}}}{{{3}}}}$$ Therefore, y -intercept is $$\displaystyle{\left({0},{\frac{{{2}}}{{{3}}}}\right)}$$. ### Relevant Questions asked 2020-11-01 Find the x-and y-intercepts of the graph of the equation algebraically. $$\displaystyle{y}={\frac{{{3}}}{{{4}}}}{x}-{\frac{{{1}}}{{{4}}}}$$ asked 2021-03-06 Find the x-and y-intercepts of the graph of the equation algebraically. $$\displaystyle{\frac{{{8}{x}}}{{{3}}}}+{50}-{2}{y}={0}$$ asked 2020-11-08 Find the x-and y-intercepts of the graph of the equation algebraically. $$\displaystyle{3}{y}+{2.5}{x}-{3.4}={0}$$ asked 2020-11-01 Find the x-and y-intercepts of the graph of the equation algebraically. $$\displaystyle{y}=-{3}{\left({2}{x}+{1}\right)}$$ asked 2021-02-12 Find the x-and y-intercepts of the graph of the equation algebraically. $$\displaystyle{y}={4}{y}-{0.75}{x}+{1.2}={0}$$ asked 2021-02-18 Find the x-and y-intercepts of the graph of the equation algebraically. $$\displaystyle{\frac{{{2}{x}}}{{{5}}}}+{8}-{3}{y}={0}$$ asked 2020-10-28 Find the x-and y-intercepts of the graph of the equation algebraically. $$\displaystyle{y}={2}{\left({x}-{4}\right)}$$ asked 2021-01-02 Find the x-and y-intercepts of the graph of the equation algebraically. $$\displaystyle{y}={4}{\left({7}{x}+{1}\right)}$$ asked 2021-01-31 Find the x-and y-intercepts of the graph of the equation algebraically. $$\displaystyle{y}={3}{x}-{1}$$ asked 2021-02-12 Find the x- and y-intercepts of the graph of the equation. $$\displaystyle{y}={\frac{{{1}}}{{{3}}}}{x}-{5}$$ ...
# Coulomb's Law and electric fields ## Homework Statement three point charges are placed at the following points on the x-axis +2 uC at x=0, -3uC at x=40 cm, -5 uC at x=120 cm. find the force (a) on the -3 uC charge, (b) on the -5 uC charge ans. (a) -0.55N ; (b) 0.15 N uC=nano coulomb Fm=qvB ? Fe=|E|(q)? Fe=kq1q2/r^2 ## The Attempt at a Solution I cannot seem to solve such a simple problem, i need sufficient help. I have the idea that it has something to do with minusing each Fe charge by eachother but im uncertain please need help with a solution Related Advanced Physics Homework Help News on Phys.org I cannot seem to solve such a simple problem, i need sufficient help. I have the idea that it has something to do with minusing each Fe charge by eachother but im uncertain please need help with a solution You'll use the 3rd equation, and you will sum the forces. For instance, for the -3 nC charge, you will have to figure out the force created by the +2 nC Charge, then for the -5 nC charge. Once you get those two numbers, just add them together. but wait, try it for yourself, apparently you dont get the given answer of -0.55 N, what is the answer u thus get? Well, I didn't get -0.55 N exactly, but I did get -0.5479 N. Which is close enough. I came to this solution saying the uC is actually micro-coulombs. Usually nano-coulombs is denoted nC, and if you don't want to go into LaTex, microcoulombs is uC. This is because u is close enough to the Greek Letter mu. A few more hints on this problem.... Draw a free-body diagram. Then think about what "should" be happening, like which direction a force should go. got it now im trying part b thanks man
# wrapper for common subset of auto_ptr and unique_ptr API I read an interesting old question on the Software Engineering SE about how to transition away from std::auto_ptr. So I wrote a wrapper around the common subset of std::auto_ptr and std::unique_ptr. The wrapper's mission in life at runtime is to clean up pointers created with new when the scope ends regardless of how the scope is exited. Its job at compile time is to make compilation fail as informatively as possible when fake_autoptr is used in a non-lowest-common-denominator way. fake_autoptr is supposed to make it easier to transition away from std::auto_ptr and support both C++11 and C++03 until support for C++03 is dropped. It should behave the same way whether it is backed by an auto_ptr or a unique_ptr. The example given in the old question is this. This example is not leveraging many of the things that an autoptr can do. I think, but am not 100% certain that the autoptr's job here is just to run delete when its destructor is called and not to steal resources from other autoptrs. // NOT MINE DO NOT REVIEW Foo* GetFoo() { autoptr<Foo> ptr(new Foo); // Initialize Foo ptr->Initialize(...); // Now configure remaining attributes ptr->SomeSetting(...); return ptr.release(); } Here is the wrapper I came up with. #ifndef FAKE_AUTOPTR_FAKE_AUTOPTR_INCLUDED #define FAKE_AUTOPTR_FAKE_AUTOPTR_INCLUDED 1 #include <memory> #if __cplusplus >= 201103L #include <type_traits> #endif namespace fake_autoptr_ns { namespace detail { template <class T> void destroy(T* goner) { delete goner; } } template <class T> class fake_autoptr { public: #if __cplusplus >= 201103L std::unique_ptr<T, decltype(&detail::destroy<T>)> smartptr_; typedef decltype(smartptr_) smartptr_type; #else std::auto_ptr<T> smartptr_; typedef std::auto_ptr<T> smartptr_type; #endif #if __cplusplus >= 201103L fake_autoptr() = delete; ~fake_autoptr() = default; #else private: fake_autoptr(); public: #endif #if __cplusplus >= 201103L template <class CtorArg> explicit fake_autoptr(CtorArg something) : smartptr_(something, detail::destroy<T>) { static_assert(std::is_same<T*, CtorArg>::value, "constructor argument must be T*"); } #else template <class CtorArg> explicit fake_autoptr(CtorArg something) : smartptr_(something) {} #endif // delete special member functions #if __cplusplus >= 201103L explicit fake_autoptr(const fake_autoptr<T>&) = delete; explicit fake_autoptr(fake_autoptr<T>&&) = delete; fake_autoptr& operator=(const fake_autoptr<T>&) = delete; fake_autoptr& operator=(fake_autoptr<T> &&) = delete; #else private: explicit fake_autoptr(const fake_autoptr<T>&); fake_autoptr& operator=(const fake_autoptr<T>&); public: #endif #if __cplusplus >= 201103L T& operator*() = delete; T* get() = delete; #endif const smartptr_type& operator->() const { return smartptr_; } smartptr_type& operator->() { return smartptr_; } T* release() { return smartptr_.release(); } #if __cplusplus >= 201103L const T* release() const = delete; void reset() = delete; void reset() const = delete; #endif }; } #endif // FAKE_AUTOPTR_FAKE_AUTOPTR_INCLUDED This is less interesting, but here's a smoke test to make sure it works #include "fake_autoptr.hpp" #include <cstdio> struct TwoInts { int int1; int int2; void print_first_int() { printf("1st %d\n", int1); } void print_second_int() { printf("2nd %d\n", int2); } }; TwoInts* GetInt() { using namespace fake_autoptr_ns; TwoInts *t = new TwoInts(); t->int1 = 3; t->int2 = 7; fake_autoptr<TwoInts> ptr(t); ptr->print_first_int(); ptr->print_second_int(); return ptr.release(); } int main() { TwoInts *t = GetInt(); delete t; return 0; } • Can you explain your use-case better? When would I want to use fake_autoptr<T> in preference to std::unique_ptr<T>? The only advantage to std::auto_ptr is that it compiles as C++03... but your fake_autoptr is C++11-only, so that's not why you're using it. Why not just use std::unique_ptr? – Quuxplusone Mar 20 '19 at 1:30 • @Quuxplusone, I've edited the code so it compiles as either C++11 or C++03 ... – Gregory Nisbet Mar 20 '19 at 2:30 I'm not a 100% convinced that you should put effort in supporting C++98/03. Especially since you can upgrade your code with Clang tidy modernize However, I see the arguments on moving slowly. That said, your code looks good. However, I do have some remarks. #ifdef is used a lot. So often, that one can wonder whether it makes sense to use a single ifdef with separate class definitions. It might improve the readability. I really like the deleted methods and the shadow private variants. It can help a lot in ensuring the compatibility. Looking at the stored unique_ptr, you use a helper function to delete the stored instance. WHY? This is what the default already does with a better implementation. (No extra memory needed) I don't see a compatibility argument as you don't use it with the auto_ptr. I see the templated constructor, however, I don't see the point of having it as a template. Instead you could just use T* directly in the wrapper? The thing I find the strangest is your operator-> which doesn't return a raw pointer. Instead you expose the underlying storage in that signature.
# Centre of a matrix ring are $\operatorname{diag}\{ a, a, …, a \}$ with $a\in Z(R)$ [duplicate] Show that $$Z(M_n(R))$$ consist of $$\operatorname{diag}\{ a, a, ..., a \}$$ with $$a\in Z(R)$$ ## marked as duplicate by rschwieb abstract-algebra StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Feb 5 '15 at 20:32 • We do not like taking orders. Instead, please indicate how you came across this problem; why it interests you; what you already know about it, and about the concepts mentioned in it; how far you got in your efforts to solve it; where you got stuck; and so on, and so on. Engage with us, so we can engage with you. – Gerry Myerson Jan 22 '13 at 6:32 • Please, try to make the title of your question more informative. E.g., Why does $a<b$ imply $a+c<b+c$? is much more useful for other users than A question about inequality. From How can I ask a good question?: Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader. – Julian Kuelshammer Jan 22 '13 at 6:35 • For some basic information about writing math at this site see e.g. here, here, here and here. – Julian Kuelshammer Jan 22 '13 at 6:37 Suppose $A=(a_{ij})\in Z(M_n(R))$. Let $E_{ij}$ be the matrix whose $i,j$ entry is $1$, and all other entries are $0$. Then the equations $$E_{ii}A=AE_{ii}$$ for $1\leq i\leq n$ implies that $A$ is necessarily diagonal. (Why?) Furthermore, $$AE_{ij}=E_{ij}A$$ for $1\leq i,j\leq n$ implies that $a_{ii}=a_{jj}$ for all $i$ and $j$. (Why?) Hence $A=aI_n$ for some $a\in R$. But notice that $$aI_n(bI_n)=bI_n(aI_n),\quad \forall b\in R$$ implies that $a\in Z(R)$. • This answer assumes that $R$ contains 1, which we are not given. – Ceph Nov 14 '17 at 20:23 • Fair point. I guess if it's just a rng the claim isn't always true. One could take $R$ the rng of square zero, then $M_n(R)$ also has zero multiplication, so is commutative. But then the center is not just the diagonal matrices. – Ben West Nov 14 '17 at 20:53 • I see the argument with $E_{ii}$, but not yet the one with $E_{ij}$. – Jos van Nieuwman Feb 26 at 21:38 • @JosvanNieuwman You can use the formula for finding the entries of a product of matrices. Let $B=AE_{ij}$. Then the $(k,l)$ entry of $B$ is $b_{kl}=\sum_{s=1}^na_{ks}e_{sl}=a_{kk}e_{kl}$ since $A$ is diagonal. In particular, when $k=i$ and $l=j$, one concludes $b_{ij}=a_{ii}e_{ij}=a_{ii}$. Similarly, since $B=E_{ij}A$, the same argument shows that $b_{ij}=a_{jj}$, so $a_{ii}=a_{jj}$. – Ben West Feb 26 at 21:57
# User Portlet Twan van der Schoot Discussions Lazy evaluation is quite handy in optimising interactive code like Manipulate when you don't want to compute a whole set of data anew prior to the start of Manipulate or at every "refresh". Oops, didn't read the first response well enough.
# 4.3 Transformation of graphs by greatest integer function Page 1 / 2 Drawings of graphs resulting from transformation applied by greatest integer function (GIF) follow the same reasoning and steps as deliberated for modulus operator. Before, we proceed to draw graphs for different function forms, we need to recapitulate the graph of greatest integer function (GIF) and also infer thereupon few of the values of GIF around zero. For clarity, we apply circular symbols : solid circle to denote inclusion of point and empty circle to denote exclusion of point. Using solid circle is optional, but helps to identify points on the graph. The values of GIF around zero are (we can write these expressions by observing graph. A bit of practice to write down these intervals helps.) : $\left[x\right]=-3;\phantom{\rule{1em}{0ex}}-3\le x<-2$ $\left[x\right]=-2;\phantom{\rule{1em}{0ex}}-2\le x<-1$ $\left[x\right]=-1;\phantom{\rule{1em}{0ex}}-1\le x<0$ $\left[x\right]=0;\phantom{\rule{1em}{0ex}}0\le x<1$ $\left[x\right]=1;\phantom{\rule{1em}{0ex}}1\le x<2$ $\left[x\right]=2;\phantom{\rule{1em}{0ex}}2\le x<3$ $\left[x\right]=3;\phantom{\rule{1em}{0ex}}3\le x<4$ Important point to note is that lower integer in the interval is included and higher integer is excluded. For negative interval like $-3\le x<-2$ , note that -3 is lower end whereas -2 is higher end. Yet another feature of this function is that domain of the function is continuous in R. It means, there need to be a function value corresponding to all x. A function like y=f(x) has different elements. We can apply GIF to these elements of the function. There are following different possibilities : 1 : y= f([x]) 2 : y=[f(x)] 3 : [y]=f(x) ## Greatest integer operator applied to independent variable The form of transformation is depicted as : $y=f\left(x\right)\phantom{\rule{1em}{0ex}}⇒\phantom{\rule{1em}{0ex}}y=f\left(\left[x\right]\right)$ The graph of y=f(x) is transformed in y=f([x]) by virtue of changes in the argument values due to operation on independent variable. The independent variable of the function is subjected to greatest function operator. This changes the normal real value input to the function. Instead of real numbers, independent variable to function is rendered to be integers – depending on the value of x and interval it belongs to. A value like x= - 2.3 is passed to the function as -3 in the interval $-3\le x<-2$ . Clearly, real values of “x” are truncated to integer values in the interval of unity i.e. [-1,0), [0,1), [1.2) etc. It means that values of the function y=f(|x|) will remain same as that of its value corresponding to integral value of “x” till value of “x” changes to next interval. We need to apply modification to the curve to reflect this effect. Knowing that truncation takes place for successive integral values of x, we divide graph of y=f(x) to correspond to 1 unit segments of x-axis. For this, we draw lines parallel to y-axis at integral points along x-axis. From intersection point of lines drawn and function graph, we draw lines parallel to x-axis for the whole interval which extends for a unit value. This ensures that function values remain same to that of function value for the lower integral value of x in a particular interval of one. From the point of construction of the graph of y=f([x]), we need to modify the graph of y=f(x) as : 1 : Draw lines parallel to y-axis (vertical lines) at integral values along x-axis to cover the graph of y=f(x). where we get a research paper on Nano chemistry....? what are the products of Nano chemistry? There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others.. learn Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level learn da no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts Bhagvanji Preparation and Applications of Nanomaterial for Drug Delivery revolt da Application of nanotechnology in medicine what is variations in raman spectra for nanomaterials I only see partial conversation and what's the question here! what about nanotechnology for water purification please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment. Damian yes that's correct Professor I think Professor Nasa has use it in the 60's, copper as water purification in the moon travel. Alexandre nanocopper obvius Alexandre what is the stm is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.? Rafiq industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong Damian How we are making nano material? what is a peer What is meant by 'nano scale'? What is STMs full form? LITNING scanning tunneling microscope Sahil how nano science is used for hydrophobicity Santosh Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq Rafiq what is differents between GO and RGO? Mahi what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq Rafiq if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION Anam analytical skills graphene is prepared to kill any type viruses . Anam Any one who tell me about Preparation and application of Nanomaterial for drug Delivery Hafiz what is Nano technology ? write examples of Nano molecule? Bob The nanotechnology is as new science, to scale nanometric brayan nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale Damian Is there any normative that regulates the use of silver nanoparticles? what king of growth are you checking .? Renato What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ? why we need to study biomolecules, molecular biology in nanotechnology? ? Kyle yes I'm doing my masters in nanotechnology, we are being studying all these domains as well.. why? what school? Kyle biomolecules are e building blocks of every organics and inorganic materials. Joe What is power set Period of sin^6 3x+ cos^6 3x Period of sin^6 3x+ cos^6 3x
# AP 9th Class Maths Important Questions Chapter 5 Co-Ordinate Geometry These AP 9th Class Maths Important Questions 5th Lesson Co-Ordinate Geometry will help students prepare well for the exams. ## AP State Syllabus 9th Class Maths 5th Lesson Important Questions and Answers Co-Ordinate Geometry Question 1. Write any point lies on $$\overline{\text { OY }}$$ (Positive Y – axis) and any point lies on $$\overline{\text { OX }}$$ (Negative X-axis). Solution: Point lies on $$\overline{\text { OY }}$$ be (x = 0, y ≥ 0) example : (0, 2) (0, 3). Point lies on $$\overline{\text { OX }}$$ be (x = 0, y ≤ 0) example : (2, 0) (3, 0). Question 2. The position of (3, 4) and (4, 3) are not the same on graph. Why? Solution: Given points (3, 4) and (4, 3) having x and y coordinates are equal. Question 3. The points such as (0, x), (0, -x), (0, y) and (0, -y) lie on the same line. Name the line. Solution: That line is Y – axis. Question 4. The co-ordinates of a point M(4, – 3). What are the distances of the point M from axes? Solution: Given point = M(4, -3) Distance from x -axis to the M is | -3 | units = 3 Distance from y – axis to the M is | 4 | units = 4 Question 5. From the figure given below, write the co-ordinates of the points A, B, P and Q. Solution: A(5,3), B(-4, -3), P(2, -2), Q(-3, 4) Question 6. What is a cartesian plane? Explain with a diagram. Solution: 1) To locate the exact position of a point on a number line we need only a single reference. 2) To describe the exact position of a point on a Cartesian plane we need two references. 3) The two perpendicular lines taken in any direction are referred to as co-ordinate axes. 4) The horizontal line is called X – axis. 5) The vertical line is called Y – axis. 6) The meeting point of the axes is called the origin. 7) The distance of a point from Y – axis is called the x co-ordinate or abscissa. 8) The distance of a point from X-axis is called the y co-ordinate or ordinate. 9) The co-ordinates of origin are (0, 0), 10 ) The co-ordinate plane is divided into four quadrants namely Q1; Q2, Q3, Q4 i.e., first, second, third and fourth quadrants respectively. 11) The signs of co-ordinates of a point are as follows. Q1(+, +); Q2; (-, +) Q3(-, -); Q4; (+, -) The coordinates of P are (1, – 2). The coordinates of Q are (3, 4). The coordinates of R are (- 2, – 5). The co-ordinates of S are (- 4, 3). Question 7. Without using graph sheet write the location of points given below. (-1, 3), (2, 0), (-3, -1), (0, -6) Solution: Given points A(-1, 3), B(2, 0), C(-3, -1) and D(0, -6) Question 8. Plot the points A (2, 2) B (6, 2) C (8, 5) and D (4, 5) in a graph sheet. Join all the points to make it a parallelogram. Find its area. Solution: Area of parallelogram = AB × BC AB = | x2 – x1 | = | 6 – 2 | = 4 BC = | y2 – y1 | = | 5 – 2 | = 3 ∴ Area = 4 × 3 = 12 sq. units. Question 9. i) The point belongs to Q3 ii) The abscissa of the point C iii) The point lie on X – axis iv) The coordinates of origin v) The point satisfy x > 0, y < 0 vi) The point satisfy x – y = 1 vii) The position of point B Solution: i) D ii) 3 iii) F, H iv) 0,0 v) C (3, – 2) vi) A (2, 1) Vii) Positive Y-axis viii) Q4 Question 10. i) Plot the points 0(0, 0), A(0, 3), B(4, 3), D(4, 0) on a graph sheet. iii) Find its area. Solution: i) Given points are O(0, 0), A(0, 3), B(4, 3), D(4, 0) ii) OABD represents a rectangle. iii) Area of a rectangle OABD = l × b = OD × BD = 4 × 3 = 12 sq units. Question 11. i) Plot the points A(2, 3), B(6, 3), C(4, 7) on a graph sheet. ii) Join the points to form triangle ABC. Identify the type of triangle and justify your answer. iii) Find its area, Solution: i) given points are A(2, 3), B(6, 3), C(4, 7) ii) ΔABC is formed, which is an Isosceles triangle. CD = | 7 – 3 |= 4 units AB = |16 – 2 | =4 units iii) Area of ΔABC = $$\frac{1}{2}$$ × b × h . = $$\frac{1}{2}$$ × AB × CD = $$\frac{1}{2}$$ × 4 × 4 = 2 × 4 = 8 sq units
# Rendering mountains around a tile layer [closed] When making a 2D Pokémon game, I just faked elevation by putting mountain tiles underneath the land. Now my tiles are 3D models, so I'm using layer properties to define their elevation. What I don't know though is how to generate a 'mountain' around them. The tilemap is kinda' like this: Layer 1: Layer 2: Layer 3: .... \\\\ \\\\ .... \..\ \\.\ .... \..\ \\\\ .... \\\\ \\\\ Layer 2 has y-offset set to 1, and Layer 3 has y-offset set to 2. All they do right now is float in the air. What I'm trying to do is render a mountain around them. ## closed as unclear what you're asking by Kromster says support Monica, Josh♦Jan 11 '15 at 17:28 Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question. • What have you tried? What does it mean to "add mountains?" Do you just need to know how to put them in your sprite sheet? How to generate them in a level? Et cetera. – Josh Jan 11 '15 at 17:29 • Sorry! I made some progress, but I'm stuck again. – Shien Jan 14 '15 at 5:25
Mathematics # What do you mean by linear pair of angles ? ##### SOLUTION Two adjacent angles form a linear pair of angle, if their non-common arms are two opposite rays. Sum of angles of linear pair is always 180$^{o}$. You're just one step away Subjective Medium Published on 09th 09, 2020 Questions 120418 Subjects 10 Chapters 88 Enrolled Students 86 #### Realted Questions Q1 Subjective Medium In figure given, PQ is parallel to RS, find x. Asked in: Mathematics - Straight Lines 1 Verified Answer | Published on 17th 08, 2020 Q2 Subjective Medium In Fig. sides $QP$ and $RQ$ of $\Delta PQR$ are produced to points $S$ and $T$ respectively. If $\angle SPR={ 135 }^{ }$ and $\angle PQT={ 110 }^{ }$, find $\angle PRQ$. Asked in: Mathematics - Lines and Angles 1 Verified Answer | Published on 09th 09, 2020 Q3 Single Correct Medium The measure of an angle which is four times its supplementary angle is: • A. $36^o$ • B. $180^o$ • C. $150^o$ • D. $144^o$ Asked in: Mathematics - Lines and Angles 1 Verified Answer | Published on 09th 09, 2020 Q4 Single Correct Medium If in triangles $XYZ, XY=XZ$ and $M,N$ are the midpoints of $XY,YZ$ and which one of the following is correct? • A. $MN=YZ$ • B. $NY=NZ=MN$ • C. $MX=MY=NY$ • D. $MN=MX=MY$ Asked in: Mathematics - Straight Lines 1 Verified Answer | Published on 17th 08, 2020 Q5 Subjective Medium What is an Obtuse Angle ? Asked in: Mathematics - Lines and Angles 1 Verified Answer | Published on 09th 09, 2020
# sRGB transform library ## Introduction The sRGB standard defines a color space, and a non-linear transfer function that maps numerical values to linear intensities. In particular, sRGB maps 0.0 to pure black and 1.0 to the white point of the device, but the sRGB value of 0.5 is not half the physical brightness of white (in fact it is 21.4% as bright). All popular computer displays and software use sRGB to represent colors, but doing image processing properly requires doing math in the linear domain. Hence conversions between sRGB and linear values are necessary for high-fidelity image processing. While the sRGB transform formulas are short, they are not easy to remember and require some care to avoid subtle problems. This small library saves the effort of repeatedly writing sRGB conversion functions in every application program and verifying the correctness of each copy. Java C C++ Python JavaScript TypeScript ## Math notes The transforms are defined as follows: • $$\text{srgbToLinear}(x) = \begin{cases} x / 12.92 & \text{if }0.0 ≤ x ≤ 0.04045 \\ \left(\frac{x + 0.055}{1.055}\right)^{2.4} & \text{if } 0.04045 < x ≤ 1.0 \end{cases}.$$ • $$\text{linearToSrgb}(x) = \begin{cases} 12.92x & \text{if }0.0 ≤ x ≤ 0.0031308 \\ 1.055 x^{1/2.4} - 0.055 & \text{if } 0.0031308 < x ≤ 1.0 \end{cases}.$$ The numerical constants in the formulas are inexact and lead to subtle consequences. The function srgbToLinear maps the input range [0.0, 0.04045] to the output range [0, 809/258400] = [0.0, 0.00313080495...], and maps the input range (0.04045, 1.0] to the output range ((1909/21100)2.4, 1] = (0.00313080728..., 1.0]. This function is one-to-one (injective), but its output ranges have a tiny gap of (0.00313080495..., 0.00313080728...] of length ~2×10−9. The function linearToSrgb maps the input range [0.0, 0.0031308] to the output range [0.0, 0.040449936], and maps the input range (0.0031308, 1.0] to the output range (0.04044990748..., 1.0]. Its two output ranges overlap in [0.04044993600, 0.04044990748...) with a length of ~3×10−8, making linearToSrgb not an one-to-one function. For almost all values of x ∈ [0.0, 1.0], the two possible round trip transforms from one space to the other space and back (e.g. sRGB-to-linear-to-sRGB) only yields tiny rounding errors based on the numerical precision (e.g. float vs. double). But for sRGB-to-linear-to-sRGB when x ∈ (0.040449936, 0.04045] (interval length 6.4×10−8), the result can have an error up to 3×10−8. Similarly for linear-to-sRGB-to-linear when x ∈ (0.0031308, 0.00313080728...] (interval length ~7×10−9), the result can have an error up to 3×10−9. Because these formulas imply that both round trip transforms are mathematically inexact on some values, applications should be designed to avoid sRGB/linear conversions as much as possible. For example, computer-generated graphics should process all aspects of a picture in linear color space, and at the last step convert to sRGB for image export.
# 11 points that should be noted by Amazon Redshift beginners この記事は公開されてから1年以上経過しています。情報が古い可能性がありますので、ご注意ください。 I have documented the points better to be noted that I have experienced in the project where Amazon Redshift has been used. It's nice if you feel they are helpful. If you think "What's Data Warehouse?", please refer to the following introductory articles I wrote before. (Sorry this article is Japanese version only;;) ### Difference from PostgreSQL Amazon Redshift is based on PostgreSQL. I have not used PostgreSQL in practice. If you have already got used to PostgreSQL, you should check the difference between Amazon Redshift and PostgreSQL in the following document. In this document you can check the unsupported functions, data types and so on. Amazon Redshift and PostgreSQL - Amazon Redshift And Amazon Redshift has a key and type such as sort key, distribution key, column compression type etc that PostgeSQL does not have. It's better to see the following articles when you design tables. Amazon Redshift Best Practices for Designing Tables - Amazon Redshift The following is a brief summary: Distribution key You can define only one distribution key per table. It can't be altered after table is made. Sort key You can define multi-column sort key. You can define a maximum of 400 SORTKEY columns per table. They can't be altered after table is made. Column compression type It can't be altered after table is made. If it is undefined and no data, you can set it automatically by setting the COMPUPDATE option 'ON' when running the COPY command. ### Too Slow if you insert data one by one You use ETL tools to load data from one database to another database. It's very useful, but Amazon Redshift is bad at INSERT a record one by one. If you want to load data at a faster pace, you should use the COPY command to load data. INSERT - Amazon Redshift However it is no problem that you use the INSERT command as INSERT ... SELECT statement. ### No error reported even if primary key constraints, unique constraints or foreign key constraints are violated You can define constraints by the CREATE TABLE statement. But data that violates the constraints can be inserted with no error. However the error will be reported when you violate the NOT NULL constraint. ### The COPY command inserts all records When you use the COPY command to load data, the data are loaded even if the some record with the same primary key have existed in the target table. As mentioned above, no error will be reported when the primary key constraint violation has made. If the record with the same primary key exists in the target table, there is a way that uses a staging table such as the following documents: ### When you upload CSV files It is important to note that you use the COPY command to load CSV files containing the data such as the following: • Data containing some commas. • Data containing some line breaks. • Data containing some empty character strings. • Data containing some NULL characters. If the data contains some commas or line breaks, you should use the COPY command with the CSV option, and the data between commas in the CSV file must be enclosed in double quotaions. And if the data have some empty character strings, you should consider whether you insert it as NULL or empty character string in the database. If you assume the empty character string as NULL, the EMPTYASNULL option must be presented in the COPY command. Finally, if the text data contains some NULL characters, the load process will fail. So you should delete them in advance. ### Supported data types Amazon Redshift support 11 data types. It's not so much. You can define the TEXT type or other data types in the CREATE TABLE statement then no error will be made. But the data type is converted to the VARCHAR data type internally. The column size is sometimes unwilling size, so you had better check the data type in the pg_table_def table. You would notice that there are no large object data type and binary data type. ### Character code cannot be selected In Amazon Redshift you cannot select character encoding except from UTF8. If the character encoding of the file to load is not UTF8, you convert it to UTF8. You would notice when you switch the database from another one. And if there are unsupported multibyte character in the file, the error will be made by default. You can use the COPY command with ACCEPTINVCHARS option to replace them with the specified character. ### When you add a user who has a reference privilege only By defalut, the database has a schema named 'public'. This is a specification of PostgreSQL. The user added by the CREATE USER command has CREATE and USAGE privileges by default against the schema. So you should create your original schema when you create a user who has a reference privilege only. You can use getdate function to get the system time as follows. But the timezone is UTC fixed, so you cannot get the Japan time. select getdate(); If you want to get the Japan time, use the convert_timezone function to convert the timezone as follows: select convert_timezone('JST', getdate()); If you want to get the date, use the trunc function as follows: select trunc(convert_timezone('JST', getdate())); You cannot select the storage size of Amazon Redshift instances like Amazon RDS. In case of Amazon Redshift, the storage size per node is decided by selecting the node type. So you can adjust the storage size by changing the number of nodes. The main difference between the dw1 series such as dw1.xlarge or dw1.8xlarge and the dw2 series such as dw2.large or dw2.8xlarge is that the storage is a HDD-based or a SSD-based. If you want to use a large storage, you should select the HDD-based dw1 series node type. If the node type is 8xlarge, the single node cannot be made. You need to create at least two nodes. ### When the PostgreSQL client timed out There is a case such that the connection to the Redshift instance timed out by the heavy processing when you use the SQL Workbench etc. But the requested process does not stop. You can see the request is still running in the AWS Management Console. In this case you have to cancel the request as follows: -- Identify the PID select pid, trim(user_name), starttime, substring(query,1,20) from stv_recents where status='Running'; -- Cancel the process cancel [PID]; Notice that the load continues to run in spite of the time-out. You had better define the Amazon CloudWatch alarm of the CPU usage rate or the storage usage rate. Step 6: Cancel a Query - Amazon Redshift ### Omake(Appendix) The following are useful SQL. And I often use the SQL introduced above, which identifies the PID and cancels a request. select * from stl_load_errors; --when you want to see the errors select * from pg_tables where schemaname = 'schema name' and tablename='table name'; --when you see the table list select * from pg_table_def where schemaname = 'schema name' and tablename='table name'; --when you see the column list Finally, I introduce the articles about Amazon Redshift I have seen often. (Sorry they are Japanese only;;)
• ### Axion Searches with Microwave Filters: the RADES project(1803.01243) March 3, 2018 hep-ph, hep-ex We propose, design and construct a variant of the conventional axion haloscope concept that could be competitive in the search for dark matter axions of masses in the decade 10-100 $\mu$eV. Theses masses are located somewhat above the mass range in which existing experiments have reached sensitivity to benchmark QCD axion models. Our haloscope consists of an array of small microwave cavities connected by rectangular irises, in an arrangement commonly used in radio-frequency filters. The size of the unit cavity determines the main resonant frequency, while the possibility to connect a {large} number of cavities allows to reach large detection volumes. We develop the theoretical framework of the detection concept, and present design prescriptions to optimize detection capabilities. We describe the design and realization of a first small-scale prototype of this concept, called Relic Axion Detector Exploratory Setup (RADES). It consists of a copper-coated stainless steel five-cavities microwave filter with the detecting mode operating at around 8.4 GHz. This structure has been electromagnetically characterized at 2 K and 298 K, and it is now placed in ultra-high vacuum in one of the twin-bores of the 9 T CAST dipole magnet at CERN. We describe the data acquisition system developed for relic axion detection, and present preliminary results of the electromagnetic properties of the microwave filter, which show the potential of filters to reach QCD axion window sensitivity at X-band frequencies.
# Federal Doctor Says He Was Removed For Resisting Unproven Coronavirus Mentor This thread meets the GD guidelines for discussing medical policy where politics are concerned, I know, I made that policy. How can we expect to find cures/vaccines when the doctors capable of doing it are removed? A high-ranking federal doctor focused on vaccine development says he was removed from his post because of his "insistence" that the government spend funds on "safe and scientifically vetted solutions" to address the Coronavirus crisis and not on "drugs, vaccines and other technologies that lack scientific merit." https://www.npr.org/sections/corona...doyg0CIEsrGXjDNL-yey80Yo-VR44Kdrui64MHLM9wnIM Last edited: DennisN, Klystron, Astronuc and 3 others Homework Helper 2022 Award What are we allowed to discuss...how big is the elephant in the room? sophiecentaur and BillTre Mentor What are we allowed to discuss...how big is the elephant in the room? We can discuss allowing critical valid medical work to continue without government interference. But we will not allow discussions of politics, who, etc... We will stay focused on the medicine. No mud slinging. I do not believe that any politician with no medical background should be allowed to control medicine or give medical advice to the public. "THAT" we can talk about. But we won't point fingers, this isn't politics, it's about the medicine. BillTre Homework Helper 2022 Award But it is an elephant !...(Your call). Mentor But it is an elephant !...(Your call). We only made it an elephant, we took an ant and mistakenly made it into an elephant. Our fault. Good intentions gone wrong. We didn't want political mudslinging, we had no intention of allowing important issues to be disallowed. I cannot imagine what could be more important right now. Astronuc, Dale, BillTre and 1 other person Gold Member 2022 Award But it is an elephant !...(Your call). Your use of an elephant instead of something else, say a donkey, further provokes thoughts of politics! dlgoff, vela, Astronuc and 4 others Gold Member Am i missing something ? The article can simply be boiled down to "Worker criticizes boss's stupid comment, gets canned". russ_watters Gold Member 2022 Award I do not believe that any politician with no medical background should be allowed to control medicine or give medical advice to the public. Its difficult to think of much else to say without going into specifics which related to political people and their intentions. Astronuc and Evo Mentor Am i missing something ? The article can simply be boiled down to "Worker criticizes boss's stupid comment, gets canned". Yes, you're missing what the doctor was working on and what he was resisting. xAxis, Astronuc and BillTre Mentor Its difficult to think of much else to say without going into specifics which related to political people and their intentions. I know its hard, but due to high level of reactions of, well, I can't say, due to the high level of reactions, we have to keep it as much about the science without naming names as silly as that is. hutchphd and BillTre sysprog I can't stand it when someone in charge does something like that -- especially when lives are in the balance -- and this doc is about to find the vaccine? -- what the heck? We need the freaking vaccine. People are dying way before their time. Last edited: Evo and BillTre Gold Member 2022 Award Well, it just another example of the extremely poor management of this whole mess by those who do the administrating nationally in this country, reagrdless of its consequences for the health and safety of its citizens. Klystron, Evo and sysprog Gold Member North of the 49th, our peerless feeder - after dedicating $120billion to "fight the coronavirus" has pumped a whole$20mil into vaccine research. Woohoo. That buys a decent lab for what, a month ? a week ? Keith_McClary Homework Helper 2022 Award Am i missing something ? The article can simply be boiled down to "Worker criticizes boss's stupid comment, gets canned". We can say that. but apparently we cannot say, in this forum, "Worker criticizes stupid boss's comment, gets canned". russ_watters, phinds and sysprog sysprog North of the 49th, our peerless feeder - after dedicating $120billion to "fight the coronavirus" has pumped a whole$20mil into vaccine research. Woohoo. That buys a decent lab for what, a month ? a week ? Although we would certainly like a vaccine to be available in less than a month, that mil number, as you seem to be strongly suggesting, doesn't even come close -- we probably should replace that 'm' with a 'b'. Last edited: Gold Member Although we would certainly like a vaccine to be available in less than a month, that mil number, as you seem to be strongly suggesting, doesn't even come close -- we probably should replace that 'm' with a 'b'. I don't think there's anybody that doesn't realize that it takes time, either ; so what's the political beef against research ? We (well, not me personally) have managed to knock out most of history's heavyweights. Staff Emeritus This will be very difficult to focus on the science, because the document that started this is a statement from a bunch of lawyers. At best this is one-side of the story, but it is not the same as a scientific paper. There is also one very odd thing about this - that Doctor X (can I call him that?) still has a job with HHS. He is a deputy assistant secretary, which means he is a political appointee (there are a handful who are career, but I did not find this listed as such on the Federal Register) so there is no reason he could not simply be replaced. The current administration has historically not held back on replacing people they would like replaced. Even odder, Dr. X began his appointment in 2016, which means he was appointed by the previous administration. It is rare, but not unheard of, for political appointees to stay on after a Change of Administration. And, while not exactly relevant, there is one more odd thing. The particular deputy assistant secretary position Dr. X held appears not to require Senate confirmation. There are only about a dozen of these positions around (there are supposed to be zero). Last edited: Infrared, russ_watters and sysprog sysprog I don't think there's anybody that doesn't realize that it takes time, either ; so what's the political beef against research ? We (well, not me personally) have managed to knock out most of history's heavyweights. I was trying to agree with a point that you made -- a few million dollars is not enough -- we should allocate and spend a few billion until we have a fix. Gold Member 2022 Award I do not believe that any politician with no medical background should be allowed to control medicine or give medical advice to the public. "THAT" we can talk about. Evo, If all politicians agreed with you the topic would not have come up but since at least one politician, and probably more, disagrees with you, I don't see how we can have "THAT" conversation without bringing in politics. But we won't point fingers, this isn't politics, it's about the medicine. I wish it were otherwise but I think this thread is doomed (on this forum). Bystander A Creator of the Ebola Vaccine Has Hope for Slowing Covid-19 Gary Kobinger says a vaccine targeting groups like the elderly could be ready in less than a year, and control measures are slowing the disease's spread. https://www.wired.com/story/creator-ebola-vaccine-hope-slowing-covid-19/ "You have to be very careful about creating false hope with therapies. On one hand, if you don’t have a randomized trial, it’s hard to make any claim about their effectiveness. At the same time, it’s important to listen to health care workers who are using those drugs on the front lines. They have a very good sense of what may be worth pursuing and not pursuing in trials, even if they are not using it in a randomized trial. So with drugs like chloroquine and azithromycin that are already approved, let’s put them in the clinic as soon as possible, and at same time design the best clinical study you can." [Bolding by me] Antimalarials widely used against COVID-19 heighten risk of cardiac arrest. How can doctors minimize the danger? https://www.sciencemag.org/news/202...-heighten-risk-cardiac-arrest-how-can-doctors "Evidence of potential harm from these drugs is beginning to trickle out. A clinical trial in Brazil that gave chloroquine and azithromycin to 81 people hospitalized for COVID-19 was halted after investigators found more deaths in the group getting the higher of two doses, according to a preprint the team published on 16 April on medRxiv. Electrocardiography (EKG) readouts indicating increased arrhythmia risk were also more common in the high-dose group. Researchers conducting the trial received death threats on social media, and conservative media outlets accused them of giving patients excessively high doses to purposely smear the drug. An analysis of data from 368 U.S. veterans treated for COVID-19, posted in a preprint today, found the risk of death from any cause was greater for those who received hydroxychloroquine than for those who didn’t, even after researchers adjusted for the fact that patients with more severe disease were more likely to receive the drug. And a woman in New York died this month after her general practitioner prescribed hydroxychloroquine and azithromycin for coronaviruslike symptoms, NBC News reported last week. (There’s no proof that drug-induced arrhythmia caused her death, Ackerman says, “but it smells awfully fishy.”) Now, researchers are trying pin down the rates of this side effect in COVID-19 patients and are urging diligent heart monitoring during treatment." [Bolding by me] Klystron, Astronuc and hutchphd Gold Member 2022 Award AMAZING COINCIDENCE: After making post #19, I went downstairs for breakfast and the first article I read was about how the Mayor of Philly, during the 1918 flu pandemic, left to his "health commissioner, Wilmer Krusen, a political appointee with no prior public health experience" as to whether or no to hold a massive war bond rally. Health officials had warned vehemently that the parade should not be held. Hundreds of cases had already been diagnosed and some dealths as well. It had already become clear that this was a pandemic. but Krusen merely requested that people cover their mouth if they cough. 200,000 tightly jammed spectators watched a 2-mile long parade of boy scouts, marching bands, etc go down the main avenue. Within days the city's hospitals were swamped and a month later 12,000 were dead. THEN, to really smack me in the face, the second article was about today in Iran where one of the big guns in their Academy of Medical Science is a "the most trusted adviser"of the head ayatollah of the country and this guy promotes widely debunked alternative medicine a cures for the virus. This Academy of Medical Science requires pharmacists in Iran to study homeopath for a year before getting their license because the politicians don't trust Western medicine. So, @Evo, how do you have any kind of complete discussion about things like the above and the current situation we are discussing, without any comment on the politicians involved? Don't get me wrong. I agree w/ your intent but I think you are being naive about the necessary political side of the discussion. hutchphd and atyy Gold Member I was trying to agree with a point that you made -- a few million dollars is not enough -- we should allocate and spend a few billion until we have a fix. Yes, I was agreeing with your agreeing Gold Member 2022 Award Yes, I was agreeing with your agreeing Hey guys, get a room. sysprog, BillTre and Mondayman Gold Member Hey guys, get a room. Room service menus are bad enough even without restrictions in place. On that note, it's going to be interesting(/horrifying) to see the birth stats in 7-8 months. phinds Mentor I do not believe that any politician with no medical background should be allowed to control medicine or give medical advice to the public. "THAT" we can talk about. I know we're in the midst of a crisis, but that would not be practical/possible, and isn't a feature of high level leaders/managers in any context I can think of. High level managers by nature must make decisions on issues they know little or nothing about, because it is impossible to have the expertise/experience of the hundreds or millions of people working for them. Sure, it would be nice if high level politicians during a health crisis had appropriate medical/scientific backgrounds. It would also be nice if during an economic crisis they had an applicable economics/business background. And when there's judges to appoint, a legal background. And when there's infrastructure decisions to make, an engineering/construction background. Etc., etc. That , of course, is impossible. Sometimes you can pick the one most important trade skill for a narrowly focused business, but even that will have limited applicability to that person's job as a manager. What's really needed from leaders/managers (except some in very narrowly focused industries) is leadership/management skills, not technical skills. Applied here, what's needed is: • The ability to identify/select, trust and empower experts in the necessary fields. • The ability to make decisions on matters in which they are not experts by absorbing information and using appropriate criteria to weigh and select from options provided. • The ability to communicate clearly, concisely and consistently. • Decisiveness; Choosing a path and staying with it for long enough for it to develop. • Flexibility; The ability to change path at an appropriate time in the face of new information. • A high level of confidence. • Interpersonal and political skills. I believe the technical term for this is "schmoozing". hutchphd, Klystron, sysprog and 4 others Mentor AMAZING COINCIDENCE: After making post #19, I went downstairs for breakfast and the first article I read was about how the Mayor of Philly, during the 1918 flu pandemic, left to his "health commissioner, Wilmer Krusen, a political appointee with no prior public health experience" as to whether or no to hold a massive war bond rally. Health officials had warned vehemently that the parade should not be held. Hundreds of cases had already been diagnosed and some dealths as well. It had already become clear that this was a pandemic. but Krusen merely requested that people cover their mouth if they cough. 200,000 tightly jammed spectators watched a 2-mile long parade of boy scouts, marching bands, etc go down the main avenue. Within days the city's hospitals were swamped and a month later 12,000 were dead. THEN, to really smack me in the face, the second article was about today in Iran where one of the big guns in their Academy of Medical Science is a "the most trusted adviser"of the head ayatollah of the country and this guy promotes widely debunked alternative medicine a cures for the virus. This Academy of Medical Science requires pharmacists in Iran to study homeopath for a year before getting their license because the politicians don't trust Western medicine. So, @Evo, how do you have any kind of complete discussion about things like the above and the current situation we are discussing, without any comment on the politicians involved? Don't get me wrong. I agree w/ your intent but I think you are being naive about the necessary political side of the discussion. It's not that I think we can have a complete discussion of the situation without comment of who was involved, but , we're not allowed to, I've asked to have the rule relaxed due to the pandemic and I've been overruled. The best we can do is show what's happening, maybe people that see it can get involved elsewhere. Klystron, hutchphd and phinds Staff Emeritus Sure, it would be nice if high level politicians during a health crisis had appropriate medical/scientific backgrounds. The "doctor" in question is not a medical doctor. His bio says he does have a PhD, but normally that does not make someone a "doctor". His boss, however, is a medical doctor. His boss is a lawyer. His boss is an elected official. russ_watters Mentor Sometimes you can pick the one most important trade skill for a narrowly focused business, but even that will have limited applicability to that person's job as a manager. What's really needed from leaders/managers (except some in very narrowly focused industries) is leadership/management skills, not technical skills. Applied here, what's needed is: • The ability to identify/select, trust and empower experts in the necessary fields. • The ability to make decisions on matters in which they are not experts by absorbing information and using appropriate criteria to weigh and select from options provided. • The ability to communicate clearly, concisely and consistently. • Decisiveness; Choosing a path and staying with it for long enough for it to develop. • Flexibility; The ability to change path at an appropriate time in the face of new information. • A high level of confidence. • Interpersonal and political skills. I believe the technical term for this is "schmoozing". *Know when not to act out in revenge when you feel slighted Klystron, russ_watters, phinds and 2 others I wrote a long response to this thread. Then I deleted it. Now I feel better. ChemAir, Klystron, jbriggs444 and 9 others Gold Member 2022 Award I wrote a long response to this thread. Then I deleted it. Now I feel better. Abe Lincoln used to write long vicious letters to political opponents, put them in a drawer, then take them out a week later and tear them up. He would agree with you. atyy, wukunlin, Astronuc and 6 others Gold Member My view is that government scientists should have full academic freedom in speaking and publishing on purely scientific matters, but when they are speaking as representatives of government institutions, there can be reasonable restrictions regarding what they say on public policy matters. If an employee disregards reasonable restrictions when speaking on public policy matters, removal is an option. If someone is really that good a scientist, there should be available work in the private sector. russ_watters Gold Member 2022 Award My view is that government scientists should have full academic freedom in speaking and publishing on purely scientific matters, but when they are speaking as representatives of government institutions, there can be reasonable restrictions regarding what they say on public policy matters. This thread is not about a pubic health official commenting on policy matters and getting in trouble but on a public official / scientist talking about scientific fact and getting in trouble. There has been a lot of that lately in America. Evo and BillTre Homework Helper 2022 Award My view is that government scientists should have full academic freedom in speaking and publishing on purely scientific matters, but when they are speaking as representatives of government institutions, there can be reasonable restrictions regarding what they say on public policy matters. If an employee disregards reasonable restrictions when speaking on public policy matters, removal is an option. If someone is really that good a scientist, there should be available work in the private sector. I'm sorry but this is so generic as to be cryptic. 1. Scientific and Public Policy matters are almost never distinct. 2. How is reasonable determined? Do we allow the mentally ill to do it? 3. The private sector is almost certainly more restrictive: one of the lures of public service is that it is, well, public BillTre Staff Emeritus Should a DOE program manager be able to say "Despite the administration's objections, the science of a Chinese high energy pp collider is compelling and the US should participate."? russ_watters Gold Member Should a DOE program manager be able to say "Despite the administration's objections, the science of a Chinese high energy pp collider is compelling and the US should participate."? I think this issue is very clearly one of policy, whereas the issue of which treatments for a disease deserve more funding (the issue over which Richard Bright was allegedly removed from his position) is more clearly a scientific issue. Ultimately, the administration has the ability to make funding decisions like these, but if the decision was really made to place the scientific judgement of the President on the effectiveness of chloroquine as a treatment over the scientific judgement of Bright, I believe that this reflects some very bad practices within the leadership of the administration. Speaking of unproven Coronavirus treatments, here is a selection from the transcript of yesterday's presidential Coronavirus briefing: THE PRESIDENT: Thank you very much. So I asked Bill a question that probably some of you are thinking of, if you’re totally into that world, which I find to be very interesting. So, supposing we hit the body with a tremendous — whether it’s ultraviolet or just very powerful light — and I think you said that that hasn’t been checked, but you’re going to test it. And then I said, supposing you brought the light inside the body, which you can do either through the skin or in some other way, and I think you said you’re going to test that too. It sounds interesting. ACTING UNDER SECRETARY BRYAN: We’ll get to the right folks who could. THE PRESIDENT: Right. And then I see the disinfectant, where it knocks it out in a minute. One minute. And is there a way we can do something like that, by injection inside or almost a cleaning. Because you see it gets in the lungs and it does a tremendous number on the lungs. So it would be interesting to check that. So, that, you’re going to have to use medical doctors with. But it sounds — it sounds interesting to me. So we’ll see. But the whole concept of the light, the way it kills it in one minute, that’s — that’s pretty powerful.
# IPMAT Question Paper 2019 | IPM Indore Quants ###### IPMAT Sample Paper | IPMAT Question Paper | Question 39 IPMAT 2019 Question Paper IPM Indore Quantitative Ability. Solve questions from IPMAT 2019 Question Paper from IPM Indore and check the solutions to get adequate practice. The best way to ace IPMAT is by solving IPMAT Question Paper. To solve other IPMAT Sample papers, go here:IPM Sample Paper Question 39: The function f(x) = $$frac{x^{3} - 5x^{2} - 8x}{3}\\$ is 1. positive and monotonically increasing for x $\in$-$infty, \frac{5-\sqrt{57}}{2}\\$) and x $\in$$frac{5+\sqrt{57}}{2}, +\infty\\$) 2. negative and monotonically decreasing for x $\in$-$infty, \frac{5-\sqrt{57}}{2}\\$ and x $\in$$frac{5+\sqrt{57}}{2},+\infty\\$) 3. negative and monotonically increasing for x $\in$-$infty, \frac{5-\sqrt{57}}{2}\\$) and positive and monotonically increasing for x $\in$$frac{5+\sqrt{57}}{2},+\infty\\$) 4. positive and monotonically increasing for x $\in$-$infty, \frac{5-\sqrt{57}}{2}\\$) and negative and monotonically decreasing for x $\in$$frac{5+\sqrt{57}}{2},+\infty\\$) ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer Let’s find the roots of the function, That is where the function takes the value 0. f$x) = 0. $$frac{x^{3} - 5x^{2} - 8x}{3}\\$ = 0 x3- 5x2- 8x = 0 x$x2−5x−8) = 0 x = 0 or x2−5x−8 = 0 x2−5x−8 = 0 x2−5x + $$frac{25}{4}\\$ −$\frac{25}{4}\\$ −8 = 0$x - $$frac{5}{2}\\$ )2- $\frac{57}{4}\\$ = 0$x - $$frac{5}{2}\\$ )2= $\frac{57}{4}\\$ x - $\frac{5}{2}\\$ = +$\frac{\sqrt{57}}{2}\\$$or) x - $$frac{5}{2}\\$ = - $\frac{\sqrt{57}}{2}\\$ x = $\frac{5}{2}\\$ + $\frac{\sqrt{57}}{2}\\$ or x = $\frac{5}{2}\\$ - $\frac{\sqrt{57}}{2}\\$ Therefore, the roots of the equation $\frac{x^{3} - 5x^{2} - 8x}{3}\\$ are 0, $\frac{5}{2}\\$ + $\frac{\sqrt{57}}{2}\\$, $\frac{5}{2}\\$ - $\frac{\sqrt{57}}{2}\\$ That means, when plotted f$x) will be 0 at 3 points when x = 0 or $$frac{5}{2}\\$ + $\frac{\sqrt{57}}{2}\\$ or $\frac{5}{2}\\$ - $\frac{\sqrt{57}}{2}\\$ Arranged in increasing order the roots are $\frac{5}{2}\\$ - $\frac{\sqrt{57}}{2}\\$ , 0 , $\frac{5}{2}\\$ + $\frac{\sqrt{57}}{2}\\$. Check f$x) at a point which is less than $$frac{5}{2}\\$ - $\frac{\sqrt{57}}{2}\\$ and at a point greater than $\frac{5}{2}\\$ + $\frac{\sqrt{57}}{2}\\$ f$-2) = $$frac{$-2$^{3} - 5(-2)^{2} - 8(-2)}{3}$ = $\frac{-8-20-16}{3}\\$ = $\frac{-44}{3}\\$ = -ve. f$10) = $$frac{$10$^{3} - 5(10)^{2} - 8(10)}{3}$ = $\frac{1000-500-80}{3}\\$ = $\frac{420}{3}\\$ = 140 =+ve Since f$x) is negative below $$frac{5}{2}\\$ - $\frac{\sqrt{57}}{2}\\$ and positive above $\frac{5}{2}\\$ + $\frac{\sqrt{57}}{2}\\$. And since it is a continuous function, the function looks something like this. From the graph, only Option C is correct. f$x) is negative and monotonically increasing for x $$in$-$infty, \frac{5-\sqrt{57}}{2}\\$) and positive and monotonically increasing for x $\in$$frac{5+\sqrt{57}}{2},+\infty\\$) The question is"The function f$x) = $$frac{x^{3} - 5x^{2} - 8x}{3}\\$ is" ##### Hence, the answer is negative and monotonically increasing for x $\in$-$infty, \frac{5-\sqrt{57}}{2}\\$) and positive and monotonically increasing for x $\in$$frac{5+\sqrt{57}}{2},+\infty\\$) Choice C is the correct answer ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ###### Already have an Account? ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Mobile:$91) 99626 48484 / 94459 38484 WhatsApp: WhatsApp Now Email: [email protected]
# In any metric space$(M,D)$, prove that $D(a_1,a_n)\leq D(a_1,a_2)+D(a_2,a_3)+\cdots+D(a_{n-1},a_n)$ In any metric space $$(M,D)$$, prove that $$D(a_1,a_n)\leq D(a_1,a_2)+D(a_2,a_3)+\cdots+D(a_{n-1},a_n)$$ for any $$a_1,a_2,a_3,\ldots,a_n \in M$$ how to we approach this problem is we prove by Mathematical Induction • Just iterate the triangle inequality. – Francesco Polizzi Sep 6 '17 at 15:15 • @FrancescoPolizzi..sorry i did't get can you give me one more step – Inverse Problem Sep 6 '17 at 15:18 For $n=2$, it is trivial. If it holds for a certain $n$, then\begin{align}D(a_1,a_{n+1})&\leqslant D(a_1,a_n)+D(a_n,a_{n+1})\\&\leqslant D(a_1,a_2)+D(a_2,a_3)+\cdots+D(a_{n-1},a_n)+D(a_n,a_{n+1}).\end{align}
# The .NET Framework Analyzer You can use the .NET Framework Analyzer to find potential issues in your .NET Framework-based application code. This analyzer finds potential issues and suggests fixes to them. The analyzer runs interactively in Visual Studio as you write your code or as part of a CI build. You should add the analyzer to your project as early as possible in your development. The sooner you find any potential issues in your code, the easier they are to fix. However, you can add it at any time in the development cycle. It finds any issues with the existing code and warns about new issues as you keep developing. ## Installing and configuring the .NET Framework Analyzer The .NET Security Analyzers must be installed as a NuGet package on every project where you want them to run. Only one developer needs to add them to the project. The analyzer package is a project dependency and will run on every developer's machine once it has the updated solution. The .NET Framework Analyzer is delivered in the Microsoft.NetFramework.Analyzers NuGet package. This package provides only the analyzers specific to the .NET Framework, which includes security analyzers. In most cases, you'll want the Microsoft.CodeAnalysis.FxCopAnalyzers NuGet package. The FxCopAnalyzers aggregate package contains all the framework analyzers included in the Framework.Analyzers package as well as the following analyzers: To install it, right-click on the project, and select "Manage Dependencies". From the NuGet explorer, search for "NetFramework Analyzer", or if you prefer, "Fx Cop Analyzer". Install the latest stable version in all projects in your solution. ## Using the .NET Framework Analyzer Once the NuGet package is installed, build your solution. The analyzer will report any issues it locates in your codebase. The issues are reported as warnings in the Visual Studio Error List window, as shown in the following image: As you write code, you see squiggles underneath any potential issue in your code. Hover over any issue and you see details about the issue, and suggestions for any possible fix, as shown in the following image: The analyzers examine the code in your solution and provide you with a list of warnings for any of these issues: ### CA1058: Types should not extend certain base types There are a small number of types in the .NET Framework that you should not derived from directly. Category: Design Severity: Warning Additional information: CA:1058: Types should not extend certain base types ### CA2153: Do not catch corrupted state exceptions Catching corrupted state exceptions could mask errors (such as access violations), resulting in an inconsistent state of execution or making it easier for attackers to compromise a system. Instead, catch and handle a more specific set of exception type(s) or re-throw the exception Category: Security Severity: Warning Additional information: ## CA2153: Do not catch corrupted state exceptions ### CA2229: Implement serialization constructors The analyzer generates this warning when you create a type that implements the ISerializable interface but does not define the required serialization constructor. To fix a violation of this rule, implement the serialization constructor. For a sealed class, make the constructor private; otherwise, make it protected. The serialization constructor has the following signature: public class MyItemType { // The special constructor is used to deserialize values. public MyItemType(SerializationInfo info, StreamingContext context) { // implementation removed. } } Category: Usage Severity: Warning Additional information: CA2229: Implement serialization constructors ### CA2235: Mark all non-serializable fields An instance field of a type that is not serializable is declared in a type that is serializable. You must explicitly mark that field with the NonSerializedAttribute to fix this warning. Category: Usage Severity: Warning Additional information: CA2235: Mark all non-serializable fields ### CA2237: Mark ISerializable types with serializable To be recognized by the common language runtime as serializable, types must be marked by using the SerializableAttribute attribute even when the type uses a custom serialization routine by implementing the ISerializable interface. Category: Usage Severity: Warning Additional information: CA2237: Mark ISerializable types with serializable ### CA3075: Insecure DTD processing in XML If you use insecure DtdProcessing instances or reference external entity sources, the parser may accept untrusted input and disclose sensitive information to attackers. Category: Security Severity: Warning Additional information: A3075: Insecure DTD processing in XML ### CA5350: Do not use weak cryptographic algorithms Cryptographic algorithms degrade over time as attacks become more advanced. Depending on the type and application of this cryptographic algorithm, further degradation of its cryptographic strength may allow attackers to read enciphered messages, tamper with enciphered messages, forge digital signatures, tamper with hashed content, or otherwise compromise any cryptosystem based on this algorithm. For encryption, use an AES algorithm (AES-256, AES-192 and AES-128 are acceptable) with a key length greater than or equal to 128 bits. For hashing, use a hashing function in the SHA-2 family, such as SHA-2 512, SHA-2 384, or SHA-2 256. Category: Security Severity: Warning Additional information: CA5350: Do not use weak cryptographic algorithms ### CA5351: Do not use broken cryptographic algorithms An attack making it computationally feasible to break this algorithm exists. This allows attackers to break the cryptographic guarantees it is designed to provide. Depending on the type and application of this cryptographic algorithm, this may allow attackers to read enciphered messages, tamper with enciphered messages, forge digital signatures, tamper with hashed content, or otherwise compromise any cryptosystem based on this algorithm. For encryption, use an AES algorithm (AES-256, AES-192 and AES-128 are acceptable) with a key length greater than or equal to 128 bits. For hashing, use a hashing function in the SHA-2 family, such as SHA512, SHA384, or SHA256. For digital signatures, use RSA with a key length greater than or equal to 2048-bits, or ECDSA with a key length greater than or equal to 256 bits. Category: Security Severity: Warning Additional Information: CA5351: Do not use broken cryptographic algorithms
C64 maze generator T-shirts! Spiral program T-shirts! Pixel Deer T-shirts! BASIC code T-shirts! Breakout T-shirts! Shooting gallery T-shirts! Vector ship T-shirts! Pak Pak Monster T-shirts! This mini forum is intended to provide a simple means of discussion about the Datapoint Corporation Datapoint 2200 computer. If you want to share your own experience or memories, or add relevant information about this system: post a message! For other purposes like sales messages, hardware & software questions or information requests, please use our main forum. Friday 6th May 2011 dave_schummers (california) i had the pleasure of working @the disk works in mt.view,as the equipment maintenance mechanic from aprox 82-87,i maintained the westec single side disk polishers,the strasbaugh 6sr4,the plating lines and all related equipment .,in the end ,our division was absorbed by xebec corp.and i was included in a group that went to "information memories corp",another pilot type plating set up..most colorful character-co worker,Mel Dike Monday 4th April 2011 Richard DesChenes (Florida) I worked at Datapoint in test engineering, and did failure analysis on the production floor. It was a challenge to troubleshoot the 2200''s microprocessor made of discrete components. Working in machine language became second nature. The place was a circus and things changed daily, it was a fun place to work. Wednesday 9th March 2011 Robert J. Stevens (Menomnee Falls, Wisconsin, USA) I first became acquainted with Datapoint while working as a Computer Operator arond 1975 in New Jersey when the Boss brought in a Datapoint. I had gone to Programming School and told him that I could Program the Machine. He gave me the Job. It was one of the Machines that used Cassettes for I/O. The manual said "Go have a cup of coffee while the machine copied your work from one Cassette to another". I was writing Software to transfer Hospital Census Data from the Hospital to our Computer Site for Processing. By that time they had a Datapoint System that would write to a Computer Tape and I added a routine that played "Shave $Haircut Six Bits" when the tape was ready to be transfered to the Univac 9300. Later on I was asked to produce a Program that would allow up to 33 lines of input for a Hospital Admissions Form. Since the Machine only allowed 11 Lines I had to DUMP the 8K of Memory to the Printer then Decode it and reassemble it into a System that Mimic''d DataBus. I even added interrupt control so one could back up fields to re-enter them. It took me 6 months but it ended up on the ROUND file. I worked with Datapoints until 1979 when I left New Jersey and moved to Wisconsin. Friday 18th February 2011 Barney Fleetwood (US) I became familiar with Datapoint products as a user in the early 70''s. I worked for a time sharing company and we started replacing our Teletype terminals with 3300''s. When the 2200 was introduced we purchased one mainly to see if a genuine computer could really fit on a desktop. These were the days when our mainframes took up massive amounts of space and resources. I joined Datapoint in early 1979 as a product support engineer in San Antonio. My first products were the 6600 and the Channel Adapter. I saw an earlier post on here by Steve Wolf. He and I traveled around the country supporting the Channel Adapter. He was software support and I was hardware support. Steve definitely got the short end of the stick as the hardware was considerably more stable than the software but he always prevailed. I was laid off from Datapoint in 1985 (thank you Asher Edelman) and came back to Intelogic Trace in 1986 where I stayed until 1994. It was a great ride while it lasted and the people I worked with and for were absolutely incredible. Wednesday 16th February 2011 Stephen Deane (Toronto / Canada) I''m an ex-datapoint canada employed Just saying HELLO Wednesday 15th December 2010 Robert Jackson (Australia) I worked for Datapoint as a technician in their Australian board repair centre at Artarmon Sydney circa 1981-83. I did chip level debug and repair of the 2200, 5500 and 6600 main circuit boards. It was a great experience to see how a CPU was constructed from TTL gates. Friday 19th November 2010 Carl Zettner (US) Family FotoFinder FYI we are now (trying) to put up the complete history of Datapiont and the 2200 at our (still being built) site www.Datapoint.org. If you are an ex-Datapointer or just curious please join us there. Thursday 29th July 2010 Igor (North Carolina/USA) Frank! We did indeed have a great time working in Penn Plaza for Datapoint in those heady days in the early ''80s. Things have never been as great as that ever since. Friday 6th November 2009 Frank Rocco (NY) Started out of DeVry in 1979. I worked out of Penn Plaza and covered Manhattan. I wioked on the 1100, but also the 2200. Was a heavy piece of equipment. Also learned Arcnet and printers during my years there. Had a lot of good times but left in 1983. Friday 6th February 2009 Steve Parrish (Westminster, SC) Employed at Datapoint from 1978-1989. I really enjoyed reading the forum. I joined Datapoint Corporation in 1978 as a Systems Engineer responsible for pre$ post sales support for customer accounts throughout North Carolina. In 1980, transitioned from SE to sales as an Account Manager for Leggs'' Products (the folks who used to manufacture panty hose $package them into plastic egg shells). We did a great business there as they owned 5530''s Datashare systems in each of their 5 manufacturing facilities and had a much larger system at their mail order facility. The mail order house moved from 5530$ 6600 based Datshare systems which were subsequently grown into an ARC network. The ARC had an 8800 file server with MIDs disks and 3800''s replaced the 3600 terminals previously used in the Datashare system. After that, I was transferred to San Antonio in 1980 as the sales plan was to hire 600 professional sales people in the US with computer sales experience to leverage our huge advantages over the competitors. After Sam Walker and me spent a year or so hosting, instructing new hire sales professional from all over the US on our product line from the 5500, 6600, 8800, 8600, 3800, 1800,1500, Light Link, our ARC based resource sharing and all the wonders of the Datapoint developments. I recall at one time during the early 80''s when the stock split twice two-for-one over a 13 month period. While mainframe and other mini-computer competitors were explaining how they grew their systems (forklift model) relative to our ability to simply "clip-on" additional processing power as needed without the need for re-programming absolutely blew the competition away. Incremantal growth as processing requirements demanded was the mantra. We would have a class of around 30 new hires for two weeks before they returned to their respective territories to engage in marketing Datapoints'' product line. During this period, we had all the who''s who of the fortune accounts as customers. Subsequently, after the hiring frenzy of Steve James and G. Millard Allen subsided. I joined the likes of Buck Buchanan, Sal Bruno, Jim Whitehouse and tha cast of others in Product Marketing with an assignment to "Large Systems" Subsequently joined a new division lead by John Tysall and Jim Cogan with a great team in the Small Business Computer Division where we promoted and provided sales support predominantly for the 1560 product line. The part I never could comprehend is that when Asher Adelman and his investors decided to take over the company, they announced that they were going take it over and sell and/or ''spin off'' the parts. This stopped sales dead in their tracks to Citibank, Texaco, Chase Manhatten Bank and a host of other fortune account customers we had as they wanted a "single source provider" e.g. one stop shop for computers peripherals and support. The result was, the arbitrage group crashed the company just as they were taking it over. From my view, this was much more devastating to Datapoint than all the other stuff having to do with accounting issues, shipping equipment to wharehouses, etc. etc.. Anyway, the 12 years I spent were an exciting and fulfilling experience that I''ll never forget. Cheers to all of you Datapointers! Saturday 3rd January 2009 Kevin Willois (Allentown, N.J. USA) Guy! Frank! And all the rest of the NYC techs out there. Datapoint was the first real job I got after graduating from tech school. ''81 to ''86 I think. The 2200 and the line of processors that followed were great for the time, but were really heavy and difficult to work on. Tolerances for the back plane/power supply were tight. Wires tended to short if you were careless (blue smoke generators), but no one could deny the elegance and the impact that ARC had on the computing community. I''m a musician/teacher now, would love to know what happend to the intelogic trace guys after the company was sold. Had some really good times before the company lost it''s way. Wednesday 15th October 2008 Bob Stephens (USA) I joined Datapoint as a software developer in the early ''70s when its name was Computer Terminal Corporation (CTC). I later went into the field through the Systems Engineering organization and then back into corporate in Software Support. Pretty amazing. I found this site while searching for information on Infoswitch, a Datapoint LDCS/ACD product in the ''70s. Noted several extremely talented folks on this forum which I had the privilege to work with. Definitely pioneers in their own right. Tuesday 3rd June 2008 Chris Hall (England) Hi, this is note is really aimed at John Sutherland. John I may have met you at Ventek at some point, maybe training courses, I worked out of the Epping branch from 1976 and then out of Centerfile in London till about 79. Your note about those blessed power supllies brought it all back. How many of those went bang in your face the moment they were powered on by the sliding on-off switch. As you recalled one of the biggest users were indeed BR and the recollections of trudging down the line to a signal mans box some at the dead of night seems like yesterday. I worked with a real good bunch of guys, Bob Riddel, Tony Munn, Steve Pyne. They were a good company to work for, I broke my leg in 75 and was of work for a total of 6 months and they paid me full pay for all that time and I'd only been with them 1 week, don't think that would happen today. Saturday 29th September 2007 Colin Wheeler (Melbourne, Australia) I also have many fond memories working as a technician (actually receiving the “gold” award) which still sits with pride of place in the study, leaving I think around 1987. Many laughs with folks like Joe Nanfro, Brian Mackrill, Dave Westhorpe, Gina on reception and who could forget Jeno Liptak. After leaving I had the pleasure of meeting Jonathan Schmidt and Louis Donzis purchasing Performance Technology kit to replace the old DP gear at Jetset Tours. These guys were simply geniuses. Those truly were the days. Sunday 19th August 2007 Stephen Wolf (Austin, Texas) I worked for Datapoint from 1977 to 1984. I worked in the field, support, and development. The people I worked with were top notch. Had a lot of time and made several long term relationships. Wednesday 27th June 2007 Don Cheeseman (Houston, Texas) Wow. I wasn't even aware there was forum for the Datapoint vets. I've still got one of the older slow-scan 2200s (with a Honeywell moniker) and it still works, as well as a old 1560 that I picked up at a warehouse years ago in North Austin. I was a programmer with Datapoint from 1977 until 1986. It's nice to hear that there are still so many ex-Datapointers still out there. Tuesday 5th June 2007 Datapoint was my first real job. From 1979 to 1992. I remember opening more 3360 terminals than most surgeons open up people. It was a fantastic experience. 3360,2200,5500,6600, you name it. Don't forget the ARCNET. Loved it. Tuesday 10th April 2007 Tom Orbeck (Austin. Texas) After being a Datapoint customer in Minneapolis, I worked for Datapoint in San Antonio as a software developer and later in Software Support. It was a GREAT experience and I learned a lot. Datapoint was ahead of its time for a while and an exciting place to work. Thursday 8th February 2007 Guy Perrusio (USA) I was a field service tech for Datapoint in New Jersey from July 1978 til January 1983 and then a District Service Manager in NYC from January 1983 until January 1987. If you talk about Datapoint and CTC, you have to make mention of the old 3300 series terminals. Even in 1978, they were a bear to repair but were very successful in replacing many teletype machines. If there are any Datapoint old timers that would like to talk about the old days, please don't hesitate to reach out. Also, does anyone have a recollection of yet another spinoff - Teknikron/Infoswutch??? Thursday 11th January 2007 Paul "Jerry" Scannell (USA) I worked for Datapoint from 1977-1980 in the Waltham, MA office. I was a "Field Engineer" by trade but had started getting into software because of the Datapoint products. I installed and serviced the full gamut of Datapoint systems including the 1100/2200/5500/6600, ARC, DataShare, Control Data disk drives, and InfoSwitch! At some point I had gotten a hold of a "dis-assembler" program from someone gave meand I had decoded the DOS operating system; figured out how it worked; and decided that programming was where I should be. Now 26 years later, I have programmed in just about every conceivable platform including: hardware diagnostics, repair depot management systems, order entry systems, temperature controller firmware, and most recently web applications. I owe my career to Datapoint. My time with them was very memorable and feel truly saddened by their demise. But I am so glad to find this forum! Wednesday 27th September 2006 Murray Downes (Dunedin New Zealand) I joined Datapoint NZ in 1985, transferred to London 1987 and worked at Station House, then Neasden, Harefield... back to Neasden - finally to European Operations in Paris. Sales... 8600, 8800 then 7800... finally helped launch the AT&T Definity through European subs. This was a great experience - all of it. Does anyone know what happened to Dale Haire (ex SAT, ex Belgium...) ex Intl? Friday 4th August 2006 Rudolph J. R. Wratten (San Antonio) I worked with Datapoint on an extension of the InfoSwitch, what was later to become known as automated wiretapping. Datapoint exec's decided that this was a "second tier" market, boy were they wrong! Wednesday 2nd August 2006 AJ (London) I worked for Datapoint from 1975 to 1978 as a Hardware Engineer/Superviser repairing PCB's down to component level at the Park Royal, London repair centre. I repaired processors, memory, power supplies - you name it I did it. It was great fun and I was completely fulfilled, financially and emotionally. Opposite to what I feel now. When I joined in 1975 the company was Ventek which was soon taken over by Datapoint. This was my first entry into the world of computers and I haven't looked back, although I feel less satisfied with my position now. It's great to read other peoples experiences here. You know what? I still have Datapoint 2200 manuals etc in my garage and I was going to through them out the other day, it must be the memories that stopped me from doing so !!!! Thursday 13rd July 2006 John J. Doonan (new york ) I Started working at when it was known as CTC (Computer Terminal Corp.) Best job i ever. Thursday 16th March 2006 Paola (Italy) I made a mistake: I worked in INFOREX first, which then became DTAPOINT.. Who rimember that? Ciao Thursday 16th March 2006 Paola (Italy) Hello to all of you ! I use to work for DATAPOINT ITALY from 1973 through 1988 at the import dept: so i knew and met lot of people. I just would like to say that those years were really wonderful for me. I loved my job and I still remember those days.. I would like to know where is Linda Fuller, now: if you are here, please write me. Hope to hear news soon saluti a tutti Paola Wednesday 8th February 2006 Mike Towers (Bandera Texas) Joyce and I came to Datapoint 1981 a couple of years after I graduated from UT and she from Rice. The thinking was, unlike the east or left coast, we could walk back to Austin from San Antonio if we had to. DPT had around 10,000 employees then. I left in 1985 and started my own business. Joyce hung on for another couple of years. After several startups and a couple of public offerings (yippee!!!) and 30 years of marriage, we're still around. Joyce takes care of the grandkids and does archeology and birding and I became a cop--go figure. Too bad the senior mangement blew it. Datapoint had THE most reliable systems I've ever used or worked on from mainframes to minis to micros. They weren't as sexy as some of the stuff that was coming our of Xerox PARC at the time, but they WORKED, and kept working and working and working and working...... Saturday 14th January 2006 Mike Shaffer (dallas, tx) noumenon labs What wonderful memories this forum has brought back to me! I was pretty heavily invoved in Datapoint and Databus activities 'back in the day'. It never ceases to amaze me how much Datapoint had within their grasp, only to let it trickle between their fingers and then fade away. Datapoint equipment was generally rock-solid, and the operating system software was always reliable, even under heavy load. No blue screen of death back then, just systems that kept plugging away. Bud Hutchison, who also left a post here, was kind enough to lend me his Databus manuals back in the 80's when I was trying to refresh my skills and get a job. Bud, thank you for that, and to this day I still have those old green manuals! Thanks for the trip down memory lane! Wednesday 21st December 2005 Brett Cupitt (Sydney) I started with Datapoint in 1983 in Auckland (it was here that I met Kevin Woods who has posted an earlier contribution). The NZ subsidiary was progressive with some innovative ideas in management. We were not allowed to have Lightlink as the NZ Post Office claimed they owned the electromagnetic spectrum up to and beyond visible light. Rather innovation was in methods to make us more efficient and productive. I was transferred to Datapoint in Australia where I knew Brian Smith (also a contributor). Australia was a much larger subsidiary with as many storemen as Datapoint NZ had field engineers. I had little call to provide support on the 11xx and 22xx series, but had exposure to the later products such as the 88xx, 86xx, etc. I also worked briefly with Minx which was the code name for a video imaging system which was very successful in teh courts. The innovation was also present in Australia with a lot of development going on - the most significant item being a complete library management package which was sold to a number of libraries. Wednesday 30th November 2005 james (Melbourne, Australia) Wow! I worked for this great company at it Melbourne offices. Joined the company in 1989. I very much regret that the company fell apart. RMS and ARCnet were the most amazing technologies I had ever seen at the time. I only wish I had a 7800 and a few terminals. Oh... the memories. Friday 11th November 2005 John Love (Houston, Tx) I worked for Datapoint from 1975 to 1989,first as a field tech in Miami then as a Regional Support Spec in Houston. I worked on every product ever made and ended up in the telecomm industry through Datapoint's Infoswitch product. I have run into a lot of ex-datapointers and we still talk about what a great company it was and what great years we spent there. Wednesday 26th October 2005 Frank Rocco (NY) Worked at Datapoint from 1979-1983 as a field tech out of the Manhattan office in Penn Plaza. I was right out of DeVry and it proved a good training ground. We had a real close bunch of techs and managers. Wednesday 10th August 2005 Jerry Scannell (North Providence, RI) Worked for Datapoint from 1977-1980. Installed/worked on 1100's, 2200's, 5500's, 6600's, 1800's, ARC, DataBus, CDC Disk Drives, you name it! My Datapoint experiences propelled me into the programming career that I have had for 25 years because I used to "unassemble" the old DOS O/S, I also used to help the SE's with DataBus and DataShare issues!!! Haven't been to San Antonio since 1980. Used to go to "Gasoline Alley" every night!! Glad to see there's a forum for this kind of thing. Wednesday 27th July 2005 Ellis Hillinger (Seattle, WA) I'm another Datapoint alumni from the Seattle office of the Western Region. I'm particularly amused that Microsoft just announce Longhorn will be called Windows Vista. Once again Datapoint was ahead of everyone else, to no avail. Monday 18th July 2005 Linda Peterson (San Antonio, TX) I worked for Datapoint from 1980 to 1986 supporting the order entry system. The Friday Lunch bunch is still alive and well going to lunch at a different place each Friday. I have many fond memories of meeting support folks from all over the world because my ex-husband also worked for Datapoint on the operating systems support team Tuesday 12th July 2005 Kevin Woods (New Zealand) In the early 70's I joined a company called Ventek in the U.K. It was a subsidiary of a Canadian company called Venturetech (I think) that marketed Datapoint equipment in England. All reference to date has been to the Datapoint 2200. There was actually a Datapoint 1100 that preceded the 2200. It was similar architecture with a parallel bus with 4 memory slots each having 1K memory boards. As an engineer I was trained in how to repair this device to a component level. As all the registers and gates were actually discreet TTL logic components, the every day language we used to trace our way around the processor was actually Assembler language. In other words, we could actually identify and replace if necessary the various Registers that will be familiar to any assembler code cutters. Load "A" with 303.. Ex Address etc When addressing a parallel Printer? Well we could find the A register on the circuit board and see if octal 303 was actually loaded? In those days, when sent to a fault call, I arrived with an oscilloscope, a box of TTL and CMOS chips, and an assortment of transistors, a large book of schematic diagrams and an extender board to extend the failed board out of the machine so you could access it with power on. I would then step my way through the logic until I found the gate that was not functioning as it should and simply replaced it with my trusty soldering iron. In similar circumstances now, we just replace the whole device. The original operating system was CTOS (Cassette Tape Operating System) but this moved to proprietary DOS once the floppy drives and then the Diablo and then Wangco drives were added. It was a brilliant machine, ahead of its time, and using simple emulation programmes loaded from cassette tape, replicated the functionality of IBM and many other systems at a fraction of the cost. I was lucky to cut my teeth on it and thereby truly understand at a bit and byte level how these things actually work. Datapoint eventually bought out Ventek and marketed their products directly in the UK and Europe and was very successful for a period. The company had an amazing youthful, cocky “we can do anything” culture in the early days. Unfortunately the market was not mature enough for what it had to offer. The desktop Computer and the LAN in the 70’s was a solution to set of problems a lot of companies did not know they had at the time Wednesday 29th June 2005 Don Reid (Redwood City, CA) Great times in the Western Region. Who can ever forget the State of California EDD project with Peggy Imirie, the shortest project manager in the region, and Jerry Klink with his reading of the daily passage from the Creation Memos. I was fortunate enough to work with some of the brightest people in the business and really enjoyed those times... However, I must admit that I'm enjoying retirement just a little bit more. :) Wednesday 29th June 2005 Dave Hopkins (Livermore, CA) ImageSetters Those were the days, my friends! I remember cutting my teeth on Databus and assembler back when a few bytes were the difference between a program working or not, and coding was eloquent as well as functional (actually, I cut my teeth on the wires I stripped when making cables...) I left Datapoint in 1984. Hmmm, that date seems to be significant for some reason... Evonne (my wife whom I met and married during my Datapoint years) and I own a graphics/web design firm, now. After getting out of the programming business entirely, I've come full circle and am programming again; now we're developing web applications. I still collect Datapoint memorabilia. Remember the 8 inch floppy drives? Or the RMS belt buckles? We still use the Western Region Datapiont coffee mugs, although all the names were whited out long ago... It also seems that a lot of things that are being announced as "new technology" I recall from our Datapoint days. How about IR communicatioins between buildings in a campus environment? or VoIP? Didn't we have those things back in the 80's? At ImageSetters we have been around for 20+ years, mainly due to the strong work ethics and desire to do our best job... just like at Datapoint. I think we all benefited greatly from our experiences at the big "D" and we are just continuing to get better! Thanks, Oscar Rabinowitz, for pointing me to this site! Tuesday 28th June 2005 Patty Fennell (formerly Huhn) (UK (was Denver CO back then)) Glory be - names from the past. What a pleasure it is to see so many names I recognise! I was with Datapoint in Denver for a way long time - until 1987. How can you all remember the product numbers - I just remember all those blinking tapes we had to load in that little cassette thingey on the top (yes, I actually was semi-technical once), and lugging around a datascope to prove once again it was IBM's problem - what emulators we had! I went to Tandem in 1987, and am still here 18 years later - via Compaq and now HP. And I'm in the camp with others who say we had a great work ethic and lots of fun then. Thanks to Jim Westveer for the tipoff. Cheers! Tuesday 28th June 2005 Jim Westveer (Seattle, WA) Howdy! I worked for Datapoint in Seattle from 1979 to 1987. Aaah the good old days. But if Datapoint is now considered old-computer-museum-stuff...what does that make me......oh, ah, never-mind. Thanks to Bill Drozda for pointing this site out to me. Ciao. Friday 3rd June 2005 I have had the priviledge of working on the old 5500's 6000 series. Had a 1500 and then the 1560. wow what an upgrade of memory does. Had the dual 8" flops and then got the 10mb packs. had 300baud modem and then 1200, then got daring and got an 8800 put it in the basement blew many breakers. Got a hold of an 8600 ran RMS in the basement. Wow all the memories. Finished up on the new 5500's on the ALR chassis and RMS/Open 4. great hardware. Dave Tuesday 31st May 2005 Pat LaTouche (Houston) I worked for DPT for 14 years and it was fun and I met some of the greatest people in the computer industry. Their work ethic is far better than some of these people that I have been associated with the past several years. I have changed careers, I am now a teacher (teaching middle school since 2001). I first taught computers, but now I am teaching math. The first year of teaching, I put the question ,"Who invented Local Area Networking" on my final exam. Datapoint of course, most students missed that question but that is ok. The kids I teach and what they give me at the end of the year is better than any bonus check, I ever received. Good Luck to all former Datapointers there is Life after Datapoint. Neven, thanks for discovering this web site. Sunday 29th May 2005 Steve Venable (Tennessee) Hello everyone. Pleased to see this web site and the forum from the Datapoint Club. I wrote my first Databus program on a 1100 Series while a senior in high school which led me to an S.E. position in N.C., Onsite S.E. at USAA (San Antonio), Branch S.E. Mgr., Support Mgr and Technical Mgr. What a ride CTOS, DOS, ARCNET, RMS, MINX, and RMS/XA. I had the fortune of meeting many wonderful and talented people while with Datapoint and speak of often of my experiences with Datapoint. I wish all you x-Datapointer's a long and blessed life! Friday 13rd May 2005 Lothar (Frankfurt GERMANY) Hi Guys, I worked for Datapoint Computers from, 1979 to 1989 in Frankfurt/Main, Germany. First as a technical support engineer, second as a technical branch manger, and after that as a software support engineer. I've worked on all the Computers from the tiny 1100 up to the 8800 flagship. MIDS, anyone remember that?. Yeap, it was a CDC-Harddisk 60MB/60MB like a fridge. And not to forget the amazing ARCNET. Wednesday 30th March 2005 Brian (USA) I worked for datapoint/intelogic trace from 1980 to 1988. i had a 2200 system i picked up from a customer and used it to keep inventory contol on. Damn i worked on all of it from the 1500 to the 8800. I also picked up a MIDS system for my own use for the cost of renting a trailer to haul it. I finally left the company in december of 1988. Worked in the corpus christi texas office. Damn what a great company DATAPOINT was. I have never had a job since that even comes close to the experience of DATAPOINT. Miss it Sunday 28th November 2004 Brian Smith (Melbourne Australia) Interlegal I started life as a Databus programmer in 1981 and worked for the Australian subsidiary of Datapoint from 1985-87. I first worked on a 2200 with 2 x 2.5mb disks. Was amazed at the power of a 5500 and then there was the powerhouse 6600. Thanks to Don Wills at dbcsoftware.com I am still a Databus programmer 23 years later on a language that started back in the 60's and my company produces highly successfull commercial software using a Databus derivative. Now that's a lesson in longevity and portability that Microsoft could take note of! Wednesday 10th November 2004 Herb Toeppner (Vancouver, BC) History of Microcumputers : 1923-2003 I worked on Datapoint computers for eleven years, 1977 to 1988 in Calgary and Red Deer, Alberta, Canada. I worked for four different companies and in four different industries, manufacturing, wholesale parts distributer, retail lumber and a Customs Brokerage firm. I had the privelege of using the state of the art 5500 with 50 MB of online disk. The drives were the size of a washer and dryer. That was my first two systems. Twins actually, but 90 miles apart. I then graduated to the 6600's. Must have written 1,000,000 lines of DATABUS code. CMATCH was my favorite OP Code :) The Calgary Datapoint office showed us MYNX. Anyone remember that??? Ah, memories... Herb Friday 7th May 2004 dennis (new york) worked for datapoint and interlogic trace from 1978 to 93.\in stamford ct. remember nando,chris,joe,john singer,paul miles,woods,phil tracy and the rest.good product rotton management.rember some real half ass ones.too bad datapoint fell was a good company to work for good trainingahead of its time products. Thursday 25th December 2003 Dean Pierce (San Antonio) I started working for Datapoint in 1980 and stayed with the company and the spinoff company Intelogic Trace until 1992. I supported the home office's user community and am still amazed at the innovation at the company. Datapoint had their own email system years before it became what it is today. They had their own word processor and graphics machine. The first computer I used at Datapoint was a 3600 which had 38K memory. I remember the first machine that boasted 256K of memory, they referred to it as "Godzilla". It's amazing to think how far we have come. Wednesday 12th November 2003 Ian Catchpole (WA, USA) I found this page during some nostalgic web-searching - amazing! I worked on a Datapoint system (Buxted Poultry in Norwich England) in the early 80's. My most notable achievement being writing a workable Reversi program in Databus :-) Actually I previously worked on a CA Syfa system - and their language was virtually identical to Databus (I seem to recall that CA was created by some Datapoint rebels). Amazing to think that Databus (Datashare as I recall) still continues. Wednesday 22nd October 2003 Bud Hutchison (Tyler, Tx) Sunbelt Computer Systems, Inc. I worked for Datapoint from 1979 to 1996 as a systems consultant in the Marketing Division. I worked primarily in the Dallas area including a two year stint at the Infomart showroom. Datapoint has downsized until there is only a small company left in San Antonio. They continue to support their customer base. The Datapoint name was purchased by a European telecommunications company and that is the owner of www.datapoint.com. Dynacore is what's left of the US company we all knew and loved and is still in San Antonio, Texas. Datapoint is proof that the best products and technology don't always come in first. So now we're stuck with computers that fail anytime the cover is removed and you have to reboot daily. Sunbelt was one of the first companies to implement Databus (PL/B) on a non-Datapoint system. We have enhanced the language and tool set quite a bit in the last 20 years. Thursday 4th September 2003 Christian Cavaleri (USA) WOW,reading all this is like a time warp . I worked for Datapoint from 1982-1987 out of Stamford Conn. and was a charter member of interlogic Trace when it started. We did field service on the entire line and reading this was interesting.I wont get into specifics but most of your inputs are correct. I can tell you they had a 1100 system before the 2200. the day I went on a service call on a 1500 floppy system and saw everyone in the office crowded around one of the origional IBM pc I knew right then we were doomed as a company we invented ARCNET then fell behind the times. It was a great company to work for .Training in San Antonio was fun,but when I think about head crashes,fixed disk replacements and alighnment packs I realize how far computers have come and how old I've become. Wednesday 30th October 2002 Charles Foreman (Lemasters, PA) I have many fond memories of Datapoint. As I was growing up, my dad was moonlighting as a Databus (and even Datapoint assembler) programmer. My first real job was interfacing Datapoint 8600 systems to Intermec bar code printers. I have owned several Datapoint systems, and even ran a multi-user computer bulletin board system through Datashare running on an 8600 many years ago. I also bought a used 8800 system (the washer/dryer combo unit) from Chase Manhattan bank. You had to be careful not to fire up both units at the same time - the circuit breaker would trip every time! RMS was way ahead of its time, and Databus was a very good development environment for business applications. Monday 6th May 2002 Peter Walker (UK) Thank you for your piece on the Datapoint 2200. However, I was surprised to read that Datapoint Corporation "ceased to exist in the early 1980s". In 1981, I had a career change and joined IT. I was trained (partly) at Datapoint's office in London, UK. I worked as a Databus programmer from 1982 until 1986, using their DOS and RMS operating systems. Older hands told stories about the 2200 and its operating system (the abbreviation CTOS appeals to our old-English sense of humour). Model numbers were different in my day: the 1800 had 8-inch diskette drives; the 3600 and 8600 were discless processors which booted from a LAN server; and 3200 and 8200 were dumb VDUs. I understand that Datapoint were moving out of general IT into computer/telecommunications integration, as of the mid-1980's. I lost touch with the company after 1986, but I can testify that the London office is still there - I drove past it (complete with a big DATAPOINT sign) in April 2002. Indeed, there is now a Datapoint web site (www.datapoint.com). Tuesday 17th April 2012 Marc Desmoulins (France) matra-systems.com The first distributor of these little systems in Europe was the giant Honeywell-Bull... When the first "machines" came, we did not believe it was possible to make such an intelligent full system... The reliability was not less than the others at that time. Then, Datapoint had an agreement with the "Defense giant" MATRA, (now EADS in Europe. An affiliate was biult in common with the name of "Matra Informatique". The success came fast. There were a few divisions developing business and specialized software using the very strange "Databus" language... Probably it was not really conventional... but it was surprisingly efficient. $In 1984, things changed... the arrival of the IBM-PC, PC-Networks of all sorts and UNIX has been a revolution... I must confess that me also, with all my team, have changed in favor of the newcomer. The year after, the French affiliate was dissolved, Bye Bye.$- If Databus had been modernized, converted to the Intel base systems and adapted for Internet, it would still be a leader. Those who developed such language, operating system and hardware interfaces can be proud, it has been one of the best thing men''s brain as conceived. "Bravo". Wednesday 9th December 2009 David Neale (Guardamar del Segura$España) David Neale I worked for the Samsonite Corp (the luggage people) from 1972 until 1982. The European headquarters were located in Oudenaarde, Belgium (they still are). I programmed their order and billing system. For input of customer and sales data in branches outside Belgium (UK, France…) we used Datapoint 1100s. I wrote the little apps for these, too. Customer data and sales information was captured on cassette and transferred to Oudenaarde each evening (initially using a 300 bps acoustic coupler, later going to 1200 bps and then to a massive 2400 bps!). There they were processed on a Honeywell Bull something-or-other (can''t remember the model) and returned the following moring, again captured on cassette, for printing out invoices, error reports, stock reports, etc., at leisure. This all started in about 1976. Not bad for the time, I suppose. Monday 1st September 2008 Charles Cotham (Tennessee) Chuck''s Toys and Things Wow.... While looking for info on old systems that I''ve touched, I ran across this site. Well, a gentleman named Tom Burks and myself installed a Honeywell MTS-7500 (really a Datapoint 2200) in 1971 at National Savings Life Insurance Company in Murfreesboro, TN, programming it without a printer and debugging the code on the 12 line screen.... LOL We then joined Universal Systems in M''boro and wrote a Escrow and Title Closing System on a four diskette, Diablo printer equipped Datapoint 1100 and eventually migrated the software to Datashare on 2200''s, 5500''s, and 6600''s. We installed the software in various major title companies (the largest installation consisting of over 100 remote terminals in Oakland, CA) which put USI as the Number 1 VAR in the country during the 1970''s. Remember those days Steve Venable? The software (and myself) was sold in 1980 to a California company and I moved to Fremont where I met Dave Hopkins and his lovely wife, Evonne. I''m now retired from my last position at AOL, Reston, VA as Technical Manager - Systems Security but still find time to do consulting with health providers in Phoenix, AZ. Datapoint was ahead of their time and Tom Burks is still using DBC''s version to carry on the Escrow and Title Closing System. Friday 21st December 2007 peter nelson (Minnesota) My first job (age 15, early 1980's) was for a local bank's mortgage division, running print jobs, xmodem file transfers, and backup jobs on their Datapoint gear - your basic computer operations monkey. After a couple years on the job, for fun, I wrote a font editor, and re-programmed the entire character set, so all letters would be displayed upside down. This was meant to be a private joke, but I forgot to change things back before leaving at 10PM. The next morning when everyone booted their OS from the shared drive, they got upside down letters! In production! Fortunately for all of us, I made that little mistake on March 31st, so this all came to light the next morning, on April Fool's day. I guess they made allowances for youth, because God knows I should have been fired. The head of the department played it off as a joke, otherwise he would have had to explain why he gave "root" access to a high-school kid. Happy memories. As an aside, I've had an eBay search running for a year, trying to find an old Datapoint workstation. Nothing turned up but one sorry little advertising flier. What happened to all that gear? It can't still be running in production, can it? Sunday 23rd September 2007 John Sutherland (Scotland UK) Finding this page was an unbelievable experience. Are there really people out there that have an interest in Datapoint 2200. :-) . anyway, my experience was as an employee of Ventek in the Uk as a field Service engineer. I can remember sleppless nights fixing these damn thing at 2am in the morning in the middle of a railway siding shed. They were primarily used by British Rail in a train monitoring system. 100s of them. CTOS, Bad Power Supplies, Tape decks.. Ugh!! Sunday 5th November 2017 Paul Longoria (United States) Wow ! Glad I found this page with so many Datapoint''ers that I remember from my time there. I started in 75 and left in 1990. Best education and exposure to some of the finest minds in the country. FYI, there''s a Datapoint Facebook page called "Datapoint Remembered". with lots of photos and some more people. Thursday 21st September 2017 PHILIP J SCHWIRIAN (United States) I worked for Datapoint from 1976 to 1989 in Technical Support in San Antonio, TX starting at the woodcock building. I was hired as a senior Technical Support Engineer and was promoted to be the first and only Support Engineering Specialist (reported to Oscar Gordon a Director). I just ran into this site and decided to leave a comment. Previous to Datapoint I had worked on Main Frame computers. I remember being introduced to the Datapoint 2200 version 1 a the Permian Oil Basin Show in Odessa TX in 1975. I have supported and provided training on CTCs first product the Datapoint 3300 around 1970/1971 when I worked for a small company in Rockville MD call TST Communications. I had attended training on the 3300 in the old Kadak building in downtown San Antonio, TX which was my first introduction to San Antonio where I have resided for over 41 years. I spent almost 50 years in the IT field and am not retired! I remember my 13 years with Datapoint fondly! Friday 1st September 2017 Karl Mutch (San Francisco/Sonoma, United States) Worked at Datapoint in New Zealand at the start of my career, mainly Databus/DOS was it ?, and did a stint in Austin TX, working on a communications gateway in DASL/RMS from memory. Now living and working in San Francisco in AI. Pretty much owe it all to Datapoint and the opportunities they gave me. Some of the names here I even recognize! Tuesday 29th November 2016 Darrell Campbell (ATLANTA GA US) Worked in Atlanta sales 1980 - 1984. Worked in Communications Div. LDCS and ACD. AWESOME TIME AND PLACE Worked with Rich Pape, Max Wood, Andrew Waite and Mike Tamer. Many more early sales reps and managers under Dan Hosage. Even Survived sales forecasting under John Thornton. What memories. Friday 9th September 2016 Jim McKay (Houston, TX) I worked in Engineering at Datapoint from 1979 through 1985. I managed the Design Verification Testing Team so I was involved in testing LightLink, the Laser Printer, Impact Printers, Video and many other products that Datapoint developers and engineers thought up. There were so many products that my team was involved in testing that we rarely had a break between the Information Management products and supporting products. There was a lot of creativity coming from the mind of David Monroe and his engineers. It was a fun time to be involved in the cradle of new technology. You had to love the "can do" attitude of everyone involved in these programs. Friday 12th August 2016 G.Tisher (Houston, TX) I worked for Datapoint/Intelogic Trace for 18 years, beginning in 1975. First as a peripheral final test tech at the 9725 Datapoint Dr. location, then as a field service tech. I still work as a field service tech and owe my career to the experience I gained while working at Datapoint. It is a shame that Datapoint is not adequately credited for much of the innovations that we still see in today''s modern computers. The microprocessor, the desktop PC and the LAN just to name a few. Wednesday 18th November 2015 Shane Bolton (Melbourne / Australia) I worked for Datapoint starting in the late ''70s and finishing in the late ''80s. Started out as a Field Engineer fixing the broken ones, ended up as Support Manager in Melbourne. During my time at Datapoint I spent 3 years in San Antonio in software support. Worked with some great people: Vern Green, Tim Morrow, Harold (Skip) Peterson, Mary Keinarth, Billy Taylor, Ray Tokar, Charlie Colbert, Harry Pyle, Kay Hancock, Graham Patterson and a bunch others. I will always remember my time at Datapoint very fondly. A time of great innovation, fun, hard work and great people. Fantastic combination. Thursday 6th August 2015 Stephen Cable (Australia) I worked on Datapoint equipment for 20 odd years, firstly as a field engineer for the then distributor Sigma Data and then Datapoint Australia directly in varying roles from Field Engineer to service director. Many of the names on here from varying countries I know or recognise, certainly all of those from NZ and Australia. They were certainly the innovative days when the computer industry was fun. Infoswitch, Minx, 2200 through to the 8800, RMS and all the Vista products. Thanks for the posts here they brought back great memories. Wednesday 29th July 2015 Bob Erwin (Dallas, TX) I cut my teath on a Dataoint 2200. My father boght it for his accounting office. His had 4 floppys and a daisy wheel printer for producing all the accounting reports. This was 1976. Still doing IT today. Thursday 4th December 2014 Frank Lether (The Netherlands) Presstige Public Relations How nice to see you guys overhere. Spent almost 10 years as director of Communications (PR) at Datapoint Netherlands with much pleasure. Thursday 4th December 2014 Frank Lether (The Netherlands) Presstige Public Relations How nice to see you guys overhere. Spent almost 10 years as director of Communications (PR) at Datapoint Netherlands with much pleasure. Tuesday 28th October 2014 JJ Orn (Cincinnati) I had an 1100 model. No tape, but did have four 8" disk drives integrated. I still have a box of the disks. These were machines from Uniroyal - they made tires, rubber and plastic. My father wrote the inventory system there. Sadly to this day, I can''t even find a good picture of the machine. It was the size of a desk! I remember a certain sequence on the buttons during POST would put the machine into a memory diagnostic. The language was actually pretty easy to learn considering the age. Saturday 25th October 2014 Robert Clow (New Zealand/Australia/Hong Kong (Australia)) Wow.. The names. Hi Tim, we had some great times in HK!... Love to get in contact again. I started in NZ with 2200 (yep excitement working with the ''10 over 10s'') and first job was joining a very ambitious software billing project... as a lead... As Tim said Datapoint''s technology was very advanced Friday 22nd August 2014 EddieTheWild (Spain) Hi Datapointers, any of you have technical info about Datapoint 1560? I have one that seems to boot but nothing is shown on the monitor (it and the keyboard light on). I would like to know the pinout of the conector between the computer and monitor to try to connect the computer to any other third party monitor. Thanks in advance!! Saturday 16th August 2014 Frank Franzoi (Henderson Nv.) Hired in 1978, Laid off 1991...... Hired as a system engineer... Hi Bob etc... in Cleveland Oh.... Transfered to Detroit as Head honcho... Then became a sales person for the State of Michigan out of Lansing Mi... Had a Ball and sold over 6 million in equipment... And not a person in San Antonio would listen to us about total internet capability... Any how... got laid off and the company went away... am living off a pension etc but still miss the company and it''s capabilities that couldn''t be done because it was''t allowed by the lawyers .... Monday 28th April 2014 Sam Ward (US, TX, San Antonio,) If You are him, i need bee-keeping help$ An expert, You are. I have many and they are becoming more aggressive. Thus a problem! I wish not to hurt the honey-bees$simply to discourage and move them to some place safe. They seem to like the wild flowers these days. They never hurt me before$ i fell like they don''t appreciate my efforts no-more Monday 3rd February 2014 Greg Baker (Spokane Washington / USA) Gregbaker.com I worked for Datapoint from 1976 - 1981 From 1976 - 1978 as a Field technician in Mountain View, CA, then 1979 in San Antonio, Texas developing diagnostics, then 1979 - 1980 back in San Mateo, CA as a field tech. Then from 1980 - 1981 Product Support San Antonio Texas. Sunday 22nd December 2013 Daniel E. Chrisman (California) I was hired in 1981 to support the Order Tracking System in the Marketing Division. I worked with Linda Peterson, JoAnn Horvath and others. I supported different systems and wrote code for the Canada Order Entry system. I was terminated in the great purge and went to work for Unocal in Chicago. I remember sharing an office with Dean Pierce in an office that looked out over the 7th fairway of the Turtle Creek golf course. Sunday 8th December 2013 I worked from 1981 to 1982 in Piraeus,Greece in a computer service bureau, as an applications programmer with Databus language,DOS operating system in a Datapoint minicomputer with 2 removable disk drives ,around 10 on-line terminals,1 batch terminal and 1 printer. I still remember the program-generator we had for generating automaticaly on-line entry programs and the "rollout" command for changing from on-line to batch mode. Friday 4th October 2013 Ron Mitchell Hey Guys , worked in Charlotte NC from 78 until 93. Just wanted to say hello Thursday 24th January 2013 M. James (NYC NY) hi, I worked in the international data center at NYC Manufacturers Hanover Bank in 1985, at 4 NY Plaza, 19 floor, in Operations. We had a lot of Datapoint machines, we would start the backups up around 4PM, then kick off the batch jobs. This system ran TEPS Transcend Electronic Payment System, fancy name for remote banking. It served our clients from all over the globe, UK, Europe, Saudi, Bahrain, Australia, NZ, etc. Thses machines were great, they always ran, unless one of the programmers made an undocumented change and that is where the problems start!. I agree, they killed the goose with the golden eggs when the idiots took control of the company. Regards Monday 7th January 2013 Josh H. (USA, Texas) Both my father and my uncle worked for Datapoint in the late-70''s here in San Antonio Texas. As far as I know, my father built computer systems there. I asked a bit about it since I was born a several years after Datapoint closed up shop here in SA and my father went on to work for a company called Phototelesis. (also here in SA) Tuesday 18th December 2012 Bill Brownlow (San Antonio) Found the site when looking for information on the Convergent hardware. I started with Datapoint in ''78 working in Tech Support at the old Woodcock facility. Before Datapoint I was at Four Phase and before that with Wangco who manufactured the reel to reel tapes Datapoint used. From supporting tape drives in Tech Support I went to Infoswitch at 8410 where I ended up in New Product Support. I was the New Products Support Engineer for LightLink taking that product from preproduction through the Alpha and beta phases to final. From there I transitioned into International Support doing software support under Les Shafer. Bob Lofgren and I took the problem reports filed from all the international offices and worked those with the developers hanging out on the second floor of 8500. While doing International I ended up with the NGEN product line and handled the software support for that series. When Convergent revised the CTOS operating system and you could no longer do a static memory allocation the product died as we could no longer allocate the hard memory space for the ARCNet adapter. I then ended up with the likes of David Hovel supporting the ARCNet card and drivers in the IBM PC line. All told my time with Datapoint went from Feb. ''78 until July ''88 when my position was eliminated. Tuesday 23rd October 2012 Tim Regan (US/Japan/HK) (United States) I worked with Datapoint from 1980 till 1993$started as a systems programmer for the 2200 and then the 1500/1560, then I did work with 1800, 5500, 6600 and 8000 family. I worked in San Antonio initially as systems developer then moved to Office Automation Group, and in 1984 I worked with CJK (Japanese distributor) to add Asian Language support to OS products. That then landed me in Japan (downtown Tokyo) for 18 months, after which I became in charge of Asian operations and began working from Hong Kong with a staff of 12-15. It was a great time and experience. I recognise so many of the names below. RMS was a great OS, so far ahead of it''s time. Saturday 28th July 2012 Kaj Granlund (Finland) After a couple of years with IBM 360/370 mainframes, a Nokia salesman (believe me or not, Nokia was the local DP dealer here) showed me a DP2200 as I was looking for a warehouse solution. We went for a DP2200 with a 2,5 MB Diablo drive in 1973 (ser$ 13). Since those days I worked with DP all the way to "the bitter end". First as a Nokia emplyee and later as an independent consultant. During my time with DP computers, I wrote the first IBM-3780 emulator in 1973 (DP had only 2780) and a revised version of the Honeywell GRTS-355 emulator. As DP did not come out with an acceptable database solution together with RMS, I wrote one pipeline -based solution for RMS in about 1980. Although I loved (and still do love) assember programming, I spent most of my time writing applications in Databus/Datashare and later also in Cobol. In 1987 - 1988 I developed the ARCLINK -unit, which was sold by Datapoint for years. I also represented Datapoint in Finland from the early days of 1990''s. I still have an old DP5500 with a full set of spare parts and a couple of original CTOS and Utility cassettes. Tuesday 17th July 2012 Other comments re: confusing the 1100/2200/5500/6600 may have arisen from the fact that all of the enclosures for these models started life with 2200 molded into the plastic bezel. The 1100, 5500 and 6600 models had a separate logo that was applied over the existing 2200 logo. Since double-stick foam tapes were used, over time the tape let loose and the ‘new’ logo fell off. We had a few customer complaints re: the instant downgrading of their computers when this happened! Alas, we know that for all of those that complained, many more didn’t, giving possible rise to the confusion of what the machine actually was. Monday 21st May 2012 laurence Orchard (Blackpool, UK) found this page via Wikipedia, boy does this bring back some memories! used to work for an exhaust supply company, part of the TI (Tube Investments) Group. We and a number of other TI companies had these machines. Can''t believe we used to run 8 terminals, 2 printers and communications on what was effectively a calculator with a cassette deck and 2 huge 10 Mb disk drives that looked like a top load washer. I learned to program on this machine, rewrote the whole user system, built in error checking, wrote a report writer, that generated Databus code, in Databus so management could use their batch IBM mainframe reports. Remember some great training courses at Centrefile in Wembley, was there when they were testing the ARCNet IR link from the top of the building to the engineering site at Harlesden. Had problems cos it wouldn''t work in the fog and drizzle! Great times, great fun, BTW Databus is still used, now called PL/B Monday 16th April 2012 Stacy Browning (San Antonio, TX) Holy cow! I was just writting a paper for class and could not remember the name of the first company I worked for when I stumbled onto this site. I worked for Datapoint 1984-1989 in the accounting department. Straight out of highschool, I was the file clerk/copier girl. Now in TN, still in the accounting field. Thanks for the memories! Monday 30th January 2012 My grandpa worked with Harry Pyle and Victor Poor to develop the 2200, and I have a couple of them. I''ve been looking online to see if anyone else still has any or if they mostly just fell off the face of the earth. Sunday 11th December 2011 Thomas (San Antonio, TX USA) I worked with Datapoint gear at a large company in the late 70''s. Had to SCREAM at the manager to get smoking BANNED (as it should ALWAYS have been) in the building. I convinced the management (some who were tobacco addicts) that the smoke was RUINING the equipment AND the health of all workers! They took it to heart (and lungs, etc.) and banned all smoking in and around the building just one week later. SMOKE-FRE IS THE WAY TO BE! Saturday 7th May 2011 Mike Newcomb (London/England) (hope my recollections are correct) In the early 70''s I worked for the Building Research Establishment, and have always remembered being taken (as a junior participant) by Ventek to see a Datapoint System at the Medical Research Council in Mill Hill. The thoughts were to replace many ICL punch and verifier machines with a Datapoint network for data entry purposes. I was most impressed with the system, being a huge leap forward, meaning no more punchcards, which had been around for nearly a century then. Ventek took us to lunch at a pub in Alperton and even now whenever I go past it, I still taste the excellent steak served. Think Ventek''s offices were on the North Circular Road. Those were the days! Tuesday 15th March 2011 Wouter (Germany) Hi, Connected to Datapoint in various roles and locations, for over 12 years, I have learned a great deal on the job about frontier information technology and still earn benefits of that today. Living the hard days of being confronted with the consequences of poor management and following dissolving of the European subsidiaries, one could also learn a great deal about survival of the fittest and cash collecting cowards (managers bailing out). Anyway, best greatings to all friends abnd former colleagues. Friday 11th March 2011 ne12abaa3 please provide manuals , blue print , trouble shooting , you tube presentation , emulators Monday 4th October 2010 Paul McCard (England) A Datapoint 2200 was the first computer I ever used - at school near Liverpool, aged 12, in 1977. The photograph on this site is the first time I have seen a 2200 for about 30 years and brings back very happy memories of after-school sessions keying in BASIC programs and discovering a fascination with computing which has continued throughout my life. Until today, though, I had never realised the significant place the 2200 holds in the progress towards single-chip microprocessor CPUs! Thursday 30th September 2010 Wayne Osteen (Florida, USA) My first job out of school was night operator on a network of 4 Datapoint 7810s. I ran all the batch jobs at night and did system backups. After a few years, I moved into programming in Databus. WOW, what an ugly language! LOL I fondly remember the RMS/XA OS however. It was so ahead of its time. We finally retired that system and moved to a complete AS/400 system sometime in 1995 I believe. We definitely got our money''s worth from those systems. Monday 31st May 2010 Chris homie I DO have a Datapoint 1550, incl the dubble 8" drive !! home.hccnet.nl/c.born/DSC02854.jpg Sunday 16th December 2007 PeriSoft (Ithaca, NY) perisoft.org This also appears to be the first computer with a 2.35:1 cinemascope display. How innovative! ;) Sunday 9th December 2007 Ted Heaton (Derby, UK) I worked for a company in the UK called CMS which were based in Essex. The company in the early days was made up of ex-datapoint employees. I joined at the age of just seventeen and working my way up from the old 1004, 3600, 8200, 8220 and 8242 terminals. I worked on 1100 processor units upto the 8600 type plus all the 10 over 10 drives, CDC drives and eventually the PC based Powerservers and ARCservers. The times we had were good. The Datapoint computers were the last real items to be fixed by engineers with soldering irons and a bag of components not like now, swap out monkeys. Engineers had respect and there was always coffee on the go for the engineers on site. Friday 20th January 2006 Søren Peo Pedersen (Greve, Denmark) Peo's Page This machine is *the* very first computer I ever saw: My father programmed these things, and sometimes brought one home for a weekend to work at home. When he wasn't working on it, I, age 5 or so at the time, had a go with some demo programs. I remember there was this ASCII animation showing a man walking past a light post, followed by a dog - and guess what the dog did when it passed the light post... ;-) Tuesday 6th December 2005 Mike Altice (USA) I had been given a datapoint 1100 in the late 80s. It used to live in a tool sales company for about a decade. This particular one was perched on top of a heavy duty metal desk that included four 8 inch floppy drives and their controllers. There was a modem and a massive power supply that were attatched to the back of the desk. This particular one did not have a casette drive. I made several attempts to get it to work, but all that it ever did was beep and make lots of fan noise. Nothing ever was displayed and it wouldnt boot from any of the drives. Being such a large object, I eneded up taking it to the dump. I did keep most of the boards from the desktop console. If anybody wants them, let me know esp. if someone wants to restore one of these things. Monday 11th July 2005 Al Kossow (Silicon Valley) There is some Datapoint scanned documentation up now at www.bitsavers.org/pdf/datapoint I'm interested in finding more, esp the maintanence manual for the 2200 I'm restoring. Monday 6th September 2004 Rich Frank (Naperville, Illinois) I have a mint condition 1100 and 2200 machine, controller with a bank of 4 diskettes, GE terminet printe, manuals etcr. I bought the 2200 due to a little known fact that it ran editplus like a 5500 and I could use it from home to edit my Databus programs. It served that purpose well. Lots of original stuff at no charge to the enthusiast if anyone is interested in paying shipping to get it out of my basement. Tuesday 10th August 2004 Tony Coleby (UK) In 1987 I worked for a pensions company in London that used a Datapoint 8800 system until 1989 I believe (!) The terminals were all orange-screen mono with 80x24 or 40x24 characters (if I remember correctly). The hard disks were 80MB and around 14 inches or so in diameter. I, as the computer department junior, had the pleasure of lugging 2 of these monsters to the bank after every month's backup. Wow, to think that the average-size Compact Flash card in my several-years-old MP3 player holds more than that! I really can't recall whether there was any specialist software running on it but the thing that sticks in my mind is that was a version of the Colossal Cave text adventure game on it that used to keep me occupied during lunch break. Saturday 19th June 2004 Doug Smith (Houston, TX) I am a software developer. In 1983 I purchased a Datapoint 1560 - a whopping 128KB of RAM, and two 8" floppies in a suitcase sized box. Only \$10,000 offset by my 20% VAR discount. I kept it for years afterwards thinking it might be valuable as a collector item or for a computer museum, but my wife prevailed and I gave it to a friend needing to convert large diskettes. Anyone remember the infrared ARCNET modems that could be used to connect systems where running cable was not practical? If Datapoint had seen the opportunity in sticking a cheap ARCNET card into every IBM PC instead of selling their obsolete boxes, you would never have heard of Novell. Makes me wonder what opportunities I am not seeing due to my own ego. Thursday 27th May 2004 Al Kossow ((silicon valley)) I'm in the process of restoring a 2200 series 2 with 16k of memory and REALLY need a copy of the maintenance manual. I'm also working on archiving any surviving documentation and software for these systems. Wednesday 5th March 2003 Roger Heim (New Jersey) The Databus language is still with us. It reached ANSI standard status in 1994 and is now officially called PL/B because Datapoint would not relinquish its trademark on the name Databus. Probably the biggest supplier of modern implementations of Databus is DBC Software (www.dbcsoftware.com). I still support a Databus order entry application that originally ran on real Datapoint systems, now runs on a Novell Netware network and soon will run on a Windows 2000 network. Saturday 5th October 2002 I'm curious about this thread. As I understand it the datapoint in the UK is the logical end of the original company, but I have the feeling that it was originally a branch office involved in a "reverse takeover" as the company spun off parts in the 1980's. There's another twist as well. From what I can tell a company in the US called Dynacore Holdings bought Datapoint's patent book in order to go after patent cases -- more lawers, yeah! Wednesday 28th August 2002 James Dixon (Arizona) Big Rich Company Network http://www.datapoint.com Fascinating story, and that company is still with us today, with several offices including San Antonio, Texas. Looks like they are seriously into embedded programming markets. 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# Differential Equation - Linear Equations (Non - Homogeneous) #### cse63146 1. Homework Statement Find the general solution of $$\frac{dy}{dt} + 2y = 3t^2 + 2t -1$$ 2. Homework Equations 3. The Attempt at a Solution So just worrying about the right side $$y_p = at^2 + bt + c$$ so $$\frac{dy_p}{dt} + y_p = 2at + b +at^2 + bt + c = 3t^2+2t - 1$$ $$at^2 = 3t^2 \rightarrow a =3$$ $$2(3)t + bt = 2t \rightarrow b = -4$$ $$(-4) + c = -1 \rightarrow c = 3$$ Is that part right? Related Calculus and Beyond Homework Help News on Phys.org #### Dr.D Is that part right? Substitute it back in and see if it is right? Far better that you learn to check it yourself than for you to ask someone else if it is right. #### cse63146 Substitute it back in and see if it is right? Far better that you learn to check it yourself than for you to ask someone else if it is right. God, why didn't I think of that? Thank you. ### Physics Forums Values We Value Quality • Topics based on mainstream science • Proper English grammar and spelling We Value Civility • Positive and compassionate attitudes • Patience while debating We Value Productivity • Disciplined to remain on-topic • Recognition of own weaknesses • Solo and co-op problem solving
# Ideal Gas Law question. ## Homework Statement Is the ideal gas law, PV = mRT, only applicable to processes which are carried out isothermally? I mean, can it not be applied to a polytropic process, PVn = k. See above. ## The Attempt at a Solution N.A. Related Introductory Physics Homework Help News on Phys.org DrClaude Mentor Is the ideal gas law, PV = mRT, only applicable to processes which are carried out isothermally? No. It is an equation of state: it relates P, V, and T (assuming n fixed). It is valid everywhere (you can't have an ideal gas at pressure $P_1$ occupying volume $V_1$, and measure temperature $T_1$, and have the same amount of an ideal gas also at $P_1$ and $V_1$ and measure $T_2 \neq T_1$). For a polytropic process, the equation only tells you what remains constant during the process. In the formulation $PV^\gamma = \text{const.}$, then $T$ must change when $P$ and $V$ change, such that $PV = nRT$ is maintained. Got it. Thanks for that.
# Lagoon Pocket In The Balance Puzzles Grades 4 6 Pdf ### Balance Sheet Crossword Puzzle #2 AccountingCoach In the Balance Algebra Logic Puzzles Grades 4-6. 05/10/2016 · Can you fix 6 + 4 = 4 by moving 1 matchstick? This problem has gone viral on Facebook, with one post having over 400,000 shares. The ground rules are you can..., “Lead” is the opposite of “follow,” and “always” is the opposite of “never.” These are examples of antonyms! In second and third grade, students are thinking about word meaning, synonyms, and antonyms. Use this worksheet to give them an antonym crossword puzzle that builds on those important concepts. To complete this crossword. ### What are the answers to in the balance puzzle 8 grades 7-9 Hanging Balance puzzle solve. YouTube. In the Balance: Algebra Logic Puzzles Grades 7-9 by Lou Kroner starting at . In the Balance: Algebra Logic Puzzles Grades 7-9 has 0 available edition to buy at Alibris, Practice: Balance Puzzles 1. Click the link below to try some practice problems solving balance puzzles. For these problems, it is OK to use guess-and-check. We will learn later how to solve these puzzles …. Fifth Grade Logic Puzzles & Riddles Worksheets and Printables. Tease, stimulate and exercise fifth grade brains with these logic puzzles and riddle worksheets. Logic puzzles and riddles help to develop problem solving and critical thinking skills as well as vocabulary. The benefits of these game-based learning worksheets will last well beyond 23/04/2010 · How do you solve In The Balance puzzle number 6? The goal of the first chapter in grade 6 is to review the four basic operations with whole numbers, place value, and rounding, and to learn about exponents and problem solving. A lot of this chapter is review, and I hope this provides a gentle start for 6th grade math. In the next chapter, we will delve into some beginning algebra topics. A balance puzzle or weighing puzzle is a logic puzzle about balancing items—often coins—to determine which holds a different value, by using balance scales a limited number of times. These differ from puzzles that assign weights to items, in that only the relative mass of these items is relevant. Click an empty white square in the puzzle grid and a question box will appear. Type your answer in below the question and click Enter. Repeat the above steps until you have filled in the entire puzzle grid. To check your answers, click Check Puzzle (located below the puzzle grid). Incorrect answers will be highlighted in black. Find 9780762205523 In the Balance: Algebra Logic Puzzles Grades 7-9 by at over 30 bookstores. Buy, rent or sell. Move over Sudoku, here come Balance Benders™!You can use these activities as quick, fun logic problems or as stepping stones to success in algebra. 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Since there are 3 3 3 purple circles, we need 3 × 2 = 6 3 \times 2 = 6 3 × 2 = 6 green squares in order to balance the scale. To model this problem with equations, we get. p = 2 g 3 p = X g 3 (2 g) = 6 g = X g X = 6. Valentine's Day Puzzles (with pictures) Art Project: Stained Glass Decorations for Valentine's Day (grades K-6) Make colorful stained glass decorations for Valentine's Day (PDF file) Finish the Story Valentines for Vincent The Prize Box (Grades 2-3) Healing Hearts (Grades 3-4) Practice: Balance Puzzles 1. Click the link below to try some practice problems solving balance puzzles. For these problems, it is OK to use guess-and-check. We will learn later how to solve these puzzles … Logic Puzzles of Every Kind. Logic puzzles are commonly associated with math, since math and logic are closely related. However, logic puzzles can come in any form – a riddle, a visual puzzle or even a word puzzle. 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In the Balance: Algebra Logic Puzzles Grades 4-6 has 0 available edition to buy at Alibris Geometry and Spatial Sense, Grades 4 to 6 is a practical guide that teachers will find useful in helping students to achieve the curriculum expectations outlined for Grades 4 to 6 in the Geometry and Spatial Sense strand of The Ontario Curriculum, Grades 1–8: Mathematics, 2005. The goal of the first chapter in grade 6 is to review the four basic operations with whole numbers, place value, and rounding, and to learn about exponents and problem solving. A lot of this chapter is review, and I hope this provides a gentle start for 6th grade math. In the next chapter, we will delve into some beginning algebra topics. ## In the Balance Algebra Logic Puzzles Grades 4-6 Chess Puzzle Paradise Intermediate Technology. A balance puzzle is a mathematical puzzle which challenges the solver to distribute a subset of numbers so that the several sides of a stylized diagram representing a balance scale are equal. The balance puzzle is a classical number puzzle in the World Puzzle Championship.It consists in a mobile or tree structure, with designated positions where the player must hang specified weights, so that, 07/12/2012 · the basics on how to solve a hanging balance puzzle. 128,000 Dominoes Falling into past a journey around the world 2 Guinness World Records) YouTub - Duration: 7:13. Ahmed Samir Recommended for you. ### Balance Sheet Crossword Puzzle #2 AccountingCoach Algebra Tutorial Practice Balance Puzzles 1 MathPapa. w w w . b e s t o f t h e r e a d e r . c a Welcome This e-book is part of a series called Best of The Reader. Most of the material in the e-books, 23/04/2010 · How do you solve In The Balance puzzle number 6?. w w w . b e s t o f t h e r e a d e r . c a Welcome This e-book is part of a series called Best of The Reader. Most of the material in the e-books Balance Puzzles, In the Balance, Grades 4-6 and Grades 7-9 Prime Factorization, Eratosthenes’ Sieve Greatest Common Factor and Least Common Denominator: Ladder Venn Diagram Prime Factors Materials and Resources Attribute Circles Centimeter Paper Map Pencils Large Sheets of Graph Paper Sets of Number Cards (Venn Diagram Activity) String or tape (for the Universe) Rainbow Cubes and … Balance Puzzles, In the Balance, Grades 4-6 and Grades 7-9 Prime Factorization, Eratosthenes’ Sieve Greatest Common Factor and Least Common Denominator: Ladder Venn Diagram Prime Factors Materials and Resources Attribute Circles Centimeter Paper Map Pencils Large Sheets of Graph Paper Sets of Number Cards (Venn Diagram Activity) String or tape (for the Universe) Rainbow Cubes and … In the Balance: Algebra Logic Puzzles Grades 4-6 by Lou Kroner starting at $76.50. In the Balance: Algebra Logic Puzzles Grades 4-6 has 0 available edition to buy at Alibris A balance puzzle is a mathematical puzzle which challenges the solver to distribute a subset of numbers so that the several sides of a stylized diagram representing a balance scale are equal. The balance puzzle is a classical number puzzle in the World Puzzle Championship.It consists in a mobile or tree structure, with designated positions where the player must hang specified weights, so that In the Balance: Algebra Logic Puzzles Grades 4-6 by Lou Kroner and a great selection of related books, art and collectibles available now at AbeBooks.com. 01/01/1997 · ThriftBooks sells millions of used books at the lowest everyday prices. We personally assess every book's quality and offer rare, out-of-print treasures. We deliver the joy of reading in 100% recycled packaging with free standard shipping on U.S. orders over$10. The goal of the first chapter in grade 6 is to review the four basic operations with whole numbers, place value, and rounding, and to learn about exponents and problem solving. A lot of this chapter is review, and I hope this provides a gentle start for 6th grade math. In the next chapter, we will delve into some beginning algebra topics. Balance Puzzles, In the Balance, Grades 4-6 and Grades 7-9 Prime Factorization, Eratosthenes’ Sieve Greatest Common Factor and Least Common Denominator: Ladder Venn Diagram Prime Factors Materials and Resources Attribute Circles Centimeter Paper Map Pencils Large Sheets of Graph Paper Sets of Number Cards (Venn Diagram Activity) String or tape (for the Universe) Rainbow Cubes and … Grade 7 & 8 Math Circles October 29/30, 2013 Logic Puzzles Introduction Mathematics isn’t at all about memorizing formulas or doing procedures over and over. It’s all about thinking logically, nding patterns and connections, and solving problems. A logic puzzle is a problem, challenge, or game that requires the player to use forms of Weekly "What Am I?" challenge puzzles for kids of all ages. Word Ladders. Students change one letter in each word on the puzzle to make a new word. These are great for teaching phonics, vocabulary, and critical thinking. Word-Maze Puzzles. Connect the letters in these maze puzzles to make words from the list. Then find a science fact written in Fifth Grade Logic Puzzles & Riddles Worksheets and Printables. Tease, stimulate and exercise fifth grade brains with these logic puzzles and riddle worksheets. Logic puzzles and riddles help to develop problem solving and critical thinking skills as well as vocabulary. The benefits of these game-based learning worksheets will last well beyond Fifth Grade Logic Puzzles & Riddles Worksheets and Printables. Tease, stimulate and exercise fifth grade brains with these logic puzzles and riddle worksheets. Logic puzzles and riddles help to develop problem solving and critical thinking skills as well as vocabulary. The benefits of these game-based learning worksheets will last well beyond Weekly "What Am I?" challenge puzzles for kids of all ages. Word Ladders. Students change one letter in each word on the puzzle to make a new word. These are great for teaching phonics, vocabulary, and critical thinking. Word-Maze Puzzles. Connect the letters in these maze puzzles to make words from the list. Then find a science fact written in Click an empty white square in the puzzle grid and a question box will appear. Type your answer in below the question and click Enter. Repeat the above steps until you have filled in the entire puzzle grid. To check your answers, click Check Puzzle (located below the puzzle grid). Incorrect answers will be highlighted in black. Find 9780762205523 In the Balance: Algebra Logic Puzzles Grades 7-9 by at over 30 bookstores. Buy, rent or sell. 01/01/1997 · ThriftBooks sells millions of used books at the lowest everyday prices. We personally assess every book's quality and offer rare, out-of-print treasures. We deliver the joy of reading in 100% recycled packaging with free standard shipping on U.S. orders over $10. 28/05/2016 · Free [PDF] Downlaod Logic Posters Problems & Puzzles (Grades 3-6) READ ONLINE CLICK HERE http://softebook.xyz/?book=0590642731 Move over Sudoku, here come Balance Benders™!You can use these activities as quick, fun logic problems or as stepping stones to success in algebra. Students develop problem-solving skills and pre-algebra skills as they solve balance puzzles that are more fun and addictive than Sudoku puzzles! In the Balance: Algebra Logic Puzzles Grades 4-6 by Lou Kroner starting at$76.50. In the Balance: Algebra Logic Puzzles Grades 4-6 has 0 available edition to buy at Alibris Christmas Sudoku Puzzles: Also included in the download are 2 Christmas themed sudoku puzzles. Kids love these as well. Plus, they challenge kids to put their logical reasoning to the test again. Although sudoku puzzles seem to be more common than grid puzzles, I’ll explain how to complete these as well. Puzzle No 80: Making A Scene You need to have solved puzzle 79, speak to the Rabbit/subject 3! Find three hint coins then speak to Beacon. Answer = there are 3 people present. What are the answers to puzzle 22 in the balance grades 4-6? We need you to answer this question! If you know the answer to this question, please register to join our limited beta program and Weekly "What Am I?" challenge puzzles for kids of all ages. Word Ladders. Students change one letter in each word on the puzzle to make a new word. These are great for teaching phonics, vocabulary, and critical thinking. Word-Maze Puzzles. Connect the letters in these maze puzzles to make words from the list. Then find a science fact written in w w w . b e s t o f t h e r e a d e r . c a Welcome This e-book is part of a series called Best of The Reader. Most of the material in the e-books 23/04/2010 · How do you solve In The Balance puzzle number 6? In the Balance: Algebra Logic Puzzles Grades 4-6 by Lou Kroner starting at $76.50. In the Balance: Algebra Logic Puzzles Grades 4-6 has 0 available edition to buy at Alibris w w w . b e s t o f t h e r e a d e r . c a Welcome This e-book is part of a series called Best of The Reader. Most of the material in the e-books ### Algebra Tutorial Practice Balance Puzzles 1 MathPapa Chess Puzzle Paradise Intermediate Technology. In the Balance: Algebra Logic Puzzles Grades 4-6 by Lou Kroner starting at$76.50. In the Balance: Algebra Logic Puzzles Grades 4-6 has 0 available edition to buy at Alibris, 07/12/2012 · the basics on how to solve a hanging balance puzzle. 128,000 Dominoes Falling into past a journey around the world 2 Guinness World Records) YouTub - Duration: 7:13. Ahmed Samir Recommended for you. Hanging Balance puzzle solve. YouTube. 23/04/2010 · How do you solve In The Balance puzzle number 6?, Weekly "What Am I?" challenge puzzles for kids of all ages. Word Ladders. Students change one letter in each word on the puzzle to make a new word. These are great for teaching phonics, vocabulary, and critical thinking. Word-Maze Puzzles. Connect the letters in these maze puzzles to make words from the list. Then find a science fact written in. ### in the balance puzzles? Yahoo Answers Balance Puzzles Brilliant Math & Science Wiki. Weekly "What Am I?" challenge puzzles for kids of all ages. Word Ladders. Students change one letter in each word on the puzzle to make a new word. These are great for teaching phonics, vocabulary, and critical thinking. Word-Maze Puzzles. Connect the letters in these maze puzzles to make words from the list. Then find a science fact written in https://en.wikipedia.org/wiki/Balance_puzzle Move over Sudoku, here come Balance Benders™!You can use these activities as quick, fun logic problems or as stepping stones to success in algebra. Students develop problem-solving skills and pre-algebra skills as they solve balance puzzles that are more fun and addictive than Sudoku puzzles!. Balance Math Puzzles require students to analyze balances to deduce the missing value. 2. Inside-Out Math Puzzles require students to reverse their thinking, using the inverse relationships between addition and subtraction and multiplication and division to solve the puzzle. 3. Fifth Grade Logic Puzzles & Riddles Worksheets and Printables. Tease, stimulate and exercise fifth grade brains with these logic puzzles and riddle worksheets. Logic puzzles and riddles help to develop problem solving and critical thinking skills as well as vocabulary. The benefits of these game-based learning worksheets will last well beyond Balance Math Puzzles require students to analyze balances to deduce the missing value. 2. Inside-Out Math Puzzles require students to reverse their thinking, using the inverse relationships between addition and subtraction and multiplication and division to solve the puzzle. 3. It's hard to believe this classic puzzle isn't already documented in MSE, but FWIW, here's one of the standard "static" solutions. "Static" means that the weighings are fixed in advance - we know which coin (or ball, or whatever) goes on which arm of the balance at each step regardless of the outcomes of previous weighings. Valentine's Day Puzzles (with pictures) Art Project: Stained Glass Decorations for Valentine's Day (grades K-6) Make colorful stained glass decorations for Valentine's Day (PDF file) Finish the Story Valentines for Vincent The Prize Box (Grades 2-3) Healing Hearts (Grades 3-4) In The Balance Puzzle 6 Grades 4 6. Showing top 8 worksheets in the category - In The Balance Puzzle 6 Grades 4 6. Some of the worksheets displayed are Session 6 solving equations, Sample work from, Teacher guide puzzles, Collection of 12 logic problems, Four forces grades k 4, Kids instructor, Kids instructor guide, Maths module 6. crossword puzzles C rossword puzzles are an excellent vehicle for cooperative learning. The crossword puzzles in this section are graded into the categories of easy and challenging, based upon the difficulty of the words required for completion. Teaching techniques. Working with a classmate, students can share their knowledge of English in solving the various vocabulary or grammatical crossword puzzles C rossword puzzles are an excellent vehicle for cooperative learning. The crossword puzzles in this section are graded into the categories of easy and challenging, based upon the difficulty of the words required for completion. Teaching techniques. Working with a classmate, students can share their knowledge of English in solving the various vocabulary or grammatical 28/05/2016 · Free [PDF] Downlaod Logic Posters Problems & Puzzles (Grades 3-6) READ ONLINE CLICK HERE http://softebook.xyz/?book=0590642731 Grade 7 & 8 Math Circles October 29/30, 2013 Logic Puzzles Introduction Mathematics isn’t at all about memorizing formulas or doing procedures over and over. It’s all about thinking logically, nding patterns and connections, and solving problems. A logic puzzle is a problem, challenge, or game that requires the player to use forms of Weekly "What Am I?" challenge puzzles for kids of all ages. Word Ladders. Students change one letter in each word on the puzzle to make a new word. These are great for teaching phonics, vocabulary, and critical thinking. Word-Maze Puzzles. Connect the letters in these maze puzzles to make words from the list. Then find a science fact written in A balance puzzle is a mathematical puzzle which challenges the solver to distribute a subset of numbers so that the several sides of a stylized diagram representing a balance scale are equal. The balance puzzle is a classical number puzzle in the World Puzzle Championship.It consists in a mobile or tree structure, with designated positions where the player must hang specified weights, so that Puzzle No 80: Making A Scene You need to have solved puzzle 79, speak to the Rabbit/subject 3! Find three hint coins then speak to Beacon. Answer = there are 3 people present. 01/01/1997 · ThriftBooks sells millions of used books at the lowest everyday prices. We personally assess every book's quality and offer rare, out-of-print treasures. We deliver the joy of reading in 100% recycled packaging with free standard shipping on U.S. orders over \$10. PDF Download Free PDF 50 Skill-Building Pyramid Puzzles: Math, Grades 4-6: Self-Checking Activity Pages That Motivate Students to Practice Key Math Skills Epu… In the Balance: Algebra Logic Puzzles Grades 7-9 by Lou Kroner starting at . In the Balance: Algebra Logic Puzzles Grades 7-9 has 0 available edition to buy at Alibris View all posts in Lagoon Pocket category
# Necessary and Sufficient Conditions for the Solution of Neumann Problem Let $$\Omega$$ be a domain with smooth boundary $$\partial \Omega$$, $$\bar{\Omega}$$ is compact. The Neumann problem:$$f \in C^{\infty}(\bar{\Omega})$$,$$g\in C^{\infty}(\partial \bar{\Omega})$$. Find a function $$\varphi \in C^{\infty}(\bar{\Omega})$$ satisfying $$\Delta \varphi=f$$ on $$\bar{\Omega}$$ and $$\frac{\partial}{\partial \overrightarrow{n}}\varphi=g$$ on $$\partial \bar{\Omega}$$. ($$\Delta$$ is the Laplace operator, $$\overrightarrow{n}$$ is the unit normal vector field.) How to prove the Neumann problem has a solution if and only if $$\int_{\bar\Omega}{fdx}=\int_{\partial \bar{\Omega}}{gdS}$$ ? Maybe I can solve the case of $$g=0$$. Edit: I have changed the proof of the \eqref{cc}$$\implies$$\eqref{np} to correct an error in the reasoning pointed out by the asker. The development is now necessarily more complicated but entirely correct. I'd like to thank Prof. Alberto Cialdea for the useful discussion on the topic and the suggestion to use Fredholm theory and the equivalent Neumann problem for the Laplace equation. What we want to prove is that the following Neumann problem $$\color{green}{ \begin{cases} \Delta \varphi(x)=f(x) & x\in\bar{\Omega}\\ \frac{\partial}{\partial \vec{n}}\varphi(x)=g(x)& x\in\partial\bar{\Omega} \end{cases}\label{np}\tag{NP}}$$ is solvable if and only if the following compatibility condition $$\color{blue}{ \int\limits_\bar{\Omega}f(x)\mathrm{d}x=\int\limits_{\partial\bar{\Omega}}g(x)\mathrm{d}\sigma_x. \label{cc}\tag{CC}}$$ holds (with obvious meaning of the symbols), i.e. \eqref{np}$$\iff$$\eqref{cc}. Let's proceed with proving the two opposite implications. 1. \eqref{np}$$\implies$$\eqref{cc}. Integrating on the domain $$\bar{\Omega}$$ both members of the Poisson equation $$\Delta \varphi=f$$ from \eqref{np} we get: $$\int\limits_\bar{\Omega}\Delta \varphi(x)\mathrm{d}x=\int\limits_\bar{\Omega}f(x)\mathrm{d}x. \label{1}\tag{1}$$ Now, remembering that $$\Delta=\nabla\cdot\nabla=\operatorname{div}\operatorname{grad}$$ and applying the Gauss-Green (divergence) theorem and the Neumann boundary condition from \eqref{np} to the first side of equation \eqref{1}, we have $$\begin{split} \int\limits_\bar{\Omega}\Delta \varphi(x)\mathrm{d}x &=\int\limits_\bar{\Omega}\nabla\cdot\nabla \varphi(x)\mathrm{d}x = \int\limits_{\partial\bar{\Omega}}\nabla \varphi(x)\cdot\vec{n}_x\mathrm{d}\sigma_x \\ &= \int\limits_{\partial\bar{\Omega}}\frac{\partial}{\partial \vec{n}}\varphi(x)\mathrm{d}\sigma_x = \int\limits_{\partial\bar{\Omega}}g(x)\mathrm{d}\sigma_x, \end{split}$$ thus $$\int\limits_\bar{\Omega}\Delta \varphi(x)\mathrm{d}x=\int\limits_{\partial\bar{\Omega}}g(x)\mathrm{d}\sigma_x, \label{2}\tag{2}$$ and this implies condition \eqref{cc}. 2. \eqref{cc}$$\implies$$\eqref{np}. Perhaps the easiest (and classical) way to prove this step is to transform problem \eqref{np} into a Fredholm integral equation of the second kind, and verify that the necessary (and sufficient, see the notes below) condition for its unique solvability is \eqref{cc}. To proceed in this way, we'll reduce problem \eqref{np} to the corresponding one for the Laplace equation and then apply the result known for the Neumann problem for harmonic functions. Let $$s(x-y)= \begin{cases} \dfrac{1}{2\pi}\log|{x}-{y}| & n=2\\ \\ -\dfrac{1}{(n-2)|\sigma_n}|{x}-{y}|^{2-n} & n\ge 3 \end{cases}$$ be the fundamental solution supported in $$y\in\Omega\subset\Bbb R^n$$ of the Laplace operator: if we formally define \begin{align} \varphi^\ast(x)&=\varphi(x)-\int\limits_\bar{\Omega}s(x-y)f(y)\mathrm{d}y & x\in\Omega \\ g^\ast(x)&=g(x)-\frac{\partial}{\partial \vec{n}}\int\limits_\bar{\Omega}s(x-y)f(y)\mathrm{d}y & \: x\in\partial\Omega\label{3}\tag{3} \end{align} we have that $$\varphi(x)$$ solves \eqref{np} if and only if $$\varphi(x)$$ is harmonic and solves $$\color{brown}{ \begin{cases} \Delta \varphi^\ast(x)=0 & x\in\bar{\Omega}\\ \frac{\partial}{\partial \vec{n}}\varphi^\ast(x)=g^\ast(x)& x\in\partial\bar{\Omega} \end{cases}\label{hnp}\tag{HNP}}$$ Now let's search for $$\varphi^\ast(x)$$ by expressing it as a single layer potential, i.e. $$\varphi^\ast(x)= \int\limits_{\partial\bar{\Omega}}s(x-y) \mu(y)\mathrm{d}\sigma_y,\label{4}\tag{4}$$ and searching for the unknown (charge) density $$\mu(x)$$, $$x\in\partial\bar{\Omega}$$. By applying the classical jump formula for the first derivatives of harmonic functions to \eqref{4} (see for example [2], §22.7, pp. 304-306), i.e. $$\lim_{\substack{x\to x_0 \\ x\in \vec{n}_{x_0}^+}} \frac{\partial}{\partial \vec{n}_{x}} \int\limits_{\partial\bar{\Omega}}s(x-y)\mu(y)\mathrm{d}\sigma_y = -\frac{1}{2}\mu(x_0) + \frac{\partial}{\partial \vec{n}_{x_0}} \int\limits_{\partial\bar{\Omega}}s(x_0-y)\mu(y)\mathrm{d}\sigma_y$$ we get the following Fredholm integral equation for the unknown density $$\mu(x)$$ $$g^\ast(x)= - \frac{1}{2}\mu(x) + \int\limits_{\partial\bar{\Omega}} \frac{\partial}{\partial \vec{n}_{x}} s(x-y)\mu(y)\mathrm{d}\sigma_y \label{5}\tag{5}$$ whose sufficient condition for solvability, by Fredholm's alternative theorem (see for example [2], §16.3, pp. 225-227), is $$\color{purple}{ \int\limits_{\partial\bar{\Omega}}g^\ast(x)\mathrm{d}\sigma_x=0 \label{hcc}\tag{HCC}}$$ Now let's analyze condition \eqref{hcc}: substituting \eqref{3} in it, we have $$\begin{split} \int\limits_{\partial\bar{\Omega}}g^\ast(x)\mathrm{d}\sigma_x &= \int\limits_{\partial\bar{\Omega}}\bigg[g(x) - \frac{\partial}{\partial \vec{n}}\int\limits_\bar{\Omega}s(x-y)f(y)\mathrm{d}y\bigg]\mathrm{d}\sigma_x\\ & = \int\limits_{\partial\bar{\Omega}} g(x) \mathrm{d}\sigma_x -\int\limits_{\partial\bar{\Omega}}\frac{\partial}{\partial \vec{n}}\int\limits_\bar{\Omega}s(x-y)f(y)\mathrm{d}y\,\mathrm{d}\sigma_x\\ & \text{and applying the divergence theorem}\\ & = \int\limits_{\partial\bar{\Omega}} g(x) \mathrm{d}\sigma_x -\int\limits_\bar{\Omega} \Delta\int\limits_\bar{\Omega}s(x-y)f(y)\mathrm{d}y\,\mathrm{d}x\\ & = \int\limits_{\partial\bar{\Omega}} g(x) \mathrm{d}\sigma_x -\int\limits_\bar{\Omega} f(x) \mathrm{d}x \end{split}\label{6}\tag{6}$$ and the proof is then finished. Final notes on the method of proof of the implication \eqref{cc}$$\implies$$\eqref{np}. • The same very same method can be used to prove directly the equivalence \eqref{cc}$$\iff$$\eqref{np}: as alluded above, condition \eqref{hcc} (and his equivalent condition \eqref{cc} for Poisson's equation), is de facto a necessary and sufficient condition for the solvability of integral equation \eqref{5}. This is the approach followed for example by V.S. Vladimirov for the Laplace equation ([2], §23.5, pp. 315-318) which, however, does not explicitly deals with Poisson's equation, i.e. does not provide the ansatz \eqref{3} nor the development \eqref{6}. • The same method can also be used to prove the existence and uniqueness of the weak solution (and thus the weak formulation) of the Neumann problem \eqref{np} even for the more general divergence form equation, $$\operatorname{div}\big(k(x)\nabla \varphi(x)\big)-a(x)\varphi(x)=f(x)$$ obviously without any reference nor use of potential theory. To see why, it is sufficient to remember that the weak formulation of problem \eqref{np} is simply a set of integral identities to be satisfied by the solution $$\varphi$$: the details can be found in reference [1], chapter IV, §1.2, 1.6. [1] V. P. Mikhailov (1978), Partial differential equations, Translated from the Russian by P.C. Sinha. Revised from the 1976 Russian ed., Moscow: Mir Publishers, p. 396 MR0601389, Zbl 0388.3500. [2] V. S. Vladimirov (1971)[1967], Equations of mathematical physics, Translated from the Russian original (1967) by Audrey Littlewood. Edited by Alan Jeffrey, (English), Pure and Applied Mathematics, Vol. 3, New York: Marcel Dekker, Inc., pp. vi+418, MR0268497, Zbl 0207.09101. • Thanks, why does $CC \implies NP$ follows simply by reversing of the previously listed steps?I don't think it's obvious. – Xingying Li May 7 at 14:47 • @XingyingLi you are welcome. I will add a better explanation later, by expanding point 2. – Daniele Tampieri May 7 at 14:54 • @XingyingLi done. I tend to be quite brief on the final parts of answers, so if you need further explanations, do not hesitate asking. – Daniele Tampieri May 7 at 15:33 • I can't understand this step:since (2) implies that $$\frac{\partial}{\partial\vec{n}}\varphi(x)=g(x)\quad\text{ for almost all }x\in\partial\bar{\Omega}$$. – Xingying Li May 7 at 20:43 • I know that"$\int_{\partial{\bar{\Omega}}}{\frac{\partial}{\partial\overrightarrow{n}}\varphi ds_x}=\int_{\partial{\bar{\Omega}}}{gds_x}$". – Xingying Li May 7 at 20:49
# Math Help - Help on solving first-order NONhomogeneous PDE 1. ## Help on solving first-order NONhomogeneous PDE Hello everybody. I'm trying to solve this first-order NONhomogenous PDE. But because my awfully bad textbook only gave examples on how to solve homogeneous PDEs, I'm not sure what to do. Here's my scratch work. I also know the theorem that if two solutions solve linear NONhomogeneous PDE, then their difference solve linear homogeneous PDE. But I don't think that's going to help here. Problem: Solve $\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}=1$ Scratch work: I know how to solve the HOMOgeneous PDE: $\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}=0$ The LHS is just the directional derivative of $u$ in the direction of $[1, 1]$. So if a curve in 3D has $[1,1]$ as a tangent vector, the curve's equation is just $\frac{dy}{dx} = 1$ so $y = x + C_1$ so $x - y = -C_1 = C$. So $u(x,y) = f(x - y)$, where $f$ is differentiable. But how do I solve the NONhomogeneous question from this? Thanks everybody. 2. ## Re: Help on solving first-order NONhomogeneous PDE One solution is u = x. If you let $u = x + v$ you'll end up with $v_x + v_y = 0$. BTW - do you know the method of characteristics? 3. ## Re: Help on solving first-order NONhomogeneous PDE Originally Posted by Danny One solution is u = x. If you let $u = x + v$ uou'll end up with $v_x + v+y = 0$. BTW - do you know the method of characteristics? Hello and thanks Danny. So $u(x,y) = x$ could've been just guessed? But if $u(x,y) = x + v$, wouldn't you get $u_x + u_y = (1 + v_x) + 0$? Since $(x + v)_y = 0$ because there is no y in here. And I don't think so since I'm taking a first course in PDEs. 4. ## Re: Help on solving first-order NONhomogeneous PDE Well, you assme that $u(x,y) = v(x,y) + x$. The method of characteristics will probably come up. It's a way to solve $a(x,y,u)u_x + b(x,y,u) u_y = c(x,y,u)$. 5. ## Re: Help on solving first-order NONhomogeneous PDE Hello and thanks Danny. Originally Posted by Danny Well, you assme that $u(x,y) = v(x,y) + x$. But when you say $v(x,y)$ here, do you mean $v(x,y) = f(x - y)$ and not just any $v(x,y)$ which I found in my original post for the homogeneous PDE? And did I get $u_x + u_y = (1 + v_x) + 0$ right? 6. ## Re: Help on solving first-order NONhomogeneous PDE Well, you would end up with that $v$ in the end. Also, if you let $u = v + x$ then $u_x + u_y = 1$ gives $\left( v_x + 1\right) + \left( v_y + 0\right) = 1$ gives $v_x + v_y = 0$.
# NAG FL Interfacef12jaf (feast_​init) ## ▸▿ Contents Settings help FL Name Style: FL Specification Language: ## 1Purpose f12jaf initializes a data structure for the NAG FEAST suite of routines consisting of f12jaf, f12jbf, f12jef, f12jff, f12jgf, f12jjf, f12jkf, f12jrf, f12jsf, f12jtf, f12juf, f12jvf and f12jzf. It is used to find some of the eigenvalues, and the corresponding eigenvectors, of a standard, generalized or polynomial eigenvalue problem. The suite of routines is suitable for the solution of large, sparse eigenproblems where only those eigenvalues within a selected region of the complex plane are required. ## 2Specification Fortran Interface Subroutine f12jaf ( Integer, Intent (Inout) :: ifail Type (c_ptr), Intent (Out) :: handle #include <nag.h> void f12jaf_ (void **handle, Integer *ifail) The routine may be called by the names f12jaf or nagf_sparseig_feast_init. ## 3Description The NAG FEAST suite of routines is designed to calculate some of the eigenvalues, $\lambda$, and the corresponding eigenvectors, $x$, of a standard eigenvalue problem $Ax=\lambda x$, a generalized eigenvalue problem $Ax=\lambda Bx$, where $A$ and $B$ are large and sparse, or a polynomial eigenvalue problem ${\sum }_{i}{\lambda }^{i}{A}_{i}x=0$. It can also be used to find eigenvalues/eigenvectors of smaller scale dense problems. The NAG FEAST suite is based on the FEAST library, using contour integration to find the eigenvalues within a contour in the complex plane. f12jaf is a setup routine which must be called before the option setting routine f12jbf, before the contour definition routines f12jef, f12jff or f12jgf, and before the reverse communication solvers f12jjf, f12jkf, f12jrf, f12jsf, f12jtf, f12juf or f12jvf. This setup routine initializes the handle to a data structure used internally by the NAG FEAST suite and sets (to their default values) all options that can be set by you via the option setting routine f12jbf. For details of the options available and how to set them see Section 11.1 in f12jbf. When the handle is no longer needed, f12jzf must be called to destroy it and deallocate all the allocated memory and data within. ## 4References Polizzi E (2009) Density-Matrix-Based Algorithms for Solving Eigenvalue Problems Phys. Rev. B. 79 115112 ## 5Arguments 1: $\mathbf{handle}$Type (c_ptr) Output Note: handle does not need to be set on input. On exit: holds a handle to the internal data structure used by the NAG FEAST suite. 2: $\mathbf{ifail}$Integer Input/Output On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected. A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not. If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ or $\mathbf{1}$ is used it is essential to test the value of ifail on exit. On exit: ${\mathbf{ifail}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6). ## 6Error Indicators and Warnings If on entry ${\mathbf{ifail}}=0$ or $-1$, explanatory error messages are output on the current error message unit (as defined by x04aaf). Errors or warnings detected by the routine: ${\mathbf{ifail}}=-99$ See Section 7 in the Introduction to the NAG Library FL Interface for further information. ${\mathbf{ifail}}=-399$ Your licence key may have expired or may not have been installed correctly. See Section 8 in the Introduction to the NAG Library FL Interface for further information. ${\mathbf{ifail}}=-999$ Dynamic memory allocation failed. See Section 9 in the Introduction to the NAG Library FL Interface for further information. Not applicable.
# Effect of time duration in bandpass filtering I am new in DSP, but I am trying to process EEG data to decompose into the bands, theta, alpha, and others. The raw data is processed: 1. Remove the DC offset by subtracting the average value from the entire data channels. 2. High pass filtering. Both such as in. The using the bandpass function of Matlab it is bandpassed. delta = [0.1 4]; theta = [4 8]; alpha = [8 12]; beta = [12 30]; gamma = [30 45]; bands = [delta; theta; alpha; beta; gamma]; fs = 128; % sampling freq of the EEG % choosing a segment of data time = 2 ; % secs fs = 128; size_t = fs * time; sample_filt = af3(1:size_t); % AF3, an EEG node % band passing eeg_bands = {}; for i = 1 : size(bands, 1) eeg_bands{i} = bandpass( sample_filt, bands(i,:), fs); end % code to plot I performed bandpass for samples of different time duration, however, I saw the time duration changes the amplitudes of bands at the start and end in gamma and beta (high frequency bands). here, I plot three figures. Figure 1 of long 5 secs (for me, visually it is reasonable). Figure 2, of 2 secs of duration and notice the start of signals beta and gamma are noisy. Taking in account EEG, I ask you, 1. is there any ideal time duration (min, or max) of the signal to make band passing ? 2. Mi data has a duration of 22 minutes at 128 Hz of sampling, can I performed band pass of all the length or by small segments or windows? I thank you in advance, please feel free to comment, I need to be right to extract features in the next step.
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Author Message TAGS: Senior Manager Joined: 18 Sep 2009 Posts: 367 Followers: 3 Kudos [?]: 170 [2] , given: 2 If xy+z=x(y+z), which of the following must be true? [#permalink]  23 Sep 2010, 12:44 2 KUDOS 4 This post was BOOKMARKED 00:00 Difficulty: 35% (medium) Question Stats: 65% (01:52) correct 35% (01:03) wrong based on 344 sessions If xy+z=x(y+z), which of the following must be true? A. x=0 and y=0 B. x=1 and y=1 C. y=1 and z=0 D. x=1 or y=0 E. x=1 or z=0 [Reveal] Spoiler: OA Last edited by Bunuel on 20 Mar 2012, 22:12, edited 3 times in total. Corrected OA Math Expert Joined: 02 Sep 2009 Posts: 28352 Followers: 4486 Kudos [?]: 45467 [15] , given: 6762 Re: must be true [#permalink]  23 Sep 2010, 12:46 15 KUDOS Expert's post 2 This post was BOOKMARKED TomB wrote: If xy+z=x(y+z), which of the following must be true? A. x=0 and y=0 B. x=1 and y=1 C. y=1 and z=0 D. x=1 or y=0 E. x=1 or z=0 $$xy+z=x(y+z)$$ --> $$xy+z=xy+xz$$ --> $$xy$$ cancels out --> $$xz-z=0$$ --> $$z(x-1)=0$$ --> either $$z=0$$ (in this case $$x$$ can take ANY value) OR $$x=1$$ (in this case $$z$$ can take ANY value). To elaborate more: As the expression with $$y$$ cancels out, we can say that given expression $$xy+z=x(y+z)$$ does not depend on value of $$y$$. Which means that $$y$$ can take ANY value. So all answer choices which specify the exact value of $$y$$ are wrong. Next: "AND" in answer choices means that BOTH values must be true, but "OR" in answer choices means that EITHER value must be true. Hope it helps. _________________ Math Expert Joined: 02 Sep 2009 Posts: 28352 Followers: 4486 Kudos [?]: 45467 [3] , given: 6762 Re: If xy + z = x(y + z) [#permalink]  08 Dec 2010, 09:00 3 KUDOS Expert's post Intern Joined: 05 Mar 2013 Posts: 45 Location: India Concentration: Entrepreneurship, Marketing GMAT Date: 06-05-2013 GPA: 3.2 Followers: 1 Kudos [?]: 30 [2] , given: 14 Re: Number properties [#permalink]  13 Apr 2013, 22:53 2 KUDOS rakeshd347 wrote: singhmaharaj wrote: If xy + z = x(y+z) which of the following must be true A. X=0 and z=0 B. X=1 and y=1 C. y=1 and z=0 D. X=1 and y=0 E. X=1 and z=0 xy+z=xy+xz…cancel xy form both sides….xz=z….deduct z from both sides xz-z=0 or z(x-1)=0 so x=1 and z=0 z(x-1) = 0 .... either x-1 can be zero or z can be zero... possible options can be z=0 and x-1 be anything or z can be anything and x-1 can be zero .... Also the question didn't mention anything about x,y,z being positive _________________ "Kudos" will help me a lot!!!!!!Please donate some!!! Completed Official Quant Review OG - Quant In Progress Official Verbal Review OG 13th ed MGMAT IR AWA Structure Yet to do 100 700+ SC questions MR Verbal MR Quant Verbal is a ghost. Cant find head and tail of it. Retired Moderator Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL Joined: 04 Oct 2009 Posts: 1721 Location: Peru Schools: Harvard, Stanford, Wharton, MIT & HKS (Government) WE 1: Economic research WE 2: Banking WE 3: Government: Foreign Trade and SMEs Followers: 78 Kudos [?]: 473 [1] , given: 109 Re: must be true [#permalink]  08 Dec 2010, 09:18 1 KUDOS _________________ "Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can." My Integrated Reasoning Logbook / Diary: my-ir-logbook-diary-133264.html GMAT Club Premium Membership - big benefits and savings Magoosh GMAT Instructor Joined: 28 Dec 2011 Posts: 2432 Followers: 767 Kudos [?]: 3090 [1] , given: 38 Re: Which of the following must be true - Gmatprep [#permalink]  10 Jan 2012, 12:05 1 KUDOS Expert's post Hi there! I'm happy to help with this. So, the question: If xy + z = x(y + z), then (A) x = 0 and z = 0 (B) x = 1 and y = 1 (C) y = 1 and z = 0 (D) x = 1 or y = 0 (E) x = 1 or z = 0 So, as a very general rough approximation rule, when variables are multiplied, the mathematical consequences will far more often involve the word "or" than the word "and." That's just a rough-and-ready rule to use if all else is lost. Let's look at this question. We have: xy + z = x(y + z) Distribute on the right side: xy + z = xy + xz Subtract xy from both sides: z = xz So first of all, we get this funny equation with x & z in it, without y, so that means: there's no restriction on y, only restrictions on x & z. In solving the equation z = xz, you may be tempted to divide by z, but WHOA THERE! Before you divide by a variable, you have to ask yourself the deeply heartfelt question: could this variable equal zero? If so, then dividing by it would break all mathematical laws, and Santa Claus would find out you've been bad. So, what do we do? We'll look at two cases: (i) z = 0, and (ii) z =/ 0 (i) if z = 0, then both sides of the equation x = xz equal zero, and the equation is true. So, one possibility that makes the equation true is z = 0 (ii) if z is not equal to zero, then we can divide by z, and get 1 = x. That's the other solution that makes the equation true. The solutions are x = 1 or z = 0, answer choice E. Here's another practice question for you. http://gmat.magoosh.com/questions/110 The question at that link should be followed by a video explanation. Please let me know if you have any questions about what I've said. Good luck tomorrow!! Mike _________________ Mike McGarry Magoosh Test Prep Intern Joined: 11 Aug 2010 Posts: 23 Schools: SUNY at Stonyb Brook WE 1: 4 yrs Followers: 0 Kudos [?]: 16 [0], given: 37 Re: must be true [#permalink]  27 Oct 2010, 18:17 Thanks again Bunuel . I somehow always got stucked at option C Your explanation is awesome _________________ Consider giving Kudos if my post helped you in some way Intern Joined: 02 Sep 2010 Posts: 48 Followers: 2 Kudos [?]: 17 [0], given: 16 Re: must be true [#permalink]  05 Dec 2010, 08:19 Thanks Bunuel..The OA given is wrong its E thanks for proving it ..I was left wondering how answer could be D,Because I also got my answer as E Manager Joined: 02 Oct 2010 Posts: 159 Followers: 2 Kudos [?]: 17 [0], given: 29 Re: must be true [#permalink]  19 Dec 2010, 21:26 Bunuel wrote: TomB wrote: xy+z=x(y+z). which of the following must be true? a) x=0 and y=0 b) x=1 and y=1 c)y=1 and z=0 d)x=1 or y=0 e) x=1 or z=0 $$xy+z=x(y+z)$$ --> $$xy+z=xy+xz$$ --> $$xy$$ cancels out --> $$xz-z=0$$ --> $$z(x-1)=0$$ --> either $$z=0$$ (in this case $$x$$ can take ANY value) OR $$x=1$$ (in this case $$z$$ can take ANY value). To elaborate more: As the expression with $$y$$ cancels out, we can say that given expression $$xy+z=x(y+z)$$ does not depend on value of $$y$$. Which means that $$y$$ can take ANY value. So all answer choices which specify the exact value of $$y$$ are wrong. Next: "AND" in answer choices means that BOTH values must be true, but "OR" in answer choices means that EITHER value must be true. Hope it helps. Yeah the explanation was very helpful.. Manager Status: MBA Aspirant Joined: 12 Jun 2010 Posts: 178 Location: India WE: Information Technology (Investment Banking) Followers: 3 Kudos [?]: 39 [0], given: 1 Re: Which of the following must be true - Gmatprep [#permalink]  10 Jan 2012, 19:46 Given xy+z = xy+xz => xz-z = 0 so z(x-1) = 0 => z=0, x=1 (E) Manager Status: Seeking new horizons... Joined: 03 Sep 2010 Posts: 64 Location: Taiwan Concentration: Strategy, Technology Followers: 1 Kudos [?]: 19 [0], given: 29 Re: Which of the following must be true - Gmatprep [#permalink]  10 Jan 2012, 20:01 mikemcgarry has given an exhaustive explanation! Simply put, it's basic algebra. Simplify the expression and equate to zero. Watch out for the use of "and" and "or" in the answer choices. _________________ Learn to walk before you run. Director Status: Joined: 24 Jul 2011 Posts: 642 GMAT 1: 780 Q51 V48 GRE 1: 1540 Q800 V740 Followers: 85 Kudos [?]: 350 [0], given: 14 Re: Triple variable algebra problem [#permalink]  20 Mar 2012, 20:25 xy + z = x(y+z) => xy+z = xy + xz => z = xz => z=0 or x=1 Option (E) _________________ GyanOne | http://www.GyanOne.com | +91 9899831738 MBA Section Director Affiliations: GMAT Club Joined: 21 Feb 2012 Posts: 1817 Location: India City: Pune GPA: 3.4 Followers: 218 Kudos [?]: 1484 [0], given: 1203 Re: Number properties [#permalink]  13 Apr 2013, 20:53 Expert's post singhmaharaj wrote: If xy + z = x(y+z) which of the following must be true A. X=0 and z=0 B. X=1 and y=1 C. y=1 and z=0 D. X=1 and y=0 A. X=1 and z=0 xy + z = x(y+z)-----------> xy + z = xy+xz ---------> z = xz --------> x=1 and Z= 0 or 1 Note :- Here the value of y does not matter since xy = xy going to be zero for any value of y _________________ Be the coolest guy in the MBA Forum - Be a threadmaster! Have a blog? Feature it on GMAT Club! All MBA Resources All 'Sticky' Topics at one place GMAT Club Premium Membership - big benefits and savings Next Generation GMATClub CATS with Brilliant Analytics. Senior Manager Joined: 28 Apr 2012 Posts: 308 Location: India Concentration: Technology, General Management GMAT 1: 650 Q48 V31 GMAT 2: 770 Q50 V47 WE: Information Technology (Computer Software) Followers: 16 Kudos [?]: 251 [0], given: 142 Re: Number properties [#permalink]  13 Apr 2013, 21:49 singhmaharaj wrote: If xy + z = x(y+z) which of the following must be true A. X=0 and z=0 B. X=1 and y=1 C. y=1 and z=0 D. X=1 and y=0 A. X=1 and z=0 xy + z = x(y+z) => xy + z = xy + xz => z = xz The statement is true for both options A and E. _________________ "Appreciation is a wonderful thing. It makes what is excellent in others belong to us as well." ― Voltaire Press Kudos, if I have helped. Thanks! shit-happens-my-journey-to-172475.html#p1372807 Intern Joined: 12 Jan 2013 Posts: 1 Followers: 0 Kudos [?]: 0 [0], given: 2 Re: Number properties [#permalink]  13 Apr 2013, 23:23 Correct question is If xy+z = x(y+z), which of the following must be true? 1. x=0 and z=0 2. x=1 and y=1 3. y=1 and z=0 4. x=1 or y=0 5. x=1 or z=0 Solution : xy + z = xy + xz z = xz i.e. z(x-1) = 0 so, z = 0 or x = 1 or both Intern Joined: 14 Sep 2013 Posts: 9 Followers: 0 Kudos [?]: 0 [0], given: 1 Re: If xy+z=x(y+z), which of the following must be true? [#permalink]  20 Oct 2013, 10:33 When I substituted b the answer match up as well... Some one please explain. Math Expert Joined: 02 Sep 2009 Posts: 28352 Followers: 4486 Kudos [?]: 45467 [0], given: 6762 Re: If xy+z=x(y+z), which of the following must be true? [#permalink]  20 Oct 2013, 10:35 Expert's post haotian87 wrote: When I substituted b the answer match up as well... Some one please explain. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 5400 Followers: 311 Kudos [?]: 60 [0], given: 0 Re: If xy+z=x(y+z), which of the following must be true? [#permalink]  09 Dec 2014, 09:16 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: If xy+z=x(y+z), which of the following must be true?   [#permalink] 09 Dec 2014, 09:16 Similar topics Replies Last post Similar Topics: If xy+z=x(y+z), which of the following must be true? 9 07 Aug 2011, 02:55 39 If xy+z=x(y+z), which of the following must be true? 7 18 Jun 2011, 03:40 2 If XY+Z=X(Y+Z), which of the following must be true ? 5 25 Aug 2010, 23:20 if xy+z=x(y+z), which of the following must be true? a. 3 19 Aug 2007, 08:45 If xy+z=x(y+z), which of the following must be true? 1) 8 04 Jul 2006, 02:10 Display posts from previous: Sort by
# 1988 AIME Problems/Problem 13 ## Problem Find $a$ if $a$ and $b$ are integers such that $x^2 - x - 1$ is a factor of $ax^{17} + bx^{16} + 1$. ## Solution ### Solution 1 Let's work backwards! Let $F(x) = ax^{17} + bx^{16} + 1$ and let $P(x)$ be the polynomial such that $P(x)(x^2 - x - 1) = F(x)$. First, it's kinda obvious that the constant term of $P(x)$ must be $- 1$. Now, we have $(x^2 - x - 1)(c_1x^{15} + c_2x^{14} + \cdots + c_{15}x - 1)$, where $c_{15}$ is some random coefficient. However, since $F(x)$ has no $x$ term, it must be true that $c_{15} = - 1$. Let's find $c_{14}$ now. Notice that all we care about in finding $c_{14}$ is that $(x^2 - x - 1)(\cdots + c_{14}x^2 + x - 1) = \text{something} + 0x^2 + \text{something}$. Therefore, $c_{14} = - 2$. Undergoing a similar process, $c_{13} = 3$, $c_{12} = - 5$, $c_{11} = 8$, and we see a nice pattern. The coefficients of $P(x)$ are just the Fibonacci sequence with alternating signs! Therefore, $a = c_1 = F_{16}$, where $F_{16}$ denotes the 16th Fibonnaci number and /boxed{$a = 987$}. ### Solution 2 Let $F_n$ represent the $n$th number in the Fibonacci sequence. Therefore, $x^2 - x - 1 = 0\Longrightarrow x^n = F_n(x),\ n\in N\Longrightarrow x^{n + 2} = F_{n + 1}\cdot x + F_n,\ n\in N\ .$ The above uses the similarity between the Fibonacci recursive definition, $F_{n+2} - F_{n+1} - F_n = 0$, and the polynomial $x^2 - x - 1 = 0$. $0 = ax^{17} + bx^{16} + 1 = a(F_{17}\cdot x + F_{16}) + b(F_{16}\cdot x + F_{15}) + 1\Longrightarrow$ $(aF_{17} + bF_{16})\cdot x + (aF_{16} + bF_{15} + 1) = 0,\ x\not\in Q\Longrightarrow$ $aF_{17} + bF_{16} = 0$ and $aF_{16} + bF_{15} + 1 = 0\Longrightarrow$ $a = F_{16},\ b = - F_{17}\Longrightarrow \boxed {a = 987,\ b = - 1597}\ .$ ### Solution 3 We can long divide and search for a pattern; then the remainder would be set to zero to solve for $a$. Writing out a few examples quickly shows us that the remainders after each subtraction follow the Fibonacci sequence. Carrying out this pattern, we find that the remainder is $(F_{16} + F_{17}a)x + F_{15}b + F_{16}a + 1 = 0$. Since the coefficient of $x$ must be zero, this gives us two equations, $F_{16}b + F_{17}a = 0$ and $F_{15}b + F_{16}a + 1 = 0$. Solving these two as above, we get that $a = 987$. There are various similar solutions which yield the same pattern, such as repeated substitution of $x^2 = x + 1$ into the larger polynomial. ### Solution 4 The roots of $x^2-x-1$ are $\phi$ (the golden ratio) and $1-\phi$. These two must also be roots of $ax^{17}+bx^{16}+1$. Thus, we have two equations: $a\phi^{17}+b\phi^{16}+1=0$ and $a(1-\phi)^{17}+b(1-\phi)^{16}+1=0$. Subtract these two and divide by $\sqrt{5}$ to get $\frac{a(\phi^{17}-(1-\phi)^{17})}{\sqrt{5}}+\frac{b(\phi^{16}-(1-\phi)^{16})}{\sqrt{5}}=0$. But the formula for the nth fibonacci number is $\frac{\phi^n-(1-\phi)^n}{\sqrt{5}}$ (You may want to research this). Thus, we have $1597a+987b=0$, so since $1597$ and $987$ are relatively prime, and the anwser must be a positive integer less than $1000$, we can guess that it equals $\boxed{987}$.
# identify_format¶ astropy.io.registry.identify_format(origin, data_class_required, path, fileobj, args, kwargs)[source] [edit on github] Loop through identifiers to see which formats match. Parameters: origin : str A string "read or "write" identifying whether the file is to be opened for reading or writing. data_class_required : object The specified class for the result of read or the class that is to be written. path : str, other path object or None The path to the file or None. fileobj : File object or None. An open file object to read the file’s contents, or None if the file could not be opened. args : sequence Positional arguments for the read or write function. Note that these must be provided as sequence. kwargs : dict-like Keyword arguments for the read or write function. Note that this parameter must be dict-like. valid_formats : list List of matching formats.
# The DOF problem in iris acquisition systems This is the third post in the series on Iris acquisition for biometrics. In the first and the second posts we saw that, at least in theory, iris recognition is an ideal biometric, and we went through some of the desirable properties of an iris acquisition system. However, currently most iris recognition systems require a single subject to stand (or move slowly) at a certain standoff distance from the camera in order capture and process iris images. Wouldn’t it be nice if iris recognition could be simultaneously performed for a group of people who may be standing/ moving within a large volume? Such systems could potentially be used in crowded places such as airports, stadiums, railway stations etc. In this post, we will look at one of the limitations of current iris recognition systems – the limited depth of field, the fundamental cause of this limitation, and how some of the current systems are addressing this problem. ## The problem of DOF The inability of any conventional imaging system to capture sharp images within a large volume is illustrated in the Figure 1. Figure 1 Depth of field (DOF) problem. Image of the three human-figure cut-outs with sinusoidal patterns (2 lp/mm) and artificial irises and placed apart by 11 cm from each other. The camera, with lens of 80 mm focal length and f/5 aperture, was focused on the middle cut-out (3.6 meters away from the camera). It is evident that the spatial resolution in the image falls off rapidly with increasing distance from the plane of sharp focus (middle cut-out) inhibiting the camera from resolving fine details uniformly across the imaging volume. Perfect imaging corresponds to the ability of an imager to produce a scaled replica of an object in the image  space [1].  When only a small portion of the light  wave emerging  from an infinitesimally  small point source of light is collected through a finite opening of a camera’s aperture (Figure 2 (a)), the replica in the image space is not exact even in the absence of aberrations; instead, the image of the point spreads out in space due to diffraction at the aperture. This dispersed response in the three-dimensional image space is called Point Spread Function (PSF).  The spreading of the PSF along   the transverse (xy-axis) direction (a 2D PSF) restricts an imager’s ability to resolve fine details (spatial frequency) in the image. For an extended object, which is made of several points, the 2D PSF smears the responses from neighboring points into each other causing blur. Similarly, the spread along the longitudinal direction (z-axis) limits the ability to discriminate points staggered closely in the direction of the optical axis causing a region of uncertainty; however, the extension of the 3D PSF along the optical axis enables multiple spatially-separated objects (or points) within a volume in the object space to form acceptably sharp images at once.  Conversely, an (point) object in the object space may be placed anywhere within this zone and still form a satisfactory image. This zone of tolerance in the object space is called depth of field. The corresponding zone in the image space is called depth of focus [2]. In this post, the acronym “DOF” is used for both depth of field and depth of focus wherever its meaning is apparent from the context. In the image space, the DOF is defined as the region of the 3D PSF where the intensity is above 80% of the central maximum [3,4]. This zone is in the shape of a prolate spheroid. In the absence of aberrations, the maximum intensity occurs at the geometric focal point, $z_g$, where contributions from all parts of the pupil are all in phase. Figure 2 (b) shows the aberration-free intensity distribution, $I_n(r, \delta z)$, as a function of defocus $\delta z = z_i - z_g$ about the geometric focal point for a light source placed at 100 millimeters from a lens of focal-length of 25 mm and aperture diameter of 5 mm. The expression for the distribution—normalized to make $I_n(0,0)$ equal to unity—is obtained using scalar diffraction theory and paraxial assumptions. Figure 2 Incoherent impulse response and DOF. (a) The image A’ of a point source A spreads out in space forming a zone of tolerance called Depth of Focus (DOF) in the image space; (b) The normalized focal intensity distribution of the 3D PSF of a 25mm, f/5 lens imaging an axial point source at a distance of 100mm. The expression for the 3D PSF was obtained for a circular aperture using scalar diffraction theory and paraxial assumption. The DOF, having prolate spheroidal shape, is defined as the region within which the intensity has above 80% of the intensity at the geometric focus point. The figure shows iso-surfaces representing 0.8, 0.2, 0.05 and 0.01 intensity levels. The ticks on the left vertical side indicate the locations of the first zeroes of the Airy pattern in the focal plane. The vertical axis has been exaggerated by 10 times in order to improve the display of the distribution. The shape—length and breadth—of the 80% intensity region (Figure 2(b)) dictates the quality of the image acquired by an imager in terms of lateral spatial resolution and DOF. # Ambiguity function (AF) and its use in OTF analysis ## The 2D Ambiguity Function (AF) and its relation to 1D Optical Transfer Function (OTF) The Ambiguity Function (AF) is an useful tool for optical system analysis. This post is a basic introduction to AF, and how it can be useful for analyzing incoherent optical systems. We will see that the AF simultaneously contains all the OTFs associated with an rectangularly separable incoherent optical system with varying degree of defocus [2-4]. Thus by inspecting the AF of an optical system, one can easily predict the performance of the system in the presence of defocus. It has been used in the design of extended-depth-of-field cubic phase mask system. NOTE: This post was created using an IPython notebook. The most recent version of the IPython notebook can be found here. To understand the basic theory, we shall consider a one-dimensional pupil function, which is defined as: $(1) \hspace{40pt} P(x) = \begin{cases} 1 & \text{if } |x| \leq 1, \\ 0 & \text{if } |x| > 1, \end{cases}$ The *generalized pupil function* associated with $P(x)$ is the complex function $\mathcal{P}(x)$ given by the expression [1]: $(2) \hspace{40pt} \mathcal{P}(x) = P(x)e^{jkW(x)}$ where $W(x)$ is the aberration function. Then, the amplitude PSF of an aberrated optical system is the Fraunhofer diffraction pattern (Fourier transform with the frequency variable $f_x$ equal to $x/\lambda z_i$) of the generalized pupil function, and the intensity PSF is the squared magnitude of the amplitude PSF [1]. Note that $z_i$ is the distance between the diffraction pattern/screen and the aperture/pupil. # Desirable properties of iris acquisition systems In my last post, I described briefly how iris recognition works. I also described the four main modules that make up a general iris recognition system. In this post I am going to discuss some of the desirable properties of the iris acquisition module, or simply the iris camera. Although the acquisition module is the first block in the iris authentication/verification pipeline and it plays a very important role, the module has received much less attention of the researchers compared to the others. Iris recognition algorithms have become quite mature and robust in past decade due to the rapid expansion of research both in industry and academia  [1–3]. Figure 1 shows a plot of the scientific publications (in English) on iris recognition between 1990 and 2013. The plot also shows the relative number of papers exclusively addressing the problems of the acquisition module, which is really very minuscule, compared to the total number of papers on iris recognition. Figure 1. Number of publications in (English) journals on iris recognition between 1990 and 2013. The data was collected using Google scholar by searching the keywords IRIS + RECOGNITION + ACQUISITION + SEGMENTATION + NORMALIZATION + MATCHING. The plot shows that although the total number of research papers on iris recognition has grown tremendously during the last decade, the problems associated with iris acquisition have been overlooked. The accuracy of iris recognition is highly dependent on the quality of iris images captured by the acquisition module. The key design constraints of the acquisition system are spatial resolution, standoff distance (the distance between the front of the lens and the subject), capture volume, subject motion, subject gaze direction and ambient environment [4]. Perhaps the most important of these are spatial resolution, standoff distance, and capture volume. They are described in details in the following paragraphs. # Primer on iris recognition As part of my PhD research, I am working on  extending the depth-of-field of iris recognition cameras. In a series of blog posts (in the near future) I would like to share some of the things that I have learnt during the project. This post, the first one in the series, is an introduction to iris recognition biometric technology. I believe the material presented here could benefit someone new to iris recognition get a quick yet comprehensive overview of the field. In the following paragraphs, I have described the iris anatomy, and what makes it so special as a biometric technology, followed by the general basis of iris based verification, and the four major constituents of a general iris recognition system. The human iris is the colored portion of the eye having a diameter which ranges between 10 mm and 13 mm [1,2]. The iris is perhaps the most complex tissue structure in the human body that is visible externally. The iris pattern has most of the desirable properties of an ideal biomarker, such as uniqueness, stability over time, and relatively easy accessibility. Being an internal organ, it is also protected from damage due to injuries and/or intentional fudging [3]. The presence or absence of specific features in the iris is largely determined by heredity (based on genetics); however the spatial distribution of the cells that form a particular iris pattern during embryonic development is highly chaotic. This pseudo-random morphogenesis, which is determined by epigenetic factors, results in unique patterns of the irises in all individuals including that of identical twins [2,4,5]. Even the iris patterns of the two eyes from the same individual are largely different. The diverse microstructures in the iris that manifest at multiple spatial scales [6] are shown in Figure 1. These textures, unique to each eye, provide distinctive biometric traits that are encoded by an iris recognition system into distinctive templates for the purpose of identity authentication. It is important to note that the color of the iris is not used as a biomarker since it is determined by genetics, which is not sufficiently discriminative. Figure 1. Complexity and uniqueness of human iris. Fine textures on the iris forms unique biometric patterns which are encoded by iris recognition systems. (Original image processed to emphasize features). # Plotting algebraic surfaces using Mayavi Who says math is not beautiful? Anyone who doubts the beauty in math must check out algebraic surfaces. An implicit functions has the form: $F(x,y,z, ...)=c$ where, $c$ is an arbitrary constant. For example, the implicit equation of the unit circle is $x^2 + y^2 = 1$ and the equation $x^2 + y^2 + z^2 = 1$ describes a sphere of radius 1. An algebraic surface is described by an implicit function $F(x,y,z) = c$. It may be rendered using Mayavi by evaluating the expression $F(x,y,z)-c=0$ on a regular (specified) grid, and then generate isosurface of contour value equal to 0. Here are some examples of algebraic surfaces plotted using Mayavi: I wrote a quick function called implicit_plot for plotting algebraic surfaces using Mayavi. The most important argument to the function is of course the expression  $F(x,y,z)-c=0$ as a string. It is probably not the best function, but the idea is to show how to plot implicit surfaces. The code snippet is included at the end of this post. Suggestions for improvement are always welcome. # Progression of pixel resolution in digital cameras Thanks to the megapixel war, pixels in digital sensors have shrunk considerably over the years. Consequently, the pixel resolution (number of pixels in a digital image) has improved. Currently, the pixel resolution (assuming gray-scale sensor) can compete with the aerial resolution of lenses —on paper. This post is about a plot I created sometime back (for a different presentation) which shows the growth of pixel count and the diminishing of pixel size over the years for three popular segments of digital cameras. The green line plots the diffraction-limited (aberration free) optical resolution 3 stops below the maximum aperture available for off-the-shelf lenses during the same period. The optical resolution line doesn’t mean much; however, it is plotted to compare the sensor resolution with the optical resolution over time. The graph shows that while the sensor resolution has improved by leaps and bounds, the optical resolution hasn’t. It is no surprise though, because the optical resolution, which is limited by the fundamental nature of light —diffraction. Improving the optical resolution by traditional means is very expensive, and results in bulky lenses. The time is just right for exploring computational methods for improving the system resolution of imaging systems. Other interesting data-points in the graphs are: 1. The Kodak DSC460, based on a Nikon SLR, was one of the first digital cameras. 2. The Sharp J-SH04 was the cellphone with a camera. The number of mega-pixels and the pixel resolution (decrease in pixel size) has increased rapidly for the cellphone and point-and-shoot cameras, probably driven by marketing rather than by picture quality. In the more professional segment, clearly the strategy has been different. This may be because of two main reasons — one, the image quality dictated by noise, color reproduction, low-light performance, etc are more important for these shooters, and two, building high-quality large lens is relatively more expensive. # Does the F/2.0 phone camera match the F/2.0 DSLR’s optical resolution? Summary: Most cellphone cameras today come with “large aperture” lens such as F/2.0 or F/2.2. Since the optical resolution of a “perfect” lens (a lens devoid of any aberration) is inversely proportional to the F/# (the relation is shown in equation 1), one may assume that a F/2.0 cellphone camera lens should be able to resolve fine details on an object as well as a F/2.0 DSLR lens. $\Delta_r = \frac{1}{1.22 \lambda F/\#}$         (1) where, $F/\# = f/D$, $f$ is the focal length, and $D$ is the aperture diameter of the lens. The above image shows two lenses of same F/#, and also of equal normalized focal length. The one on the left is a lens whose 35 mm focal length is about 28 mm (with complete camera module, including the image sensor) from a cellphone, and the lens on the right is a 28 mm DSLR lens. The optical resolution of a lens determines how close two line-objects or point-objects be placed before the objects cannot be distinguished from each other when viewing through the lens. The minimum resolvable separation, $\Delta_s$, is the inverse of $\Delta_r$. The larger the value of $\Delta_r$ (usually measured in line-pairs-per-mm), the better is the resolving ability of the lens. So if the f-number, $F/\#$, of a cellphone lens matches the $F/\#$ of a DSLR lens, then the equation (1) seems to suggest that they have the same optical resolution! However, as it is shown in the following paragraphs, the ability to resolve fine details of a F/2.0 DSLR lens is in fact much better than a F/2.0 cellphone camera lens. Concretely, if the focal length and the aperture diameter of the cellphone lens is 1/k (k>1) times the respective parameters of the DSLR lens, then the  $F/\#$ of the two systems are equal but the resolving ability of the cellphone lens is $1/k$ times that of the DSLR lens. For example, a 50 mm, F/2.0 lens (D = 25 mm), which is a first order approximation of a 50 mm DSLR lens, can resolve details as fine as 54 microns focused at a distance of 2 meters. Whereas a 5 mm, F/2.0 lens (D = 2.5 mm), a close approximation of a typical cellphone camera lens, can resolve details only up to about 540 microns focused at the same distance. This is essentially a manifestation of the difference in magnifications (or angular resolution) of the lenses.
is absolutely right. Boundary defense is typically an organization’s first line of protection against outside threats. Similarly the network boundary between—let’s say—a WAN or a LAN could be defined as: WAN traffic begins and ends at the router for inbound traffic unless ports are opened on the router to allow further access. Our methodology for reviewing system architecture is a systematic, repeatable process that. Great! That router sees my connection, allows my connection but then says, “Nope, no further for you…”. A machine that is not directly connected to your LAN is outside your network boundary, and you cannot contact it. Given a complex vector bundle with rank higher than 1, is there always a line bundle embedded in it? Your … A network address is also known as the numerical network part of an IP address. To achieve a holistic understanding of the system, the review team should include personnel with diverse backgrounds. on the terminals and network servers that act as end points. In this post, we presented an outside-in approach to security architecture reviews that has worked for us, starting with two focus areas, System Boundary and Boundary Protection. How do I interpret the results from the distance matrix? In some cases, a large boundary can encompass the entire operating environment, including directory services, DNS, email, and other shared services. rev 2020.12.8.38142, Sorry, we no longer support Internet Explorer, The best answers are voted up and rise to the top, Super User works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. What is creating the utun0 network interface on OSX? But a linked net (LAN)/subnet is consistent w/ examples. boundary definition: 1. a real or imagined line that marks the edge or limit of something: 2. the limit of a subject or…. Boundary definition, something that indicates bounds or limits; a limiting or bounding line. So if you go from a 172.16.5.0/24 network to a 172.16.200.0/24 network, that will not be considered a network boundary since both of those networks are part of the class B network of 172.16.0.0/16. Network boundary defense must be configured in such a way, either network security policies drop/deny identified malicious requests or make it harder for hackers to further exploit network access. The Internet Protocol (IP) is the principal communications protocol in Thus port forwarding on a router from the WAN to a LAN system bridges the network boundary. Protection is achieved through the use of gateways, routers, firewalls, guards, and encrypted tunnels. This information can be used to ensure that system network communications are denied by default and allowed by exception, in accordance with the security design principle of Least Privilege. yes that is the traditional definition of "network" from the old days when there was no Internet (eg 1954 - 1975 or so) and WAN links, if they existed were point-to-point trunks provided by the telephone company by physically connecting a circuit between both locations. Figure 1 presents a notional enterprise architecture with two high-value systems residing in a high security zone (HSZ). Definition of boundary in the Definitions.net dictionary. For a group or individual hacker who is targeting organization using APT (Advance persistent threat), network boundary defense policies matter a lot. Define NR Network Boundary. Making statements based on opinion; back them up with references or personal experience. Boundary protection demarcates logical or physical boundaries between unknown users and protected information and systems. boundary network käännös sanakirjassa englanti - suomi Glosbessa, ilmaisessa online-sanakirjassa. With a defined system boundary, the organization should have a well-defined and documented diagram depicting of all of the entities that store or process system data. The health care sector is a context that is rich in isolated clusters, such as silos and professional “tribes,” in need of connectivity. In the OSI model the internet is an Internetwork, a system of interconnected networks, which is implemented by a common protocol which operates at OSI layer 3, and allows the use of Routers, which convey traffic from LAN to LAN as the datagrams cross the internetwork. Security architecture can take on … According to the National Institute of Standards and Technology (NIST) Special Publication (SP) 800-53, Revision 4, security architecture includes, among other things, "an architectural description [and] the placement/allocation of security functionality (including security controls)." We wouldn’t have to cross a network boundary to get…. Prime numbers that are also a prime number when reversed. Can you identify this restaurant at this address in 2011? site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. Summarize the findings and present recommendations in a written report. Then specify a new pick point. While the term was coined by Tushman, the concept was being developed by social scientists from the late 1950s onwards. Asking for help, clarification, or responding to other answers. “Stable” operating system - what does it mean exactly? How Close Is Linear Programming Class to What Solvers Actually Implement for Pivot Algorithms. The boundaries of SD-WAN are now stretching deeper and broader beyond just the WAN edge into the "Network Edge." And on a related note, systems connected via the LAN themselves are assigned IP addresses within the range that router can handle and nothing else. the Internet protocol suite for relaying datagrams across network Why are manufacturers assumed to be responsible in case of a crash? Selaa miljoonia sanoja ja sanontoja kaikilla kielillä. Regulatory requirements can play a big role in properly defining a system boundary. Our security architecture reviews have three steps: Organizations can develop a formalized, documented process to suit their needs as their security architecture review capability matures. What is an escrow and how does it work? Boundary Spanning Roles. Electricity Network Boundaries in New Zealand. Collect relevant information by reviewing the system's security and design documentation and conducting interviews with subject matter experts. The border or limit so indicated. Did my 2015 rim have wear indicators on the brake surface? What exactly is VGA, and what is the difference between it and a video card? These boundaries occur at various levels, and vulnerabilities can become apparent as data “crosses” each one. What is for? Is there such thing as reasonable expectation for delivery time? Why is the word order in this sentence other than expected? Because of the nature of the wireless medium, 802.11 networks have fuzzy boundaries. If you enter -BOUNDARY at the Command prompt, options are displayed. Unless fitted with a Network Termination Device, the network boundary point is the first telephone point / socket wired inside the premises. Sfoglia parole milioni e frasi in tutte le lingue. boundary network Übersetzung im Glosbe-Wörterbuch Englisch-Deutsch, Online-Wörterbuch, kostenlos. Change the scope of a boundary by editing its network locations. The definition of Boundary … Using our outside-in approach, the next step is to review the system's boundary protection. If you have a small business and don't have as many technological resources as a large company, utilizing boundary spanning roles can allow your small business to flourish. There are ten subsections to this control that cover your DMZ, firewalls and proxies, IDS/IPS, NetFlow, and remote access. Back then there were no layer3 protocols (not until NCP, and then IP). It is by definition a realm of connected machines that can communicate using the OSI Data Link layer (layer 2). Boundary Scan: A boundary scan is a testing standard which helps in defining the architecture and the techniques for solving hardware issues related to components such as printed circuit boards (PCBs) and integrated circuits. Have Texas voters ever selected a Democrat for President? Well, I think Jake's answer is perfectly valid in the correct context. Where is the energy coming from to light my Christmas tree lights? It only takes a minute to sign up. boundary network translation in English-French dictionary. When analyzing the security architecture, it is critical to enumerate and document all of the applications and systems that store or process the system's data. Your risk management strategy in turn defines your ongoing risk posture assessment, continuous monitoring program, the critical elements of successfu… In his inaugural column, the author looks at a range of boundaries from smaller to larger and presents vulnerabilites and potential solutions for each case. How do you develop and implement a security architecture review process? Zoom out until all boundaries are visible. If there are critical dependencies outside the boundary and they could affect the CIA of the system, you must account for the additional risk. Boundaries are often too narrowly scoped and exclude critical dependencies--systems that could have a direct impact on the confidentiality, integrity, and availability of the high-value system being reviewed. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Learn more. The HSZ security devices provide boundary protection for the high-value systems in addition to protections provided at the enterprise level, such as the security devices between the enterprise network and the internet and DMZ. The Telecommunications Network Boundary is defined in the Telecommunications Act 1997 and: is a nominal demarcation point between carrier-owned and customer owned cabling and equipment; determines whether cabling or equipment is subject to ACMA technical regulation; and For these inherited controls, it is important to understand the implementation details for each control and the protection that the control provides. After writing my own answer, I re-considered and decided the existing answers provide right answers, & we needn't another answer to vote on. For example, if I connect to a LAN via Wi-Fi or a physical cable, but the network is restricted via MAC address and my device’s MAC address is not granted entry, the “boundary” of that network would simply be my the literal edge of that routing device. if we want to get etymological about it, the word boundary is chosen to represent a barrier or wall that represents the extent of a capability (in this case, the capability to communicate). In business, boundary spanning is when you cross the boundaries set by your organization, and collaborate with someone else to get a task done. The plane of the boundary to get… protection required by the networks i.e review team should include with. Security zone ( HSZ ) should be inspected interviews with subject matter experts access control for greater. Frasi in tutte le lingue the next step is to review the system 's security and documentation. For the hatch scale or use the Solid hatch pattern protocol, it... 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# Richard Williamson Towards a diagrammatic proof of the Poincaré conjecture for knots (Rev #4) \tableofcontents \section{Introduction} This page is unpublished research, intended in the end to become a paper. It aims to give a proof of the restriction of the Poincaré conjecture in its diagrammatic reformulation to the case of a knot diagram. \section{Realisability of a knot diagram} The key innovation of our approach is the introduction of a notion of realisability of a knot diagram. In this section, we introduce it, after some preliminaries. \begin{terminology} \label{TerminologyWordInTheArcsOfAKnot} Let $K$ be a knot diagram. Label the arcs of $K$. A word in the arcs of $K$ is a monomial $a_{1}^{\pm 1} \cdots a_{n}^{\pm 1}$, where $a_{1}, \ldots, a_{n}$ are labels of arcs of $K$. \end{terminology} \begin{defn} Let $K$ be a knot diagram, equipped with an orientation (either will do). Let $p$ be a point of $K$. Let $l$ denote the longitude of $K$ with respect to $p$ and our chosen orientation. Let $w$ be a word in the arcs of $K$. A reduction of $w$ is a word in the arcs of $K$ obtained by removing a copy of $l$ from $w$. \end{defn} Revision on August 27, 2018 at 17:47:27 by Richard Williamson?. See the history of this page for a list of all contributions to it.
User Manual | Methods | Time Scale Separation Methods # Time Scale Separation Methods ### Approach: Model Analysis by means of Time Scale Separation In order to explain the basic notions of time scale decomposition we start with a first-order kinetics system. Then, the differential equations (ODE) describing the system dynamics ${\bf y}$ are linear: $$\frac{d\,{\bf y}}{d\, t} = {\bf J} \cdot {\bf y}$$ with constant Jacobian ${\bf J}$. By using the set of right eigenvectors ${\bf A}$ of ${\bf J}$ as the new basis we can decompose the Jacobian [Golub96] $${\bf x} = {\bf A}^{-1} \cdot {\bf y}, \quad {\bf \Lambda} = {\bf A}^{-1} \cdot {\bf J} \cdot {\bf A}.$$ The components of the transformed concentration vector ${\bf x}$ are called modes. Because ${\bf \Lambda}$ is a diagonal matrix of real or complex eigenvalues $\lambda_i$ of ${\bf J}$, the transformed ODE system is fully decoupled: $$\frac{d\, x^i}{d\, t}=\lambda^i x^i, \ i=1,...,N.$$ Thus, the modes $x^i \sim e^{\lambda^i t}$ evolve independently of each other. The reciprocals of $\Re(\lambda^i):$ $$\tau_i = -\frac{1}{\Re(\lambda^i)}$$ have a dimension of time and are called time scales (TS). Ordering them w.r.t. magnitudes $\tau_1 < \tau_2 < ... < \tau_N$ leads to approximate speed ranking of the modes [Lam93]. The modes corresponding to fast time scales (eigenvalues with large negative real part) approach $0$ very quickly and can be eliminated from the system for $t \gg \tau_M$, where $\tau_M$ is a fast time scale. For general nonlinear problems the Jacobian is time-dependent. Its eigenvalues and eigenvectors change with time. Hence, in order to obtain a reasonable characterization of the systems dynamics the time scale decomposition has to be applied repeatedly at many time points through the evaluation time of the reaction system. The methods presented here relies on the presence of a wide range of characteristic time-scales in biological systems and are based on the local analysis of the Jacobian, which is partitioned into fast and slow components at the initial point of a user chosen interval. All the three methods involves numerical integration using the LSODA solver [Petzold83], deterministic simulation. The TSSA methods uses Schur transformation and the solution of Sylvester equation [Golub96] (ILDM and Modified ILDM) performed by CLAPACK.
# Homework Help: Integration by parts 1. Feb 26, 2009 ### apples I am stuck with 2 questions. 1. http://132.239.150.164/math/img/math_967.5_fabcf8ac5b3f2459050993af33426844.png[/URL] 2. http://132.239.150.164/math/img/math_972_41ec111060693034ac0775fd52778392.png[/URL] 2. Relevant equations http://132.239.150.164/math/img/math_989.5_89c6805f9e6a047e24c9d1b535209efd.png 3. The attempt at a solution 1. I take u= (4-x)^(1/2) dv = xdx du = 1/2* (4-x)^(-1/2) v= (x^2)/2 I get stuck at ((x^2)/2)*(4-x)^(1/2)- ∫[(x^2)dx/4*(4-x)^(1/2) 2. I take u= (arcsin x)^2 dv=dx or 1 du= (2arcsin x)/((1-x^2)^(1/2)] v=x so x(arcsin x)^2 -2 ∫[(x arcsin x dx)/(1-x^2)^(1/2)] I don't know what to do after that. How do I solve the red. Last edited by a moderator: Apr 24, 2017 2. Feb 26, 2009 ### gabbagabbahey Try $u=x$ and $dv=\sqrt{4-x}dx$ instead Try by parts once more, this time use $u=\arcsin(x)$ and $dv=\frac{x}{\sqrt{1-x^2}}dx$ 3. Feb 27, 2009 ### Staff: Mentor A much simpler approach is to let u = 4 - x, so du = -dx. The indefinite integral becomes $$\int -(4 - u)u^{1/2}du = -\int (4u^{1/2} - u^{3/2})du$$ After you have an antiderivative, undo the substitution and use your limits of integration. You should always check to see if an ordinary substitution will get the job done before bringing in the big guns, such as integration by parts. Last edited by a moderator: Apr 24, 2017
# Q&A - Ask Doubts and Get Answers ## Filters Clear All In that case, one of the points lies in the plane if the value is zero then quotient point is in the plane and vice versa 93 Views   | As we learned,   Direction Cosines - If are the angles which a vector makes with positive X-axis,Y-axis and Z-axis respectively then are known as diresction cosines, generally denoted by (l,m,n). - wherein       Substitute (i) in (ii)   and   m=-n                                                                                                  m=-2n l+5n-3n=0                         ... 93 Views   | As we learnt in  Shortest distance between two skew lines (Cartesian form) - Shortest distance between and is given by Where    -    Normal vector of line is Put z=0 We get x+y=3 2x+3y=4 y=-2, x=5 (5,-2,0) is the point Equation of line will be Equation of z-axis is Shortest distance = Option 1) 1 This is incorrect option Option 2) 2 This is correct option Option 3) 3 This is... Exams Articles Questions
An error was encountered while trying to add the item to the cart. Please try again. Copy To Clipboard Successfully Copied! Lectures on the Mathematics of Finance Ioannis Karatzas Columbia University, New York, NY A co-publication of the AMS and Centre de Recherches Mathématiques Available Formats: Electronic ISBN: 978-1-4704-3854-8 Product Code: CRMM/8.E List Price: $50.00 MAA Member Price:$45.00 AMS Member Price: $40.00 Click above image for expanded view Lectures on the Mathematics of Finance Ioannis Karatzas Columbia University, New York, NY A co-publication of the AMS and Centre de Recherches Mathématiques Available Formats: Electronic ISBN: 978-1-4704-3854-8 Product Code: CRMM/8.E List Price:$50.00 MAA Member Price: $45.00 AMS Member Price:$40.00 • Book Details CRM Monograph Series Volume: 81997; 148 pp MSC: Primary 90; Secondary 60; 93; In this text, the author discusses the main aspects of mathematical finance. These include arbitrage, hedging and pricing of contingent claims, portfolio optimization, incomplete and/or constrained markets, equilibrium, and transaction costs. The book outlines advances made possible during the last fifteen years due to the methodologies of stochastic analysis and control. Readers are presented with current research, and open problems are suggested. This tutorial survey of the rapidly expanding field of mathematical finance is addressed primarily to graduate students in mathematics. Familiarity is assumed with stochastic analysis and parabolic partial differential equations. The text makes significant use of students' mathematical skills, but always in connection with interesting applied problems. Graduate students in mathematics, statistics, physics, and engineering who want to learn about the Mathematics of Finance. • Chapters • Chapter 0. The model • Part 1. Complete Markets • Chapter 1. Pricing • Chapter 2. Optimization • Chapter 3. Equilibrium • Part 2. Incomplete Markets • Chapter 4. Hedging • Chapter 5. Optimization • Chapter 6. Pricing • Chapter 7. Transaction costs • Reviews • Readers are presented with current research, and open problems are suggested. This tutorial survey of the rapidly expanding field of mathematical finance is addressed primarily to graduate students in mathematics. Familiarity is assumed with stochastic analysis and parabolic partial differential equations. The text makes significant use of students' mathematical skills, but always in connection with interesting applied problems. Zentralblatt für Didaktik der Mathematik • Provides an excellent introduction to a wide range of topics in mathematical finance. Mathematical Reviews • The young researcher/postgraduate student will be able to glance at the forefront of current research in mathematical finance. The author's clear and careful writing makes reading a pleasure. A lot of material, hitherto available only in research papers, will now reach a wider audience. This is a most useful addition to the fast growing literature on mathematical finance. Short Book Reviews, a publication of the International Statistical Institute • Requests Review Copy – for reviewers who would like to review an AMS book Accessibility – to request an alternate format of an AMS title Volume: 81997; 148 pp MSC: Primary 90; Secondary 60; 93; In this text, the author discusses the main aspects of mathematical finance. These include arbitrage, hedging and pricing of contingent claims, portfolio optimization, incomplete and/or constrained markets, equilibrium, and transaction costs. The book outlines advances made possible during the last fifteen years due to the methodologies of stochastic analysis and control. Readers are presented with current research, and open problems are suggested. This tutorial survey of the rapidly expanding field of mathematical finance is addressed primarily to graduate students in mathematics. Familiarity is assumed with stochastic analysis and parabolic partial differential equations. The text makes significant use of students' mathematical skills, but always in connection with interesting applied problems. Graduate students in mathematics, statistics, physics, and engineering who want to learn about the Mathematics of Finance. • Chapters • Chapter 0. The model • Part 1. Complete Markets • Chapter 1. Pricing • Chapter 2. Optimization • Chapter 3. Equilibrium • Part 2. Incomplete Markets • Chapter 4. Hedging • Chapter 5. Optimization • Chapter 6. Pricing • Chapter 7. Transaction costs • Readers are presented with current research, and open problems are suggested. This tutorial survey of the rapidly expanding field of mathematical finance is addressed primarily to graduate students in mathematics. Familiarity is assumed with stochastic analysis and parabolic partial differential equations. The text makes significant use of students' mathematical skills, but always in connection with interesting applied problems. Zentralblatt für Didaktik der Mathematik • Provides an excellent introduction to a wide range of topics in mathematical finance. Mathematical Reviews • The young researcher/postgraduate student will be able to glance at the forefront of current research in mathematical finance. The author's clear and careful writing makes reading a pleasure. A lot of material, hitherto available only in research papers, will now reach a wider audience. This is a most useful addition to the fast growing literature on mathematical finance. Short Book Reviews, a publication of the International Statistical Institute Review Copy – for reviewers who would like to review an AMS book Accessibility – to request an alternate format of an AMS title Please select which format for which you are requesting permissions.
# t-SNE Corpus Visualization¶ One very popular method for visualizing document similarity is to use t-distributed stochastic neighbor embedding, t-SNE. Scikit-Learn implements this decomposition method as the sklearn.manifold.TSNE transformer. By decomposing high-dimensional document vectors into 2 dimensions using probability distributions from both the original dimensionality and the decomposed dimensionality, t-SNE is able to effectively cluster similar documents. By decomposing to 2 or 3 dimensions, the documents can be visualized with a scatter plot. Unfortunately, TSNE is very expensive, so typically a simpler decomposition method such as SVD or PCA is applied ahead of time. The TSNEVisualizer creates an inner transformer pipeline that applies such a decomposition first (SVD with 50 components by default), then performs the t-SNE embedding. The visualizer then plots the scatter plot, coloring by cluster or by class, or neither if a structural analysis is required. from yellowbrick.text import TSNEVisualizer from sklearn.feature_extraction.text import TfidfVectorizer After importing the required tools, we can load the corpus and vectorize the text using TF-IDF. # Load the data and create document vectors tfidf = TfidfVectorizer() docs = tfidf.fit_transform(corpus.data) labels = corpus.target Now that the corpus is vectorized we can visualize it, showing the distribution of classes. # Create the visualizer and draw the vectors tsne = TSNEVisualizer() tsne.fit(docs, labels) tsne.poof() We can also filter the classes that we want to view: # Only visualize the sports, cinema, and gaming classes tsne = TSNEVisualizer(classes=['sports', 'cinema', 'gaming']) tsne.fit(docs, labels) tsne.poof() Or we can omit labels all together: # Don't color points with their classes tsne = TSNEVisualizer() tsne.fit(docs) tsne.poof() Finally, we don’t have to use class labels at all, instead we can use cluster membership from K-Means to label each document: # Apply clustering instead of class names. from sklearn.cluster import KMeans clusters = KMeans(n_clusters=5) clusters.fit(docs) tsne = TSNEVisualizer() tsne.fit(docs, ["c{}".format(c) for c in clusters.labels_]) tsne.poof() ## API Reference¶ Implements TSNE visualizations of documents in 2D space. class yellowbrick.text.tsne.TSNEVisualizer(ax=None, decompose='svd', decompose_by=50, classes=None, colors=None, colormap=None, **kwargs)[source] Bases: yellowbrick.text.base.TextVisualizer Display a projection of a vectorized corpus in two dimensions using TSNE, a nonlinear dimensionality reduction method that is particularly well suited to embedding in two or three dimensions for visualization as a scatter plot. TSNE is widely used in text analysis to show clusters or groups of documents or utterances and their relative proximities. TSNE will return a scatter plot of the vectorized corpus, such that each point represents a document or utterance. The distance between two points in the visual space is embedded using the probability distribution of pairwise similarities in the higher dimensionality; thus TSNE shows clusters of similar documents and the relationships between groups of documents as a scatter plot. TSNE can be used with either clustering or classification; by specifying the classes argument, points will be colored based on their similar traits. For example, by passing cluster.labels_ as y in fit(), all points in the same cluster will be grouped together. This extends the neighbor embedding with more information about similarity, and can allow better interpretation of both clusters and classes. For more, see https://lvdmaaten.github.io/tsne/ Parameters: ax : matplotlib axes The axes to plot the figure on. decompose : string or None A preliminary decomposition is often used prior to TSNE to make the projection faster. Specify “svd” for sparse data or “pca” for dense data. If decompose is None, the original data set will be used. decompose_by : int Specify the number of components for preliminary decomposition, by default this is 50; the more components, the slower TSNE will be. classes : list of strings The names of the classes in the target, used to create a legend. colors : list or tuple of colors Specify the colors for each individual class colormap : string or matplotlib cmap Sequential colormap for continuous target kwargs : dict Pass any additional keyword arguments to the TSNE transformer. draw(points, target=None, **kwargs)[source] Called from the fit method, this method draws the TSNE scatter plot, from a set of decomposed points in 2 dimensions. This method also accepts a third dimension, target, which is used to specify the colors of each of the points. If the target is not specified, then the points are plotted as a single cloud to show similar documents. finalize(**kwargs)[source] Finalize the drawing by adding a title and legend, and removing the axes objects that do not convey information about TNSE. fit(X, y=None, **kwargs)[source] The fit method is the primary drawing input for the TSNE projection since the visualization requires both X and an optional y value. The fit method expects an array of numeric vectors, so text documents must be vectorized before passing them to this method. Parameters: X : ndarray or DataFrame of shape n x m A matrix of n instances with m features representing the corpus of vectorized documents to visualize with tsne. y : ndarray or Series of length n An optional array or series of target or class values for instances. If this is specified, then the points will be colored according to their class. Often cluster labels are passed in to color the documents in cluster space, so this method is used both for classification and clustering methods. kwargs : dict Pass generic arguments to the drawing method self : instance Returns the instance of the transformer/visualizer make_transformer(decompose='svd', decompose_by=50, tsne_kwargs={})[source] Creates an internal transformer pipeline to project the data set into 2D space using TSNE, applying an pre-decomposition technique ahead of embedding if necessary. This method will reset the transformer on the class, and can be used to explore different decompositions. Parameters: decompose : string or None A preliminary decomposition is often used prior to TSNE to make the projection faster. Specify “svd” for sparse data or “pca” for dense data. If decompose is None, the original data set will be used. decompose_by : int Specify the number of components for preliminary decomposition, by default this is 50; the more components, the slower TSNE will be. transformer : Pipeline Pipelined transformer for TSNE projections
# How do you find the discriminant, describe the number and type of root, and find the exact solution using the quadratic formula given 4x^2+7=9x? Nov 21, 2016 #### Answer: $\Delta = - 31 < 0 \text{ }$ so roots are complex. $x = \frac{9}{8} \pm i \frac{\sqrt{31}}{8}$ #### Explanation: 1) rearrange to the form ""ax^2+bx+c=0 $4 {x}^{2} + 7 = 9 x$ $4 {x}^{2} - 9 x + 7 = 0$ 2) check the discriminant$\text{ } \Delta = {b}^{2} - 4 a c$ $\Delta = {\left(- 9\right)}^{2} - 4 \times 4 \times 7$ $\Delta = 81 - 112 = - 31$ types of roots $\Delta > 0 \text{ }$real distinct roots $\Delta = 0 \text{ }$real and equal roots $\Delta < 0 \text{ }$roots are complex. In this case $\text{ "Delta=-31<0" }$ so roots are complex. 3) so the exact solutions using the formula $x = \frac{- b \pm \sqrt{\Delta}}{2 a}$ $x = \frac{- \left(- 9\right) \pm \sqrt{- 31}}{2 \times 4}$ $x = \frac{9 \pm i \sqrt{31}}{8}$ $x = \frac{9}{8} \pm i \frac{\sqrt{31}}{8}$
## Saturday, March 8, 2014 ### Significant Albums: Yes - Drama (1980) In the process of getting into Yes and their many records, it took a little while to check out the later 70's records, I think partially due to the way the "classic" period was so talked about and revered. And albums like Going for the One (1977) and Tormato (1978), while I came to enjoy some of, I never became as won over by as their earlier stuff like The Yes Album, Fragile and especially Relayer. And I had heard the more recent Yes (90125 and parts of Big Generator and Talk) and more or less grew bored by them easily. So, I think that is why it took me a few more years to checkout Drama. I recall Dream Theater played the intro to "Machine Messiah" on the 5 Years in a Livetime video from the footage/medley with Steve Howe at the Ronnie Scott Jazz Club in 1995. But for some reason, I never investigated that original song or the album it came from until finally checking this album out like 4 or 5 years later. But when I finally did, I was almost shocked and blown away by a few things;. 1) how heavy it was at times. I'm referring to Machine Messiah's riff mostly. 2) the style and tempos and production seemed to sound more modern. Now mind you, I 1st heard it from a Remastered version that was released sometime in the 90's, which probably helped give the modern or improved production from hearing those other post-classic Yes period records. 3) hearing both Geoff Downes and especially Trevor Horn, sort of reinvented Yes's sound a bit, but not as dramatically from the later 80's Trevor Rabin Yes sound. I really got won over by Trevor Horn's voice. He was like Jon Anderson in some ways and the vocals were like the Jon Anderson's in some ways. Higher pitched, chanting, spiritual, rhyming at times for the way it sounded. And while he was still not sounding identical to Jon Anderson, I found his style fit with what Steve Howe and Chris Squire were writing musically. I also sort of heard the music from Drama being technical, heavy at points too, as sort of proto-Prog Metal in some ways, which go figure for someone who loved Dream Theater, to get into a slightly new kind of music from Yes sounding heavy. But, I suppose Drama includes a lot of music that isn't sounding like Prog Metal at the same time. Songs like "White Car" or "Run Through the Light" were more mid tempo and textured. Including some of the Buggles? elements of using voice effects or vocoders. "Does it Really Happen?" is a more uptempo piece that probably gets overlooked more than it should. It's sort of dancey in some ways, or even a song you could work out to. A bit like mathrock, or how some math-rock sounds in some ways. Maybe it was influenced by that period of King Crimson? Alan White even uses some what sounds like eastern percussion. After about the 5 minute mark, there's a quiet refrain and the bring back the basic melody. But I would say Drama's greatest parts are on 3 tracks especially. "Machine Messiah" and it's driving riff, movements from heavy to majestic. The way vocals and guitars layered together and gradually build I just love. I even don't mind how Trevor sings this line Machine, Messiah The mindless Search for a higher Controller Take me to the fire rhyming "Messiah" with "Higher" and "Fire" It's one of those songs that the production and layers of vocals and guitar and keys come in gradually, that they end up all complementing each other. And it also is a very strong ear worm, as I will have the melody and parts of verses in my head for hours. But as much as I loved that multi-part opening track, I came to love "Into the Lens" even more. The way that songs builds and the energy is breathtaking. I was doing my data entry work while listening to this album, and that song alone totally got my work production up a ton. So much so, sometimes I would hit repeat on it. The flaring fast vocals and Howe's arpeggio runs just blaze through this song like it's white on rice, lol. The whole "I am, I am..a ca-merrr-ahh!" while lyrically seems silly, the way it sounds with the drumming and momentum at times totally work. I mean I guess the 1st couple of verses of "Into the Lens" sound almost like The Buggles or some other 80's song, but that song's crescendo is unbelievable. And the more I listened to it and this record, the more I always looked forward to that part. That climax section Here, by the waterside There, where the lens is wide You and me By the sea Taken in tranquility I almost get like a realization (for lack of a better word) about not only that song and their music, but something else. Like something from a movie, or one of these moments something hits you like a ton of bricks about learning something you never knew or discovering something that fascinates you. I love this record, but I marvel at that song, and maybe because I would not have expected to be so blown away by it. It sounds more like a standard 80's pop song texturally at the beginning, but after listening to it 5 or more times, I totally saw/heard it in a completely different way. But beyond the amazement of "Into the Lens," the track "Tempus Fugit" became the 3rd most go-to track on Drama. I recall knowing that song before hearing this album, I think from a Yes tribute album and possibly a compilation I had. But I hadn't really listened to it closely. Like "Into the Lens," it features in the 1st couple of verses, those fast-ly sang vocals that still in rhythm, fit the tempo and pattern of the song. Then the chorus comes in In the north sky time flies faster than morning The cold of the dawn it meant nothing to us You were keeping your best situation (Yes, Yes) And the moment I see you (Yes, Yes) It's so good to be near you (Yes, Yes) And the feeling you give me (Yes, Yes) Makes me want to be with you (Yes, Yes) If we wait for an answer (Yes, Yes) Will the silence be broken (Yes, Yes) Should we wait for an answer (Yes, Yes) Do we leave it unspoken The way Steve Howe's guitar runs lead up to the slower tempo chorus, and then echoing chorus which includes some of the best keyboard layers contributing from Geoff Downes adds a lot to take-in from this song, and part of 'Tempus Fugit." It's really an uplifting song and melody. Even just using the repeated "Yes!" I always thought was ironic or odd as I don't recall many if any lyrics previously, where the band mentioned their name, especially with a name with a word so commonly used. I also sort of hear a romantic message in the lyrics, even though Yes's lyrics don't go as far with me as say Genesis or some other bands. I kind of wonder if they had the repeated phrase of "Yes" to sort of reintroduce themselves in lyric and song, given Jon Anderson and Rick Wakeman were not with them at that point. Summarizing though, this record I listened to a ton about 10 years ago, and I think the biggest reason was how well the flow and energy of it was. "White Car" I think is brilliant, but a little too short. And I came to feel the album was so good, I wanted more after it finished, which is why I almost always would listen to the demos and bonus tracks on the remaster I had. The "Run Through the Light" with the vocoder comes to mind as a favorite, among them. I loved the vibe of the way so much of this album sounded, I really found I couldn't get enough of it. So much so, I came to feel it was my favorite Yes record only to Relayer. I know a lot of fans don't agree, even that enjoy this album. I just found it was Yes in a new way, with a fresh start in some ways, that happened to be at a point of transition. Perhaps after Tormato was a transition, Drama ended up refining some of the new ideas they tried on Tormato but didn't work. And I say that, not so much given Jon Anderson wasn't singing, but I think from a SONGWRITING standpoint. I suppose some of demos help, but I have often wondered how Jon Anderson would have sounded on many of these songs. I know it's kind of a question he poo-poos, save for maybe playing "Tempus Fugit" live once in a blue moon. The Fly From Here situation, I'm not sure so much, although it was a demo that the band had from that period. And I like some of it, but didn't fully fall in love with it, despite the Drama-elements to it. Maybe it was the lack of Trevor (although I recall he produced it), or something else. I suppose it speaks to timing and Yes made Drama then and only in 1979 and 1980 could have this or any other music with their lineup then, turned out this good. Maybe sad, but true. Regardless, this remains a favorite Yes record of mine and one of those records I likely will always love. If I need a go-to Yes record, for an uplifting or energetic feeling, Drama is at the top of my list. ## Friday, March 7, 2014 ### Significant Albums: Genesis - Foxtrot (1972) When I 1st checked out Genesis, I believe it was again Mike Portnoy, talking about The Lamb Lies Down on Broadway, likely on Dream Theater's official site. I recall liking much of that record, namely track "In the Cage," but I guess I never fully fell in love with it nor the band until later. Maybe partially due to Peter Gabriel's voice. I guess I kind of wanted to get into them like I got into Marillion, but it didn't really happen too quickly. But then a few years later, when I went to Nearfest and hanging out the friends I was with there, and the other fans at NF, and maybe even when Transatlantic covered some Genesis at that show in 2000, my motivation to invest more time into Genesis, especially the Peter Gabriel records went up. And I went through them somewhat meticulously, but after about 18 months or so (just guessing), I came to a conclusion: -All of their albums with Peter Gabriel were better than any album they released after he left (save for their debut, From Genesis to Revelation, which to this day, I still have yet to hear,lol). -Among the 5 definitive Gabriel records, The Lamb was THE WORST, even though I came to love a lot of it. Among the other four, they are about equal, but given the achievement of "Supper's Ready," I came to see Foxtrot as my favorite. And it's not just due to what some consider the definitive progressive rock epic piece, but it's hard to ignore. It's one of those epics that has a ton of ideas, segued to together extremely well. I guess I'll mention a couple of my favorite moments in it for now. The Guaranteed Eternal Sanctuary Man certainly. I know a farmer who looks after the farm. With water clear, he cares for all his harvest. I know a fireman who looks after the fire. You, can't you see he's fooled you all. Yes, he's here again, can't you see he's fooled you all. Share his peace, Sign the lease. He's a supersonic scientist, He's the guaranteed eternal sanctuary man. Look, look into my mouth he cries, And all the children lost down many paths, I bet my life you'll walk inside Hand in hand, gland in gland With a spoonful of miracle, He's the guaranteed eternal sanctuary. We will rock you, rock you little snake, We will keep you snug and warm. I get goosebumps every bloody time I hear that part, right when Peter Gabriel sings that 1st line "I Know a farmer, who looks after the farrrrrrrrrrm...." I just am in awe of the way it introduces such a magical piece of music and the sound of the chord progressions, crescendo and Gabriel's expressive vocal lines. the movement that follows [Ikhnaton And Itsacon And Their Band Of Merry Men] , I think of for a a couple of things. But we saw a host of dark skinned warriors standing still below the ground, Waiting for battle. The fight's begun, they've been released. Killing foe for peace...bang, bang, bang. Bang, bang, bang... And they're giving me a wonderful potion, 'Cos I cannot contain my emotion. And even though I'm feeling good, Something tells me I'd better activate my prayer capsule. Today's a day to celebrate, the foe have met their fate. The order for rejoicing and dancing has come from our warlord. Right when and after Peter sings "waiting for BAHHHHTUHHL" the music really starts to move. Tony Banks lays in such great harmonic lines that complement Peter's vocal phrasing. The whole "today's the day to celebrate.." even though the subject matter is talking about a battle or fighting, the melody is actually really happy sounding or *celebratory*. Some of the Steve Hackett refrains also stand out at times here. [Apocalypse In 9/8 (Co-Starring the delicious talents of Gabble Ratchet)] Most people love this part of this piece most, which while I do still enjoy it, I'm not as fond of as those previous two sections I mentioned. But the way it builds methodically, just fits perfect for the grand finale of this story and album. The way Genesis keeps bringing in track after track, adding to a mass of tracks, by the end, you're kind of thinking how much BIGGER can this song get? Now, there is the whole other side to Supper's Ready, being the story/subject matter. Which I often don't hold too much importance  most music, compared to the music itself, but with the Gabriel Genesis especially, I ended up getting more into the lyrics and stories for some reason. The fables or tales Gabriel created somehow. "Supper's Ready," I think of a few similar ideas or stories, but probably the biggest most direct is Dr.Moreau's Island. The way the genetic hybrid and experiments are described. And per the artwork, which shows an *Island*. "Get Em Out By Friday" is another favorite that is also quite story driven. The line: This is an announcement from Genetic Control: "It is my sad duty to inform you of a four foot restriction on humanoid height." Referring to "Genetic Control" and the directors-of and such, I came to think about the scene in the Terry Gilliam movie Brazil. In the movie, the organization isn't identified with Genetics exactly, but if I recall, they have to more or less kick people out of their living space for possibly many reasons. I mean in a real-world level, it does cite the idea of people being evicted, population control and overcrowding. But with the reference to "Genetics" specifically, it seems to infer a more inherit purpose with humankind, not just purely social. "Can-Utility and Coastliners" is one of the most underrated  or overlooked tracks in the Gabriel-Genesis canon. It's a terrific, multi-part piece with your time changes and dynamics. I do love Tony's textures and mellotron on this piece in the middle especially. It's so moody,and \it harmonizes with Hackett's acoustic guitar lines really well; I actually could have gone for that instrumental section go on for a few minute longer than it does. Then when Gabriel comes in and Tony's organ takes the lead, it's so thematic. You can almost sway to it it, or dance in a mid-tempo way.  And then it segues to feature Mike Rutherford's upfront bass lines. And later features Tony Banks organ solo. I really can't get enough of that solo he takes. Its parts or sections of music like that where I began to really LOVE Genesis and this period. They are like a drug that the more I heard them, the more I came to love them. And even though I don't listen to them nearly as often as I did 10 years ago, I swear, their music never gets old to me. I'm not sure why, but there's something so unique about the way they used instrumental passages and tones, with moods and Peter Gabriel's vocals telling stories, I was and am still am in awe of. "Watcher of the Skies" in some ways may be the most known or thought-of Gabriel-Genesis track (maybe along with" Firth of Fifth," or "I Know What I Like"). It opens up this record and sets the stage for a trip within each track. Is it about a Stargazer? maybe. Musically, the way it goes from slow to soaring parts. The bass-line rhythm which has often been said to be using Morse Code, which is rather distinct, as I don't know much if any music who did that sort of thing before that. The only piece I sort of think of in a similar way is Rush's "YYZ", but that was many years later. Watcher is also another track that features Tony's mellotron, which is rather distinct. Judge not this race by empty remains Do you judge God by his creatures when they are dead? For now, the lizard's shed it's tail This is the end of man's long union with Earth. That is one lyric I often think of. I used to think Peter Gabriel sang "the end of man's universe" instead "union with earth." Which in some ways could be meaning the same thing. The section after where Peter is sort of telling a history of life or someone's life; I almost think this song is not so much about a Stargazer, but someone whose been through history. Maybe human history on Earth, or just a few lifetimes. It's so storybook or fairy tale-like. I don't think I've ever really thought about music and lyrics in such a way.I'm sure Gabriel and some of the other guys don't think all that much about the stories and fiction they were creating when they were that young and early in their careers as musicians/artists, but I think it's some of the most creative works of telling stories. Fables, Fairy Tales, etc. And among the many stories that the Peter Gabriel period of Genesis made, on Foxtrot, I came to find to be the most interesting as-a-whole or rather, on 1-album. Being cohesive still (Lamb, I'm looking at you :p). "Supper's Ready" is a landmark piece of music, composed like a piece of classical music, that in Rock music, hadn't been done maybe as successfully and with the narrative moments that got me so engaged. And maybe why Genesis never made another 20 minute epic again, because how were they ever going to make something that good again? I dunno. And the rest of the music on this record complements it so well. It's almost like a a bunch of incredible appetizers (not thinking about the lyric "human bacon" with the metaphor mind you :). "Time Table" and "Horizons" included. "Horizons" being a solo acoustic Steve Hackett piece, which is simple, yet beautiful. I suppose not only seeing Steve perform that tune live a few times, but also it's similarity (if not being identical) to the Make-A-Wish Foundation theme or music used in the spots that used to air on television when I was a kid. It may have just been in the Twin Cities (although a Wikipedia entry shows Make A Wish isn't/wasn't exclusive to my hometown). that those ads aired. But I recall trying-to but never being able to find some old commercials to hear that theme and compare. But Make-A-Wish didn't start until 1980. It may be pure coincidence, but who knows, the founders or producers of those PSAs may have been fans of Genesis, Foxtrot and/or the "Horizons" piece. But from memory of those commercials, the acoustic guitar music and chord progression, tempo, is nearly identical. Although I suppose Hackett has mentioned the inspiration/influence on Horizons was some classical guitar pieces (JS Bach?), so that may have been the influence/inspiration on the Make-A-Wish theme as well. I just came to conclude how similar they sounded. I remember some woman singing over that acoustic guitar "Young chiiiiiiild" but I have failed to find a video online of the PSA/PSAs that I recall at this point. I am heading to see most-of this record performed live by The Musical Box in Minneapolis tonight. I expect nothing less than being wow-ed and in awe, like I was when I saw them in Milwaukee about 10 years ago, as getting to hear and see music-from one of these significant records performed live should be. Save for the band doing a reunion with Peter Gabriel, I would hope something like that (or someone like Kevin Gilbert) would also be given to other people who come to love this record and the Gabriel Genesis as much as I do. ### Crippled Black Phoenix - White Light Generator (2014) I enjoy a lot of the records this band has made, even if some of the pieces seem to/can overstay their welcome a bit. And this record doesn't appear to be too short like some of their other extensive-ideas based albums. But, it's coming in only a couple of weeks, and I usually enjoy more than enough from them to still want to go back to it. Also interesting how the title almost looks like the great Typhoon record from 2013, White Lighter. Maybe the 2 bands should tour together? Preorder Link Release Date March 17th 1. Sweeter Than You 2. NO! (pt 1) 3. NO! (pt 2) 4. Let's Have An Apocalypse Now! 5. Black Light Generator 6. Parasites 7. _______ 8. Northern Comfort 9. Wake Me Up When It's Time To Sleep 10. Caring Breeds The Horror 11. You'll Be Murdered 12. We Remember You 13. A Brighter Tomorrow Bonus tracks (vinyl and iTunes Deluxe Edition only): 1. Now You're Gone 2. Self Seeking Man Soundcloud stream w/ NO Embed for "A Brighter Tomorrow" ## Thursday, March 6, 2014 ### Opus Dai - Insectum Vol. 1 (2014) ["Disconnect the Dots" +"Start Again"] damn. Not that I totally forgot how good this band is/was, but other than a song or 2 over the last 5 or more years, I haven't thought all that much about Opus Dai. But this new track certainly rekindles the flame. Quite epic. Dynamics, layers of guitars, soaring vocals. Free Download here on their website (w/ a suggested pay-what-you-want paypal donation, as I just did) So, in just scanning their Facebook, this a track from an upcoming release "Insectum Vol. 1" and part of a collection of music the band have been working on for many years they refer to as "Insectum." Also a new video is coming for the "Moth to Flame" soon as pics from the video shoot were posted recently on Facebook. edit: I guess the original projection for this album was in 2012 per its entry on Rateyourmusic.com With Fair to Midland on some unreported hiatus and the latest from Karnivool and Dead Letter Circus being a bit lower on my radar, this may be the band and album that will fill that sort of alt/prog metal void. edit 2: here's another new track "Start Again" (also available to download free as the video shows) per 2012: ## Monday, March 3, 2014 ### Chromeo - White Women (2014) 3/3/14 10:07PM New song "Jealous" on Soundcloud Here 2/17/14 9:22PM being released May 12th exclaim.ca story Cover art, which was 1st revealed on this Minneapolis Craigslist post. I'm (or my girlfriend is) not fully clear as to why the ad was posted in the Minneapolis Craigslist (as opposed to Toronto?); the album isn't even being released until 6 days after the show at First Avenue on May 6th. Perhaps it has something to do with the Chromeo guys appreciation for not only Prince but The Time? 1/7/14 1:02AM New song is pretty sweet "Come Alive."..Minneapolis Tuesday May 6th! http://chromeo.net/tours/ 01 / 09 / 14 HOLY SHIP (DJ SET) Miami, FL 03 / 21 / 14 BUKU Music + Art Project New Orleans, LA 03 / 22 / 14 BUKU Music + Art Project New Orleans, LA 04 / 06 / 14 COME ALIVE TOUR (special guest: Tokimonsta), House Of Blues Houston, TX 04 / 07 / 14 COME ALIVE TOUR (special guest: Tokimonsta), Stubbs Austin, TX 04 / 08 / 14 COME ALIVE TOUR (special guest: Tokimonsta), House Of Blues Dallas, TX 04 / 12 / 14 COME ALIVE TOUR (special guest: Tokimonsta), Independent San Francisco, CA 04 / 14 / 14 COME ALIVE TOUR (special guest: Tokimonsta), Roseland Portland, OR 04 / 15 / 14 COME ALIVE TOUR (special guest: Tokimonsta), Commodore Ballroom Vancouver, BC 04 / 16 / 14 COME ALIVE TOUR (special guest: Tokimonsta), Showbox Market Seattle, WA 04 / 19 / 14 COME ALIVE TOUR (special guest: Tokimonsta), Marquee Phoenix, AZ 04 / 30 / 14 COME ALIVE TOUR (special guest: Oliver), House Of Blues Boston, MA 05 / 01 / 14 COME ALIVE TOUR (special guest: Oliver), Corona Theater Montreal, QC 05 / 02 / 14 COME ALIVE TOUR (special guest: Oliver), Danforth Music Hall Toronto, ON 05 / 05 / 14 COME ALIVE TOUR (special guest: Oliver), Lincoln Hall Chicago, IL 05 / 06 / 14 COME ALIVE TOUR (special guest: Oliver), First Avenue Minneapolis, MN 05 / 07 / 14 COME ALIVE TOUR (special guest: Oliver), The Pageant St. Louis, MO 05 / 09 / 14 COME ALIVE TOUR (special guest: Oliver), Royal Oak Music Hall Detroit, MI 05 / 12 / 14 COME ALIVE TOUR (special guest: Oliver), Variety Playhouse Atlanta, GA 05 / 13 / 14 COME ALIVE TOUR (special guest: Oliver), The National Richmond, VA 05 / 14 / 14 COME ALIVE TOUR (special guest: Oliver), Union Transfer Philadelphia, PA 05 / 16 / 14 COME ALIVE TOUR (special guest: Oliver), Terminal 5 New York, NY 06 / 03 / 14 COME ALIVE TOUR, La Cigale Paris, FR 06 / 04 / 14 COME ALIVE TOUR, Paradiso Amsterdam, NL 06 / 06 / 14 COME ALIVE TOUR, Roundhouse 11/10/13 11:02PM This is a somewhat long-awaited 4th album from Canadian electronic-dance/soul duo Chromeo. I guess I know them mostly from my girlfriend's talk/exposing them to me over the last couple of years. Although, I can't forget the fact I saw their name on more than 1 occasion a few years ago, before I knew her. I kind of hear groups like Kool and the Gang and some other 80's dance/pop synthy music in their sound. "Smooth" might be 1 of the most common adjectives to describe them. And maybe 1 reason my gf talks about them is Mayer Hawthorne opened for them back in 2011, and she says it may have been the best show she's ever seen. At any case, they have 2 singles out already, and this record is expected in early 2014 (I thought I saw 1 site that said March). I'll try and update this entry when the tracklist, artwork and release date comes soon. ### Significant Albums: King's X - Gretchen Goes to Nebraska (1989) The Summer of 1996 I recall 1st checking out King's X. I think the name was 1st mentioned to me on the ole Rush DejaNews Newsgroup when I was in college the year or 2 before. Just something about a ton of Rush fans liking King's X, etc. And, I'm not sure it was exactly at the point, but around the time I saw an ad in Citypages or the old Twin Cities Reader (or a flyer?) with their picture and a show coming to the long since closed "The Mirage" club in Minneapolis, with Galactic Cowboys as well. Their lead singer had a mohawk in the picture which struck me as odd yet curious. I also recall seeing a dealer at the Twin Cities record shows selling a bunch of King's X bootleg VHS tapes, who happened to be the same dealer who I had purchased Dream Theater and Fates Warning videos from. In then checking them out, I kind of felt they were a bit like Lenny Kravitz, but maybe not as good initially. But I invested some time within their reasonable size catalog and got very won over soon after. I recall either around the time or soon after Ear Candy was released which I enjoyed a fair amount, especially after seeing that show. But I can't deny, I came to love their 1st 4 records more than their last 2, Dogman and Ear Candy. Which then leads me to Gretchen... I came to love those 4 Sam Taylor records all nearly equally over the subsequent years, but I guess among those 4, it was Gretchen, like a lot of fans, that grabbed me the most. Maybe it was their most progrressive, or at least due to the fact it was a concept album that included a very cool story that seemed inspired by fantasy/sciti stuff I love like The Wizard of Oz. Maybe because the artwork, or maybe because the flow of the damn thing. It maybe (which I'm not sure why I keep using that word?) has my favorite track the band has done, in the opener "Out of the Silent Planet." The rhythm and groove is infectious, and the vocal harmonies create such a great, dreamy atmosphere. It does seem to take me in or onto a journey. I often feel like I am been brought into the world of this girl (Gretchen) and her adventure home to Nebraska and the other places she ends up. Then you have "Over My Head" which, as memorable as the countless versions I've heard live, the studio version is still as a rocking a track as the band has ever made. The guitar riff just is so punchy and catchy. "Music Music I Hear Music, Music I Hear Music. Music I Hear Music. Music. Music oh oh lohhhrd, music over my head.' That line IS King's X in a nutshell dUg's screaming, chanting and even the lyrics and the story/stories behind them add so much to that song And I think the band has played it for nearly every concert they've played since they wrote it, for that reason. The way dUg tells the story of his grandmother praying and his growing up with her telling him what was right and wrong, preaching, praying for him, etc. I think he's probably told the story 10,000 times and maybe even in 10,000 different variations. At any case, the story this album tells from track to track is just something I always enjoy. "Summerland" is rather mystical. The line "Summerland, the wind is getting cold. Summerland, you're finally getting old." I've always thought the lyrics to be a little ironic referring to cold and Summer. But while it's a slower methodical piece compared to "Over My Head," I love the mood and vibe it creates. I kind of think of it as it is setting the stage for a long journey or story. The other track I recall initially I got into was "Pleiades" which the band played live at that show I saw the Summer of 1996. I always found the tone and lyrics to be trippy. The sound of Ty Tabor's vocals on that song namely, are soft yet hold my attention. "far off in the field i see a castle (far off in the feeeeeeld) today the people gather at the pole he tried to tell us all the world was spherical they burned his body but not his soul" I guess that track adds to the story of Gretchen's experience or adventure. The term "pleiades" actually refers to a cluster of stars, so the way the lyrics refer to gazing up at the stars fits. Perhaps in the story, Gretchen becomes so disenchanted or tired of trying to get home, she wishes or wonders what it would be like on another planet. Then again, the planet the story takes place on, may not be Earth ("Out of the Silent Planet"?). But the rest of this record I came to enjoy more and more, and like a lot of records, they become known for a few specific tracks, but often some of the others end up being more interesting or "under-rated" vs "over" or accurately rated. "Everybody Knows a Little Bit of Something" is a great inspiring piece. I sort of see it as a universal thing. Everyone whose born has (or eventually will discover they have) some special knowledge or have a unique skill or skills. I really enjoy the last verse with the tone and call and response change from the chorus. Another great dUg vocal line and lyric. I saw the man stare in silence Why can't he be honest with who he wants to believe A cry for help was written on the cover of the magazine And I know what it means 'The Difference" is a nice almost acoustic ballad kind of piece, that is a nice contrast to the tracks that preceded it. The echoing "Ihhh, Ihhh can feel the difference" is a part I always think of it for and enjoy. "I'll Never Be the Same" has great poetic lyrics. That verse in the bridge for the chorus is another favorite section of this album. In re-reading the lyrics, it's interesting how they do actually refer to *Gretchen* herself at the end. "The way looks awful lonely So long or maybe less The time has passed so slowly There's pressure on my chest So tell me what I'm feeling In seven words, so speak" "Fall On Me" is a total groove rocker track. This track almost reminds me of among some other King's X tunes, 'Moan Jam" which is a song they wrote on the following record, Faith Hope Love. The way the instrumental part of the song just flows and goes on for awhile without it seeming too long or boring. Maybe that's why it's a song that has worked so well live as well. "Don't Believe It (It's Easier Said Than Done)" has a very strong chorus or ear-worm of sorts. I swear, this phrase using that "It's Easier Said Than Done" could be the most memorable lyric King's X  has ever written. And it APPLIES like "Everybody Knows a Little Bit of Something" in a  universal lyric, kind of way. I probably think of that line more than once a week. "It's easier, it's easier, said than done. It's easier, easier, to get up and run, it's easy-errrrrrrrrrrrr..don't believe, it's a lie (it's A lie!)" The opening line also seems to apply "this is not the end of the road, it goes on for maybe, miles and miles" which both with the story of the record and metaphorically, I seem to think of. "A Message" and "Burning Down" close this record out well. With "A Message" I think of the line in the chorus "There's trouble in the kingdom send a mesage to the king ([echoing] messssss-ijjjjj)" And "Burning Down" is just a *cool down* piece, that whether Gretchen actually does find Nebraska or not, seems to give me the impression she is at least at peace, which may be ultimately what she and many are seeking out anyway. As the old adage can go in these stories, it's about the journey, not the destination anyway. To sum up though, this I do see as King's X's finest work, although I do regard the 1st 4 records produced by Sam Taylor to be their best 4 and really, all very close in quality. But given I do love a concept album, or one that tells a fictional story (and Scifi or Fantasy as well), I have a slightly more romantic attachment to this one over the other 3. I shouldn't forget, I will always think of the fact when I purchased my copy in 1996, the story that Jerry Gaskill wrote was incomplete. I recall tracking the story about the girl who meets the old woman, online a year or 2 later on 1 of the early websites or email lists. But the cd booklet was incomplete with my copy, and it wasn't until just a few years ago when I found a copy on Vinyl per Ebay or 1 of the other vinyl selling import sites, that I finally possessed a printed copy of Jerry's cool story that accompanied this great record. Like The Lamb Lies Down on Broadway and some others, the extra little story adds even more of the unique quality of this album. ## Saturday, March 1, 2014 ### Imogen Heap - Sparks (2014) 3/1/14 12:00PM This (below) is supposedly 1-of the tracklists, per the Deluxe Boxed Set, which I will admit to not ordering. And unfortunately, I read was pushed back a bit, until April or May. But the release date was set to March 3rd a while ago. I have not seen many official sites mentioning, just the standard version. Promos, reviews, etc. Why I wonder if the March 3rd street date is still accurate. But if it is, I'll be looking to check this record out on Monday or at least in the next week or two. edit:  per Wikipedia Sparks is the forthcoming fourth studio album by English recording artist Imogen Heap. The album will be released, via RCA on 3 March 2014, in two editions: standard and deluxe box set. The standard edition will consist of 14 tracks and will include all of Heap's 2011–2013 singles. On 21 February 2014, a video was posted on her official site stating that the release date has been changed to April. 1 You Know Where to Find Me 2 Entanglement 3 The Listening Chair 4 Cycle Song 5 Telemiscommunication 6 Lifeline 7 Neglected Space 8 Minds Without Fear 9 Me the Machine 10 Run-Time 11 Climb to Sakteng 12 The Beast 13 Xizi She Knows 14 Propeller Seeds Even the standard ARTWORK I'm not finding at this time. The Deluxe Boxed Set shows some artwork. I do like the way the Deluxe Boxed Set includes Here's a re-cap of what's included: • Sparks album on CD A special ticket that grants you access to a sound check on Imogen's 2014 world tour • 10 inch Sparks double gatefold vinyl album • 12 DVD data discs with lossless versions of each Heapsong inc HD music videos + making-of videos of each song, packaged in beautiful case bound books with 16 page colour booklet • Making of the album DVD featuring all box set material • 120 page photo book telling the story of 'Sparks' • Deck of 52 playing cards that unlock exclusive web content • Specially blended paper made from objects Immi use to make the album http://www.imogenheap.com/deluxeboxset/ 9/20/13 11:45AM From the Mailing List: We are delighted to announce that Imogen's brand new album 'Sparks' will be released on 3rd March 2014. We are giving mailing list members the chance to pre-order the strictly limited edition deluxe boxset for delivery a week earlier, on 24th February 2014. What's more, if you pre-order before 30th September 2013 you can upload your footprints and they will become part of the 'Sparks' album cover across all formats. The first 100 people to order also get to visit Immi's house! A message from Immi: Hello there. Hope all's well with you. I've been little miss hermit heap in my studio the Hideaway these past months with a real push to get the audio for the album finished in time for my sanity to stay intact! It's turned out to be a monster of an album and even though I finished it two weeks ago, it still hasn't dawned on me. A bit like your last day at school! For all the other bits, like making of documentaries, photos, music videos, commentaries etc, I realised pretty early on (about 2 years ago) that it won't fit onto your average CD, so I've been cooking up a Deluxe box set! I've made a little video for you to explain a bit more about what's in it. You can watch it here :) I may have a glass of champagne when I get mine as It pretty much represents my musical life since March 2011 with all the projects I've been involved in, connecting to a song. WOO HOO! Really hope you love the music and this rather sexy deluxe box set to accompany it! xxx immi xxx Visit the deluxe website to pre-order your boxset now and upload your footprints which will become part of the album cover! All these wonderful details aside, this DELUXE BOXED SET is well, rather DELUXE being 10 discs, a DVD-Doc, and Vinyl. The price on the site shows a cool $299.99. So, yeah, I'd love a copy, but I also would love to use the$260+ extra to use on a plane ticket to Arizona or my savings account. There's only a limited number of the Boxed Sets anyway, so who knows if they are already sold out. But at least we do know the actual Title being SPARKS (not Spark), and the release date being March 3rd of 2014. 9/3/13 8:53PM just a follow up to  this Entry "Imogen Heap: 2012 Recap This is just information she's posted at scattered points throughout the last 3 years. But taking this info to be somewhat if not rather accurate. this upcoming LP will be coming out in November. The title "Spark" is a *POSSIBLE* title as that twitter post linked on Wikipedia does not really sound certain at all (and it was from just a few months ago, in July). But assuming the November release happens and that track list is close if not fully accurate (and the order for that matter), more of the details shouldn't be far away. Spark is the tentative title[1] of the upcoming fourth studio album by English recording artist Imogen Heap. The album will be released on Megaphonic Records in November 2013 in two packages: standard edition and deluxe album box set. The standard edition will consist of 14 tracks and will include all of Heap's singles released between 2011 and 2013. ## Background Spark is a concept album. Each song that is related to a certain project has been released every three months. On 14 March 2011, Heap started work on a new record as fans sent in nearly 900 "sound seeds", or samples of everyday sounds such as a "dishwasher door", a "bicycle" or a "burning match". Heap says the concept for this album will be to record one track over a two-week period every three months. Each song and video will be released immediately. The first song, initially entitled "#heapsong1" and later retitled "Lifeline", premiered worldwide on 28 March 2011 via Ustream[2] along with a live remix by Tim Exile. "Lifeline" was released on 30 March 2011 as a digital download from Imogen's website and via iTunes, Amazon and other digital retailers. Released alongside this was a 12-page 3DiCD package (a 3D virtual CD) including crowd sourced (and paid for) images, the instrumental version of the song, the "seeds and solos only" version and "heap speaks seeds and solos" - an-18-minute commentary by Heap on how the sounds and solos were used in "Lifeline". The song is a tribute to the victims of the2011 Tōhoku earthquake and tsunami. The second song, "Propeller Seeds", was recorded using 3D audio effects and headphones are recommended for listeners to get the full effect. The third song, "Neglected Space", incorporates concepts, people and sounds from a lab organized by the Clear Village Charitable Trust to restore a walled garden in Bedfords Park.[3] The fourth song, "Minds Without Fear", was the first song to be featured on the 2011 Indian show, The Dewarists. The fifth song, "Xizi She Knows", was recorded during Heap's six-week trip at Hangzhou, China.[4] The sixth song, "Me, the Machine", was recorded using the musical gloves. The seventh song, "You Know Where to Find Me", was recorded in London and is thematically about the River Thames.[5] The eighth song, "Telemiscommunications", is a collaboration with Canadian house producer deadmau5which is included in his sixth album Album Title Goes Here. ## Track listing All songs written and composed by Imogen Heap. No. Title Length 1. "Lifeline" 4:47 2. "Propeller Seeds" 3:52 3. "Neglected Space" 5:20 4. "Minds Without Fear" (with Vishal-Shekhar) 3:41 5. "Xizi She Knows" 4:41 6. "You Know Where to Find Me" 4:56 7. "Telemiscommunications" (with deadmau5) 4:07 8. "The Listening Chair" 9. "Me, the Machine" 10. "Entanglement" 11. "Run-Time" 12. "Climb to Sakteng" 13. "Cycle Song" 14. "TBA (new song)" ### Anathema - TBA (2014) 3/1/14 10:28AM Vague/Brief Update: Recently, Anathema's singer/multi-instrumentalist Daniel Cavanagh announced that the band has been working on its 10th studio album, and that it is scheduled for release in May of this year. Cavanagh stated that he was influenced by Radiohead and Atoms for Peace, and that some tracks will have a slightly more electronic feel. He also talked about a possible short acapella song. He says the next album will follow the same path than the previous two, but he stated that, on those past releases, the band has played it a bit safe, and that Anathema plans to gradually shift away from that on the next few albums. this may be from a mailing list or something, and not that I have anything against Sputnik music, but it's a bit lazy to not at least include an actual SOURCE or link. However, other than the May part, pretty much the other details in this post were known, at least for those who checked out That Drummer Guy's interview with Danny last September. I guess the Radiohead/Atoms for Peace and electronic influence doesn't concern me given it's not actually Thom Yorke singing, but, obviously no guarantees. But if this record is being released in May, I would think more details will be announced pretty soon. 12/6/13 3:50AM This is just a brief heads up about their upcoming new album, which is supposed to be coming out in the Spring or maybe Summer of 2014. Weather Systems and We're Because We're Here were both outstanding records, so naturally there's some reasonable hope for this next record as well. Here's a few brief clips per their Facebook. Post by ANATHEMA - official band page. Post by ANATHEMA - official band page. ## Friday, February 28, 2014 ### Cloud Caverns - Gypsy Loft (2014) 1. Sparrow 2. The New Colossus 3. Clatters, Swells, and Tosses 4. The Reservoir 5. Memory Leaks 8. MacArthur 9. A Warm Glow 10. Greenlawn 11. Gypsy Loft 12. Overlook Being released May 4th. Brandon Peterson did the engineering and AJ Estrada the artwork, so it has still some influence and connections with Hotel of the Laughing Tree. Not that this is huge on my radar, but I did like that EP from last year a bit,so I wouldn't be surprised if this is more of the same if not better. Previous Cloud Caverns entry ### Bend Sinister - Animals (2014)..TEACHER + PREORDER/PLEDGEMUSIC 2/28/14 5:34AM 1 Best of You 8:35 2 Fancy Pants 5:07 3 I Got Love 3:08 4 Better Things to Do 4:59 5 Thunder and Lightning 4:39 6 Teacher 5:09 7 Seventeen 3:32 8 You Remind Me 4:10 9 Through the Week 4:53 10 It Will Never End 4:40 also the Pledgemusic is up to 79% with 12 days left! 2/18/14 5:24PM Teacher video: awesome song, It starts out almost like Led Zeppelin's "In the Light." Cool, trippy video. Also the Pledgemusic is up to 52%!  with 22 days left. Damn, my interest in this album keeps going up. 2014 might be the biggest year of Bend Sinister's career. 1/17/14 5:30PM Pledgemusic/Pre-Order I just pledged/preordered the signed Vinyl. One thing I'm unclear about though in this write up is "Teacher." I don't recall them sharing it. edit: Stream "Teacher" per a Facebook poll (and APPLICATION) and it Rocks! Our new album "Animals" is dropping on March 11 but if you pre-order here we'll make sure you get it before anyone else! We’re happy to announce that we’ve finished our new album called Animals! You’ve heard “Fancy Pants” and “Teacher” but we can’t wait for you to hear the rest of it. We’re gearing up to release this thing and get back on the road to play for you. As part of this we’ve decided to do a very special pre-sale with Pledge Music to give you the chance to get the new album before the general public! This is how it works – when you pre-order, or ‘pledge’, on any of the items to the right you’ll get a download of our album before the March 11th release date. You’ll gain access to the exclusive updates portion of this page where we’ll be posting a bunch of special footage and cool stuff as this album release is coming together. PLUS you’ll be able to hear some early previews and tracks which won’t be available anywhere else! We’re also making a bunch of cool items available such as special signed items, lyric sheets, tie dye, a fur hat, swag, house concerts + more. Just take a look to the right --> So there you have it. Be among the first to hear our new album and we’ll see you on the road! Thanks again and much love! - Bend Sinister Full Tour Schedule. I bought my tickets a few weels ago, for the show in St.Paul in fact, at the Turf Club. Jan 25 Rossland, BC Blizzard Fest Canada TIME: 9:00pm. AGE RESTRICTIONS: All Ages/Licensed. Jan 28 Golden, BC The Rockwater Canada TIME: 9:00pm. Jan 29 Lethbridge, AB The Slice Canada TIME: 9:00pm. Jan 30 Fernie The Northern Canada TIME: 9:00pm. Jan 31 Kelowna Habitat Canada TIME: 9:00pm. Feb 01 Kamloops The Dirty Jersey Canada TIME: 9:00pm. Mar 04 San Francisco Hotel Utah United States TIME: 9:00pm. Mar 08 Phoenix, AZ The Firehouse Gallery United States TIME: 9:00pm. Mar 09 Scottsdale Pub Rock United States TIME: 9:00pm. ADDRESS: Arizona. Mar 18 St Louis, MO Fubar United States TIME: 9:00pm. Mar 19 Pittsburgh The Smiling Moose United States TIME: 9:00pm. Mar 20 Toronto, ON The Horseshoe Canada TIME: 9:00pm. AGE RESTRICTIONS: 19+. Mar 21 Kingston, ON Clark Hall Pub United States TIME: 9:00pm. AGE RESTRICTIONS: 19+. ADDRESS: Queen’s University. Mar 21 Kingston, ON Clark Hall Pub United States TIME: 9:00pm. ADDRESS: Queen’s University. Mar 22 Montreal, QC Casa Del Popolo Canada TIME: 9:00pm. Mar 23 Ottawa Raw Sugar Canada TIME: 9:00pm. ADDRESS: 692 Somerset St. Mar 24 Hamilton, ON The Casbah Canada TIME: 9:00pm. Mar 27 Detroit PJ’s Lager House United States TIME: 9:00pm. Mar 28 Chicago Junior’s Sports Bar United States TIME: 9:00pm. Mar 29 Chicago Underground Lounge United States TIME: 9:00pm. Mar 30 Minneapolis Turf Club United States TIME: 9:00pm. Apr 02 Regina, SK O’Hanlon’s Canada TIME: 9:00pm. Apr 04 Edmonton, AB The Pawn Shop Canada TIME: 9:00pm. Apr 05 Red Deer, AB The Vat Canada TIME: 9:00pm. Apr 06 Calgary, AB Ship and Anchor Canada TIME: 9:00pm. 12/3/13 2:26PM edit: this is some kind of trailer I guess. "Fancy Pants" is there to stream. I'll try (but of course not guarantee) to add something later today as I am on break right now at work. I can't find a Track List yet, if it was posted somewhere. Fancy Pants of course is 1 of the tracks I recall hearing them play live last March. Good, catchy tune with a twist from what I recall. "Animals" being the title? I'm sure has no connection to the Pink Floyd record, but if this album is even HALF as good as that record, I will not be disappointed. Not to forget, their last album Small Fame, was an excellent proggy power/bluesy pop album from 2012. Too bad their upcoming tour isn't hitting the US or even Winnipeg, but o well, hopefully more dates will be added soon. March 11th however, this should be 1 to look fwd to (or earlier, when a stream or a preorder download is available). http://exclaim.ca/News/bend_sinister_announce_animals_lp_premiere_new_track When Bend Sinister released their album Small Fame in the summer of 2012, it had been almost four years since their prior LP. Fans won't have to wait nearly that long until the Vancouver prog-pop band's next album, since they've announced thatAnimals will drop on March 11 via File Under: Music. The album was recorded in San Diego with producer Joe Marlett (Foo Fighters, Queens of the Stone Age), and apparently the results find the band continuing to expand their sound and drawing on a range of genres. All of the members collaborated on lyrics, chord progressions and songwriting. "With this album we tried to say 'yes' to everything," guitarist Joseph Blood said in a statement. "As much as possible we let go of any preconceptions over how we think we should sound as a band and just let the songs come out." For a taste of what this sounds like, hear the jauntily bouncing, cheekily "Wonderwall"-quoting song "Fancy Pants" at the bottom of this page. Also below, peruse the band's upcoming tour schedule. It includes a number of freshly announced Canadian dates that stretch into the spring. Tour dates: 12/06 Vancouver, BC - Vogue Theatre 12/19 Vancouver, BC - Joe's Apartment Bar 01/25 Rossland, BC - The Flying Steamshovel (Blizzard Music Festival) 01/28 Golden, BC - The Rockwater Grill and Bar 01/29 Lethbridge, AB - The Slice 01/30 Fernie, BC - Northern Bar & Stage 01/31 Big White, BC - The Blarney Stone Irish Tavern 02/01 Kamloops, BC - The Dirty Jersey 03/20 Toronto, ON - The Legendary Horseshoe Tavern 03/21 Kingston, ON - Clark Hall Pub 03/22 Montreal, QC - Casa Del Popolo 03/23 Ottawa, ON - Raw Sugar Café 03/24 Hamilton, ON - The Casbah 04/02 Regina, SK - O'Hanlon's Pub 04/03 Saskatoon, SK - Vangelis Tavern 04/04 Edmonton, AB - The Pawn Shop 04/05 Red Deer, AB - The Vat 04/06 Calgary, AB - Ship & Anchor ## Monday, February 24, 2014 ### Significant Albums: The Beatles - Sgt. Pepper's Lonely Hearts Club Band (1967) The 1st vinyl record I ever bought. I have a vague yet certain memory of buying this album on vinyl LP in the year 1987, likely in the Summer. And after I bought it, which I am guessing was at the old 'Great American Music" store at Harmar Mall (or possibly Rosedale). My parents and I went to dinner after that, at I think the Green Mill at Rosedale It was around that time I had seen "Complete Beatles" which my folks had recorded on VHS tape off I think the local PBS affiliate in the Twin Cities, Channel 2. And of course that documentary spoke glaringly about this album. I recall there was one guy whose title was "musicologist" praising it to no end. I remember after seeing that title, wondering what a "musicologist" was exactly, and how does one become a musicologist. How much money could a musicologist make? etc. "Within You, Without You" in my 2nd or 3rd revisiting/renewal of my love for The Beatles music, was the song I became the most in awe of. Some of the best Beatles songs are the one's where they incorporated spiritual and middle eastern elements. Try to realise it's all within yourself No-one else can make you change And to see you're really only very small, And life flows within you and without you. When you've seen beyond yourself-then you may find, peace of mind, Is waiting there- And the time will come when you see we're all one, and life flows on within you and without you A therapeutic and meditative track, that I love the call and response between Lennon's vocals and the sitar played by George Harrison, which I'll fully admit, I use to assume was Ravi Shankar. The triippy nature of "Being for the Benefit of Mr.Kite" I also have probably appreciated more recently than back in 1987. The *circus* atmosphere Lennon wanted-to and more or less created is wonderful. It's 1 of those tracks, like "Tomorrow Never Knows" or "Strawberry Fields Forever", that is a head rush that I can't help but love. And I can't even imagine how it influenced a lot of psychedelic rock that came after it. And actually the same could be said about "Lucy in the Sky With Diamonds" which I know received more notoriety (and airplay), for one reason alone, just the whole LSD thing with the title. That tune I distinctly remember hearing as a kid and liking. I think maybe even more than the trippy odd tones coming from the music, the lyrics told a story to me. "The girl with Kaleidoscope Eyes"..the 11 or 12 year old me found that freaky. But I also remember picturing a tale of 2 younger people sort of in love. The different adjectives and references, honestly may have been the 1st time I'd heard them. "Marmalade" I remember once hearing in a kids story, that was British, because I came to often associate that word and food with the UK. Cellophane Flowers and Marshmellow Pies? yeah, I don't think I had been exposed to those before hearing this tune. Getting Better, When I'm 64, Lovely Rita, the title track and the reprise, A Little Help From My Friends were all kind of Beatles staples I got to know about, I think on the compilation record my folks had they would play. And songs like She's Leaving Home and Fixing a Hole also add to the charm of this album. And then you have "A Day in the Life," which to many is the quintessential Beatles tune. It seems like an experiment of studio technique and little movements that worked perfectly. "I heard the news today Oh Boy"..which leads And then the McCartney voiced Woke up, fell out of bed Dragged a comb across my head Found my way downstairs and drank a cup And looking up I noticed I was late Found my coat and grabbed my hat Made the bus in seconds flat Found my way upstairs and had a smoke And somebody spoke and I went into a dream to that trippy moaning from Lennon. So relate-able at first, the whole rush in the morning (which maybe the fact there is a song titled "Good Morning" was made or influenced this song, or vice-versa). But the way the lyrics talk about "a dream" this song and maybe the album as-a-whole is meant to be kind of a dream. Like Alice in Wonderland or The Wizard of Oz (or even The Secret Life of Walter Mitty even..the whole idea of a DAY DREAM). I mean this by many is regarded as the 1st *concept album* of sorts. So it sort of tells a story, but fictional. The ending of A Day in the Life kind of wraps up the experiences of the album and offers where the story of the band or just one person. I have no idea if the band intended it to be that way, or if the songs just seemed to go well together lyrically and musically. Even down to the cover art, with all the famous people and what not. It's almost like this fictional band, Sgt Pepper's, is taken or takes you, to a world where all those famous people are. Whether they were alive in the real world The Beatles themselves were in, or not. I guess I haven't read boat loads of material about the analysis of this record to know if many others interpret it in a storybook almost fantasy or scifi way, but it wouldn't surprise me. A Day in the Life though, is just one of those songs that included a ton of ideas, from dynamics, to sampling, to like I mentioned before, some clever, original studio tricks. Sgt Pepper's is historically a highly praised record, and by many, The Beatles peak. I'm not sure if I feel that way entirely, but the influence it had on not only on so much music I love, but just personally myself I can't deny. Even for the fact there was a period in the 90's, I came to shun The Beatles, I suppose due to hearing bands like Rush and thinking much of their music was too simplistic and overrated. My best friend from High School felt similarly (probably more so), and used to criticize them frequently. But I came to realize how naive I became in that thinking (whether I ever feel the same about bands like Nirvana or Radiohead, I dunno, I have my doubts though). But no, Sgt Pepper's is a work of art, a very experimental/forward thinking record that I still honestly am marveled by for nostalgia sake and for just the quality of the songs, production and historic importance of. I might even say in some ways, it was my 1st favorite album, even though I wasn't so into "albums" when I was 10 or 11 years old. Thriller and Purple Rain, I think I mainly think of the singles 1st, but Sgt Pepper's still was then and still is an *album* greater than the sum of its parts. And it really set the standard for the millions or more artists to make *albums* as opposed to just a bunch of songs. ## Saturday, February 22, 2014 ### 2014 Music Part 3: Some others This is kind of a hodgepodge of stuff I didn't include in the previous two, maybes, longshots, and hopefuls. And there are I'm sure dozens of artists who also I'm not including in here who I may in a future entry, or just throughout the course of the year. Alphabetical Order Orchestra (was My Latest Novel - Good Bees, Strong Hives?) It appears some of the members of My Latest Novel are involved in this new project and a post from early February says they have Half of an Album already written. By the end of the month we will have half an album...working titles 'Surprise Motherfuckers' or 'Facemelters'...vote here! What that means as far as My Latest Novel? who knows. But it does go along the lines of a pattern of a band from the past who ends up having the members do different things due to various possible reasons. Time, $, inspiration. I really loved My Latest Novel's last record 2009's Deaths and Entrances, but that was nearly 5 years ago. But perhaps Alphabetical Order Orchestra will be another cool group for some of the MLN members and, "Good Bees, Strong Hives" or whatever the title may be for the/a next release will happen eventually for them. Annuals (or Adam Baker?) Adam Baker, whose the lead singer and 1 of the main songwriters of Annuals, I guess he moved to LA a couple of years ago and has been writing new music. The stuff that ended up on last year's Annuals LP Time Stamp, I don't believe is stuff he wrote as recently. Him and Annuals Mike Robinson appeared in a video for a group called First Person Plural, which was nice to see, although the song itself didn't grab me all that much. But, I'm not sure if Mike and Adam did any of the actual songwriting with First Person Plural or that song. But, some I noticed a few updates from Adam on Annuals facebook including using loops or something. So, he's obviously working on new music. The Aston Shuffle - Photographs As I yesterday posted about the Mayer Hawthorne-featured track "Never Take It Away," I'm enjoying that song and potentially this group. It's kind of dancey/soul pop, that is melodic. And in some ways, reminds me of Capital Cities. Although I guess this band put out an impressive debut record 3 years ago, so maybe Capital Cities remind some of them? Regardless, this album drops on March 28th, and I will have to keep it in mind. AYNIW TEPO This is singer Misato Yamanaka of Kacica's new band/project. Or 1 of them at least as I just found out within the last day or 2. It may not be exactly like Kacica, but maybe even better? Misato is a great singer and songwriter, and what it says below, Kazuya Horiba also comes from Kacica as I just noticed he was their bassist. So, I might anticipate some Kacica-like music still here, but who knows having never heard a second of their music. Here's their bio from their site. AYNIW TEPO is a Japanese music group making very nice sound anybody never listen. By singing, using various world music instrument, we can draw the beautiful soundscape. Our band is composed mainly of two menbers, Misato Yamanaka(vo, synth) and Kazuya Hori(ba), who is member of the Japanese great band named kacica in Nara. We underwent member changing several times, Tomoe Yoshida(vo, piano, synth) joined AYNIW TEPO. And we welcome new support member,Tedder (dr) 、Takk (gu) The Barnum Meserve A late entry that slipped my mind, but they are worth including in here certainly. I discovered them last year with an EP of theirs. I forget where, but it may have been a suggestion on rateyourmusic. Anyway, I haven't revisited their music more or less since hearing it initially, but I do remember liking their style of darker toned rock. But their Facebook page says they have a new single coming that will be included on their debut album, so that suggests both very likely will be coming out this year. Entry Big Elf - Into the Maelstrom Mike Portnoy is playing on this, and his speaking out/up for these guys over the last five or more years is probably as big a reason to pay attention to them (although I 1st heard the/saw their name back in the late 90's actually). I'll likely check this out if time allows; although I'm sure many others will get more into this than me, but who knows. Portnoy's involvement does have me more curious about this than I normally would be. released March 3rd.. The Bird and the Bee - TBA The gf is into this band. This album has been made, it just has no means (money and/or a record label) to have it come out. I wonder though, if the band may just decide to either Crowd Fund its release or make it available on a bandcamp page if no record label comes their way. Fjokra Apparently an EP could be coming early in 2014. This is a band who have been around for a few years, that I wrote about a few weeks ago after noticing the cover of The Turtles "Happy Together." They have an EP titled Psycho that came out in 2012, and made some videos, but other than that, they are known for their live shows I guess. Style-wise, maybe just copying their Facebook description would be best. "Todd Rundgren in Genesis listening to Muse while hanging out with Queen, Sikth and Quincy Jones who are all shagging Prince in Rush's private studio on LSD dressed up as The Beatles mixing Psycore jamming with The Manhattan Transfer in a lost Gershwin musical somewhere in Iceland.” I think potentially, I could absolutely LOVE this band. They use a lot of styles I happen to enjoy. Kind of like sElf or Pepe Deluxe. I guess the big question though is, like a band like Painted in Exile or Sigmund Droid, when or even how long may it may before they do release a record. Flying Colors I recall reading most of the music has been written, but of course with this group's members A-jobs, the timing will factor if this does manage to come out. I would think if not in 2014, by 2015 sometime if not this year. Godspeed You Black Emperor I'm only including them as I saw some people mention their name on some other lists. Although their last record Allelujah! Don't Bend! was OLD material, recorded/updated etc. Whatever new music they may release, this year or in the future, at least will be the 1st newly written music since their hiatus ended. The Grape and the Grain Daniel Grimsland of the band Three's new project. Their Rockethub.com raised enough I suspect the progress on this upcoming record could come sooner than later. I'm certainly intrigued by this band's style of heavy ballsy blues rock, as their latest singles released last fall got my attention. What the status of the next Three record is? I have no idea, but if we don't have another Three album soon, at least Daniel is keeping busy (although between Three and Joey Eppard of course, something seems to come out nearly every year anyway..i.e. if a new Three album did come out, I would hardly be surprised). Entry Hannes Grossman - The Radial Covenant Released February 4th. This is from the drummer from technical death metal bands Obscura and Necrophagist. The list of guests, among the metal/tech-death crowds is impressive (as far as I have read). The sample I listened to earlier was impressive, but in playing and actually production. How different this is from Obscura's albums? I dunno. But from some comments from Hans on Youtube, he wrote it all and had control over all the lyrics, vocal lines and other aspects. Mayer Hawthorne He recorded like 40 songs for Where Does This Door Go, and he said he'd like to release many that didn't come out on WDTDG, And he's posted a few videos on Facebook recently, which appears could have been in the studio. I suppose the biggest reason a new record/ep or single may or may not come in 2014 for Mayer will be based on how much his touring schedule takes up of his schedule. House of Fools They posted an update or 2 in 2013 about writing new music, but given there isn't a ton of detail, and their past presence online; and the gap between their last record and Live and Learn, it's certainly no guarantee, but still wouldn't be too surprising if they did release something soon. I'd love to see it in 2014, as I do really enjoy this band, but I'm not expecting it until they start posting more stuff about it online. KXM DUg Pinnick (King's X), George Lynch (Dokken) and Ray Luzier (Korn) project which I gotta admit, the samples sound intriguing, The Self-Titled debut album drops on March 11th. Pat Metheny Unity Group - Kin The trio band, which from less than satisfactory time listening to that style/lineup, is more traditional jazz. In other words, less fusion/synthy-guitars, etc. But, especially after seeing Dean Magraw interpret a lot of that kind of style in recent years, hearing another recording from Pat and his impressive band (Christian McBride, Antonio Sanchez), I may get more won over by this, here and now even. Then again, this is Pat Metheny, anything more or less can happen. Edit: I've checked most of this out and I dig it, but other than some soprano sax, it doesn't vary all that much to most of Pat's other records. Still, I do enjoy much of it already. it should be worth revisiting throughout this year. George Michael He announced like 2 weeks ago, he has a new album in the works. Now, I won't admit to loving everything he does like my girlfriend nearly does, but I do enjoy Faith and some of the Wham music, even just for nostalgia. Plus he did own the stage when he sang with Queen at the Freddie Mercury tribute in the early 90's. And it's been many years since he released a new record (a new single came out in 2012 I recall, but the gf wasn't crazy about it). Miracles of Modern Science They had a pretty big year in 2013, so I wonder if they will be working on their next record this year. Even have already, since the MEEMS EP got them a lot of exposure (and of course their popular cover of Daft Punk's "Get Lucky"), I wonder if they may be looking to follow that up rather soon. If not 2014, soon after. Mutemath Sounds like 2014 could be a year they spend a fair amount of time in the studio, but that may not mean their next record actually gets released until late or sometime in 2015. But Odd Soul was in some ways, their best record, so the record they are working on now is certainly one to get excited about in 2014 or later. http://rollingstoneindia.com/mutemath-get-ready-for-india/ Speaking of which, it’s going to be two years since Odd Soul released. You’ve spoken a bit about the next album in previous interviews. What stage is it at right now? We are still just writing songs. We have written so many ideas at this point, and I think if we were together in a studio and work them out, we’d have who knows how many songs. I’ve never made as many instrumental tracks in preparation for an album as I have in this process. I’ve made so many songs. We are trying to be tough on ourselves and wait till we’ve done something really special. I feel like we’re still in the first phase, that starting phase. But I think we’ve spent so much time in this phase that the next phase can often happen with a lot more fluidity and ease if we do a lot of preparation. It’s been nice. We have had the luxury of festivals and shows that have been paying enough to buy us time to live, think and write and keep writing and you get more instruments and gear. I’m excited, because in two weeks, all of the guys are coming over to my house and we’re going to set up all the gear. We’re going to spend two weeks here recording ideas. We’ll try to make them as complete as we can, so that we can take them to a producer. So we’re at a stage right now where we’re talking about different producers and who to work with. Michael Nesmith and/or The Monkees The big deluxe live album is being released from his last tour, but I hope/wonder if after playing live both with The Monkees again and solo so much, if many of the songs he's put up on his Videoranch site might be released in some fashion, if he has the time I suppose. I know he's showing up at The Monkees convention for the 1st time in March, in New Jersey. And he is touring this Summer with The Monkees again, but all this touring the last few years just makes me wonder if he may want to record again. Not that I would think the odds are high, but probably better than it was a few years ago. Movies of the Mind, the live record has already been released in some forms (the$200 deluxe and super deluxe anyway). I wonder if releasing that will serve for motivation to want to release something new, soon. Although I should add, the gf mentioned a news story talking about Mike, Micky and Peter making a new record (because "Just Us" was sohhhh loved/good..which she doesn't really agree with, but she still would love to hear something from them I imagine). But if not in 2014, maybe 2015. Perhaps Mike and/or The Monkees will at least work on new music this year. Ours - Ballet the Boxer 2? As their 2013 record "Ballet the Boxer 1" implies, it's not, or may not be the last or only part or album they release with said title. Ours is in an odd place now, as they released that record last year, as fast as they could. And the truth is, I am still awaiting my vinyl copy and tote bag, which I understand to a point why, since Vinyl can take time to produce. And for a band that formed over 20 years ago, and only just released their 4th record last year, I wouldn't expect another record so soon. But, the fact is, Jimmy Gnecco and Ours have plenty of new and old songs written and in some cases, recorded perhaps. Just from the sessions when they made BtB1, it's certainly possible there are recordings that got cut. It's not like they don't have an online presence, as they do, but it can be vague or long periods of time without hearing much about their new music. Jimmy's a busy guy, a father, collaborator and a renaissance man or troubadour of sorts. And Ours and Jimmy still tour enough, which may dictate the time-frame of their next record. But Jimmy every so once will post something to his email list and on their website/twitter/facebook with an update. I wouldn't be surprised to see him do that soon and mention something about the next record, whether it is Ballet the Boxer 2 or something else. But as a fanboy, I totally look forward to it. Pain of Salvation - Clean? I noticed some stuff about this maybe even as far back as 2012. But last year, I thought some people were anticipating it. The band toured the North America finally, even though it was abbreviated since Daniel Gildenlow got sick midway through and before the scheduled show in St.Paul at Station 4. And as I write this, the band are on the Progressive Nation at Sea Cruise, without Daniel somehow, given he has been hospitalized with a required surgery due to a flesh-eating bacterial infection. The guy has not had the best run of luck with his health recently, but hopefully his luck and health will improve. But assuming that happens, perhaps this record will get made and be released soon after. The Road Salt records I am luke warm about, but I really haven't spent tons of time listening to. They are a lot different in sound (and of course membership). Not really metal, but blues rock/classic rock sounding. Who knows if "Clean" or what they/Daniel makes next will be the same, but it should be worth checking out regardless. Painted in Exile A new single/song will be coming out supposedly based on the last update they included in January. But the fact they don't have a singer  and bassist currently (that I'm aware of), may continue to delay the release of the long awaited 1st full length record. But perhaps things will escalate quicker once they do. Pharell - G I R L This album will include the single "Happy" that was featured in Despicable Me 2 and on many other stations and commercials. If you asked me a year ago who Pharrell/Pharrell Williams was, I would have had NO CLUE. But with the Daft Punk collaboration on Random Access Memories and his work with Robin Thicke and Mayer Hawthorne especially in 2013, along with "Happy," I may have to check this record out, which comes out on March 3rd. Even the interview he did with Leonard Nimoy helped increase my interest in this guy. He clearly is a talented singer/songwriter and producer, so I would not be surprised to enjoy this, his most recent work. I dunno, eventually he may end up working with other musicians I appreciate like Janelle Monae or Kimbra for example. Put Down the Muffin The return of one of the better local bands I came across in the 2000's, and 1 of the better young jazz groups. Really doing more jazz-rock or prog in a sense. Their return kind of came out of the blue, as I sort of forgot about them a few years ago. And I still have yet to see them live, but with this new record they have coming, maybe some live shows will happen too to support it. Media Addicts are gone now, but with Put Down the Muffin's return, it may fill that newer local jazz-fusion band void. Where to see them? unfortunately not The Artist Quarter . But perhaps Black Dog Cafe or 1 of the clubs in Minneapolis I still need to go to like The Icehouse. The River Empires The status of the next progressive/classical /cinematic/bluegrass release from The River Empires  is a mystery and nothing to be assumed at this point, in terms of a time frame.. Jessy Ribordy was posting stuff about the next record, Mars/Brighton II, back in 2012. But it was probably wise to just back off about news and things until something concrete and substantial was available to share. So not a single post or word was made from The River Empires in 2013. And until the record is all lined up to come out, maybe nothing will be shared, which may or may not be in 2014 or 2015 or later. But, I love the music for this project too bloody much not to at least anticipate. I am just not assuming anything soon. Falling Up perhaps as they continue to be posting things online, and naturally as I imagine the interest and income even is more consistent with them. But at the point The River Empires does return, I know there will be a lot of people very interested as well. Rx Bandits - It's being made if I recall, per a Pledgemusic or Indiegogo. Trombones? somehow I am skeptical they'll be back. But ANYTHING is great given they announced a breakup a few years ago. Sculptured Agalloch member Don Anderson's progressive rock with black metal vocals project, was last heard from in 2008 with Embodiment, a record I have always enjoyed. The samples from the short film "Camera" were among the best parts of it. I also have enjoyed some of their earlier records as well. Agalloch has a new record coming soon, but Don has posted some on Facebook about the next Sculptured record as well, so it wouldn't surprise me to see it come out either in 2014, or 2015. Look up "Matrix Metal" on Facebook and you'll see some recent updates. July 23rd: Things have been very quiet here, but I've been finalizing a few new songs for what will eventually be the 4th Sculptured album. However, my attention has mainly been given to the upcoming and fifth Agalloch album, as well as the upcoming Sol Invictus album that I guested as guitarist on. Once the Agalloch is finished I hope to dedicate the majority of my time to Sculptured. Thanks everyone for your interest! edit: double post from Part Two . i didn't realize it, although when I 1st started these, I only intended for there to be one Entry anyway. But whatevah. Nothing wrong with a 2nd reminder about this upcoming record. sElf Like The River Empires and some others, a new sElf record has been mentioned in the works for many years. And Matt himself is active on Facebook, although not typically about his own music, but just daily life like bartending and what to buy at the grocery store. But the fact is, he moved back to Tennessee and has a studio there I believe. And 2 singles were released only a couple of years ago "Could You Love Me Now" and "Looks and Money," within the period he was making music for commercials and animated films. The fact he did that TED Talk recently and with the re-release/vinyl release of Subliminal Plastic Motives, it seems he is still focusing on the sElf music, it's just when a new collection of tunes comes may or may not be just this year. But perhaps still sooner than later. Darroh Sudderth Lead singer from what appears to be the in transition or hiatus band Fair to Midland. I know in 1 or more interviews a few years ago he talked about a solo record, which I recall style-wise would not be so much like the heavy rock of FTM, but possibly more folky? And I found a post or 2 on FB from 2012 where it was mentioned a record could be coming from him. But it's now been over a year since then (I think it was in November or December). But with Fair to Midland's status unclear, maybe that solo record will come to the surface in 2014 finally. I love the man's voice and songwriting, so if/when a solo release from Darroh/Andrew comes, it'll be worth hearing. Tiles - Other Arrangements I used to be pretty into this Michigan-based progressive rock band in the mid-late 90's. Presents of Mind and their S/T especially I used to listen to a lot, even if they did sound a lot like Rush, but in a good way. Mike Portnoy is a guest on some of this record too. They have been active in the last decade or more, I just haven't been as into their recent music. But perhaps with Portnoy and some other factors, this record will renew my interest in them. Terry Brown is producing and Hugh Syme is doing the artwork again for them, so those are also pluses. The Velvet Teen This band have posted here and there about a new record in the works the past few years. I absolutely love 2004's Elysium, although I would be surprised what they may release will resemble that record much. But at this point, I am interested in hearing anything from them. Hopefully it will finally come out soon, potentially this year, since its been 4 years since their last release 2010's No Star EP, and 8 since their last full length 2006's Cum Laude. Steven Wilson The odds of the next record from Steven coming in 2014 seem slim to none, but KSCOPE music, his record label posted something yesterday (2/21) that his next record will be made in 2014.
# GATE Questions Q: In a pot, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk, the pot would be full and ratio of milk and water would become 6 : 5. Find the capacity of the pot ? A) 11 lit B) 22 lit C) 33 lit D) 44 lit Explanation: Let the capacity of the pot be 'P' litres. Quantity of milk in the mixture before adding milk = 4/9 (P - 8) After adding milk, quantity of milk in the mixture = 6/11 P. 6P/11 - 8 = 4/9(P - 8) 10P = 792 - 352 => P = 44. The capacity of the pot is 44 liters. 11 1925 Q: At what time between 3 and 4 o’clock will the minute hand and the hour hand are on the same straight line but facing opposite directions ? A) 3:15 2/8 B) 3:49 C) 3:49 1/11 D) 3:51 Explanation: On straight line means 180 degree angle. 180 = 11/2 min – 30 hrs 180 = 11/2 m – 30 × 3 180 = 11/2 m – 90 (180 + 90) 2 = 11 m m = 540/11 = 49 1/11 minutes. 7 1905 Q: Five plays K, L, M, N and O are to be staged from Monday to Friday of a week. On each day, only one play will be staged. N or O should not be either the first or last to be staged. O should be immediately followed by M. L should be staged immediately after N. One play is staged between K and L. Which is the second play to be staged ? A) L B) O C) M D) N Explanation: O should be immediately followed by M ie, the order OM should be followed. N should be immediately followed by L ie, the order NL should be followed. One play is staged between k and L and N or O should not be the first or last play. So, the order is Monday             K Tuesday            N Wednesday        L Thursday           O Friday               M 10 1893 Q: Raghu can complete a work in 12days working 9 hours a day. Arun can complete the same work in 8 days working 11 hours a day. If both Raghu and Arun work together, working 12 hours a day, in how many days can they complete the work ? A) B) C) D) A) Option A B) Option B C) Option C D) Option D Explanation: Raghu can complete the work in (12 x 9)hrs = 108 hrs. Arun can complete the work in (8 x 11)hrs = 88 hrs. Raghu's 1 hrs work = 1/108 and Arun's 1 hrs work = 1/88 (Raghu + Arun)'s 1 hrs work = $\left(\frac{1}{108}+\frac{1}{88}\right)=\frac{49}{2376}$ So, both Raghu and Arun will finish the work in Number of days of 12 hours each=$\left(\frac{2376}{49}×\frac{1}{12}\right)$ = 4 1891 Q: At what time, between 3 o’clock and 4 o’clock, both the hour hand and minute hand coincide each other  ? A) 3:16 7/11 B) 3:16 11/4 C) 3:30 D) 3:16 4/11 Explanation: Coincide means 00  angle. This can be calculated using the formulafor time A to B means  [11m/2 - 30 (A)] Here m gives minutes after A the both hands coincides. Here A = 3, B = 4 0 =11m/2 –30 × 3 11m = 90 × 2 = 180 m= 180/11 = 16 4/11 So time = 3 : 16 4/11 5 1878 Q: A watch gains 5 seconds in 3 minutes and was set right at 8 AM. What time will it show at 10 PM on the same day ? A) 10 : 27 : 41 AM B) 8 : 51 : 04 AM C) 9 : 45 : 15 PM D) 10 : 23 : 20 PM Explanation: The watch gains 5 seconds in 3 minutes = 100 seconds in 1 hour. From 8 AM to 10 PM on the same day, time passed is 14 hours. In 14 hours, the watch would have gained 1400 seconds or 23 minutes 20 seconds. So, when the correct time is 10 PM, the watch would show 10 : 23 : 20 PM 6 1865 Q: A number, when 35 is subtracted from it, reduces to its 80 percent. What is four - fifth of that number  ? A) 175 B) 140 C) 135 D) 95 Explanation: x - 35 = 80x/100 => x = 175 => 4x/5 = 4x175/5 = 140. 4 1863 Q: A girl facing north rotates 100(degree) clockwise then 190(degree) anticlockwise. what is new direction of the girl ? A) North-East B) West C) South-East D) South Explanation: First girl facing North Then she rotates 100 deg clock wise => 10 deg ES Then again she rotates 190 deg anti clock wise => for 100 deg it is North and more 90 deg means West. Therefore, the new direction of the girl is West.
# How to find $\binom {1}{k} + \binom {2}{k} + \binom{3}{k} + … + \binom{n}{k}$ Find $$\binom {1}{k} + \binom{2}{k} + \binom{3}{k} + ... + \binom {n}{k}$$ if $0 \le k \le n$ Any method for solving this problem? I've not achieved anything so far. Thanks in advance! • Well $\sum_{i=1}^n{i\choose k}=\sum_{i=k}^n{i\choose k}$ anyway. – Jp McCarthy Jan 9 '15 at 13:33 • Do an example. Pick a $k$, e.g. $k = 10$. Pick an $n$, e.g. $n = 5$. Compute the first term. Compute the last term. Now repeat with another $n$, e.g. $n = 12$. – Hans Engler Jan 9 '15 at 13:42 • Jp McCarthy, can you pls explain how? – Harshal Gajjar Jan 9 '15 at 13:45 • Consider ${2\choose k}$ with $k=3$... that is ${2\choose3}$. Now from two items, how many ways can you choose three of them? Zero. So all of the terms up to but not including ${k\choose k}$ are zero... of course ${k\choose k}=1$. – Jp McCarthy Jan 9 '15 at 13:51 • I think you've missed the edit, I had (initially) placed wrong inequalities.. – Harshal Gajjar Jan 9 '15 at 13:55 ## 5 Answers For $k=0$, the answer is $n$. For $k>0$, the answer is ${{n+1}\choose{k+1}}$. This can be seen by considering how many ways there are to choose $k+1$ integers from the set $\{1,2,\dots,n+1\}$ and conditioning on the greatest integer chosen, because there have to be $k$ choices less than the greatest integer chosen. For instance we look at ${{n+1}\choose{k+1}}={6\choose 4}$. To choose $4$ elements from $\{1,2,3,4,5,6\}$, the greatest chosen element could be $4$, and then we would have to choose $3$ elements from $\{1,2,3\}$; or the greatest chosen element could be $5$, and then we would have to choose $3$ elements from $\{1,2,3,4\}$; or the greatest chosen element could be $6$, and then we would have to choose $3$ elements from $\{1,2,3,4,5\}$. So altogether, ${6\choose 4}={3\choose 3}+{4\choose 3}+{5\choose 3}$. Note: the other terms in the sum, of the form ${i\choose k}$ with $i<k$, are all $0$. For a polynom $P(x)=a_mx^m +\dots +a_1x+a_0$ denote $[x^k]P(x)=a_k$. Notice that for $k\le i \le n$ $$\dbinom{i}{k}=[x^k](1+x)^i$$ hence \begin{align} \sum_{i=1}^n\dbinom{i}{k}&=\sum_{i=k}^n\dbinom{i}{k}\\ &=\sum_{i=1}^n[x^k](1+x)^i\\ &=[x^k]\sum_{i=k}^n(1+x)^i\\ &=[x^k]\frac{(1+x)^{n+1}-(1+x)^k}{(1+x)-1}\\ &=[x^k]\frac{(1+x)^{n+1}-(1+x)^k}{x}\\ &=[x^{k+1}]\left((1+x)^{n+1}-(1+x)^k\right)\\ &=[x^{k+1}](1+x)^{n+1}+[x^{k+1}](1+x)^{k}\\ &=\dbinom{n+1}{k+1}+0\\ &=\dbinom{n+1}{k+1} \end{align} No formal answer, but a nice illustration: The solution can exemplarically be shown by a matrix-multiplication-scheme. The following shows $S \cdot P = X$, where $X$ is simply a shifting of $P$ . The left-bottom is matrix $S$ which performs the partial summations of the columns of matrix $P$ which is in the right-top-matrix, and the result $X$ is the right-bottom-matrix: $$\small \begin{matrix} . & . & . & . & . & | & 1 & . & . & . & . & | \\ . & . & . & . & . & | & 1 & 1 & . & . & . & | \\ . & . & . & . & . & | & 1 & 2 & 1 & . & . & | \\ . & . & . & . & . & | & 1 & 3 & 3 & 1 & . & | \\ . & . & . & . & . & | & 1 & 4 & 6 & 4 & 1 & | \\ - & - & - & - & - & + & - & - & - & - & - & + \\ 1 & . & . & . & . & | & 1 & . & . & . & . & | \\ 1 & 1 & . & . & . & | & 2 & 1 & . & . & . & | \\ 1 & 1 & 1 & . & . & | & 3 & 3 & 1 & . & . & | \\ 1 & 1 & 1 & 1 & . & | & 4 & 6 & 4 & 1 & . & | \\ 1 & 1 & 1 & 1 & 1 & | & 5 & 10 & 10 & 5 & 1 & | \\ - & - & - & - & - & + & - & - & - & - & - & + \end{matrix}$$ From this a hypothetical result can easily be formulated and gives the direction of the attempt of a proof... • +1 for the answer, I would I'm going to start matrices day after tomorrow.. Would come back. :) – Harshal Gajjar Jan 9 '15 at 13:57 You can prove by induction that $$\binom {1}{k} + \binom{2}{k} + \binom{3}{k} + ... + \binom {n}{k}=\frac{(k-1)\binom{1}{k}+(n-k+1)\binom{n+1}{k}}{k+1}$$ holds for every value of $k$. The automatic solution: using the the Gosper's algorithm in Maxima: AntiDifference(binomial(i,k),i); $$\binom{i}{k}=\frac{\binom{i}{k}\,\left(k-i\right)}{k+1}-\frac{\binom{i+1}{k}\,\left(k-(i+1)\right)}{k+1}$$ and the sum telescopes.
# How Should I Think About the Dirac Equation? In Weinberg's QFT Vol. 1 he says the Dirac equation is not a true generalization of Schrodinger's equation, that it does not stand up to inspection when viewed in this light. He says it should be viewed as an approximation to a true relativistic quantum field theory of photons and electrons. • I do not understand what this means, would someone mind filling me in? (Assuming he's saying something more general & subtle than merely saying Dirac is not a one-particle equation) One of Dirac's motivations for his derivation was that Klein-Gordon was not first order in time like the non-relativistic Schrodinger equation is. • Since the 2'nd order in time Klein-Gordon equation does actually describe something physical, does this mean Dirac's point about not being first-order in time is actually flawed, and that Dirac's equation worked for some other reason? From browsing Cartan's Spinor's book it seems the Dirac equation holds for any spinor, it apparently relates left & right representations of a spinor or something, thus it holds in GR etc... There is also this great quote from Atiyah that a spinor is a square root of a geometry. • What is the Dirac equation & how does this explain why Dirac's derivation worked, why it relates representations of a spinor & explains this square root of a geometry business? • You should consider splitting up this question, which may be somewhat too broad as of right now, into separate question, each covering one (maybe 2) subquestions of the current question. – Danu Oct 18 '14 at 17:07 • Weinberg also says on the Introduction of his Lectures on QM: "there is one topic I was not sorry to skip: the relativistic wave eq. of Dirac. It seems to me that the way this is usually presented in books on QM is profoundly mistaken". Dirac thought his eq. was a relativisti generalization of Schrödinger's [...]. The right way to combine relativity and QM is through QFT, in which the Dirac wave function appears as the matrix element of a quantum field between a one-particle state and the vacuum [...]." I never understood what he meant, maybe by answering your question this can be explained. – Drarp Oct 18 '14 at 17:09 • Very interesting, will check his QM book! – bolbteppa Oct 18 '14 at 17:41 • – Name YYY Sep 9 '17 at 15:27 'Square root of geometry' A Dirac spinor field $\psi^\alpha(x)$ under Lorentz transformations behaves as, $$\psi^\alpha(x)\to S[\Lambda]^\alpha_\beta \psi^\beta(\Lambda^{-1}x)$$ where $\Lambda = \exp(\frac{1}{2} \Omega_{\rho\sigma}\mathcal{M}^{\rho\sigma})$ and $S[\Lambda] = \exp(\frac{1}{2}\Omega_{\rho\sigma}\mathcal{M}^{\rho\sigma})$, where $\mathcal{M}$ are the generators of the Lorentz transformations; they are anti-symmetric and obey the Lorenz Lie algebra. The matrices $S$ satisfy the spinor representation of the Lorenz group (exercise!), and are defined by, $$S^{\mu\nu} = \frac{1}{4}[\gamma^\mu,\gamma^\nu]$$ A general rotation matrix acting on a spinor may be written as, $$\left( \begin{array}{cc} e^{i\varphi \cdot \sigma /2} && 0\\ 0 && e^{i\varphi \cdot \sigma /2} \end{array} \right)$$ A rotation by $2\pi$, i.e. an entire turn, around the $x^3$ axis is given by the choice $\varphi = (0,0,2\pi)$, and the rotation matrix becomes, $$\left( \begin{array}{cc} e^{i\pi \sigma^3} && 0\\ 0 && e^{i\pi \sigma^3} \end{array} \right) = -1$$ Hence, under a full turn, a spinor transforms as, $\psi^\alpha(x) \to -\psi^\alpha(x)$, in other words it does not return to its original state. That's why we call them the 'square root of geometry.' You in fact have to rotate them fully twice rather than once. • Is that all it is? In Atiyah's talk "What is a Spinor" on youtube youtube.com/watch?v=SBdW978Ii_E I got the impression it was far more than that, what you're saying is more related to spin-statistics ala Finkelstein books.google.ie/… (mentioned around minute 50 in this Susskind video in terms of belts :p theoreticalminimum.com/courses/advanced-quantum-mechanics/2013/… ) which is another question I may put up. – bolbteppa Oct 18 '14 at 17:44 • @bolbteppa: There's more to it, but I can't answer at the moment on my phone. I'll try get back to you some time tonight. – JamalS Oct 18 '14 at 17:49 • @JamalS: I'd be most interested in what more you might have said. – iSeeker Oct 5 '16 at 0:34
# WEP: Why is the challenge string randomized? In WEP, the 128-bit challenge string generated by an access point would allow for approximately 340 undecillion unique strings. Would it be problematic were a string to be reused? I suppose with $2^{128}$ possible strings it would take a very long time for an access point, with an average amount of associations, to every repeat a challenge. I don't understand why the challenge must be randomized. If it is only used to authentic a client with a legitimate WEP key, then why couldn't the same challenge string be reused for every authentication attempt? Even if an eavesdropper stored all of them in order to reuse them to gain access to an access point, wouldn't it be easier to intercept a single challenge and response and just use XOR to gain access without the WEP key.
• entries 232 1462 • views 959094 # GLSL, Gas giants, Atmospheric scattering 1521 views Gas giants: I started to work the implementation of gas giants. My current approach is to use an outer sphere with atmospheric scattering, similar to the ones used on my Earth-like planets, and a set of layers ( six at the moment ). All of those are generated and displayed with the LOD ( level-of-detail ) algorithm used in the terrain engine, except that the spherical surface is not displaced by a heightmap. Each layer corresponds to a cloud layer with various colors and transparencies. Each layer is textured with a cube map, so I started to generate a "gas giant style" texture for each layer with random color combinations and turbulence. Here's an example of such a texture: The upper layers in altitude get a lower transparency while the deeper layers get more and more opaque. The bottom-most layer is fully opaque, a bit like the ground.. but I don't expect anybody to really see it, since so deep in the atmosphere, any spaceship would be dead for long.. The 6-layers idea wouldn't look very good if the layers were individually visible. Fortunately, I am hoping that with good fogging, particle/wheather effects, and good scattering, everything will blend together quite well. The gas giant texture is procedurally generated by stretching fBm noise with a large non-uniform factor, like ( 1, 30, 1 ). This generates the straight strips. To break the straightness (english?), I am actually using another fBm which returns the amount of stretching to do. In the end, it looks like this: float res = noise.fBm(ray * (4, 4, 4) );res = noise.fBm(ray * (1, 20 + res * factor, 1)); The first factor, (4, 4, 4), determines the size of the turbulence "features"; while the second factor ( factor ) determines how stretched the atmosphere looks. Gas giants planets are rotating very quickly around themselves, which is why their clouds are so stretched. This factor will later be determined by the astrophysical parameters of the planet like its rotation speed. The color table at the moment is quite random. I have to study colors of gas giants and how to generate "interesting" colors. The transparency is also a function of the noise value, plugged in a simple formula. I have to tweak it too. In the future, I will also have to experiment storms like the big red spot on Jupiter, and wheather effects such as those mentioned particles, but also lightning, etc.. Atmospheric scattering: While working on the shaders for gas giants, I realized that my scattering equations were not giving me the expected results. I don't know if anybody wondered.. imagine that a gas giant didn't have any cloud - just imagine a huge ball of gas in space. How would it look like ? Let's say the camera is in the upper atmosphere of the gas giant. The sky would appear like it does on Earth: fading from black to the sky color ( blue on Earth ), with some white haze at the horizon.. But there would be no ground. So what would you see underneath ? Scattering equations, if I'm doing no mistake, say that it should fade back to black. The exctinction coefficients depend on how much atmosphere is traversed, and underneath the camera.. there's a lot of atmosphere to traverse.. so it should be black. Unfortunately, in my previous atmospheric scattering implementation, I saw an ocean of... white. Certainly, I was wrong somewhere. That's pretty much the point I decided to rewrite my atmospheric scattering shaders from scratch, carefully watching the results of all the terms of the equations.. and in GLSL ! GLSL: Until now, I've been using assembly shaders ( in OpenGL, ARB_vertex_program and ARB_fragment_program ). Usually, it was good enough, as shaders were quite simple ( a few tens of instructions at most ). But scattering shaders are a whole new beast, requiring to intersect rays and spheres, and evaluating complex equations. I was loosing too much time to debug my ASM shaders, so I decided that it was time to switch to GLSL.. I expected the GLSL implementation to be straightforward.. how wrong I was. I spent pretty much my whole last week on it. For some reason, the GLSL interface works in a pretty different way than ASM shaders; in particular, shader constants do not belong to a specific shader ( vertex shader, or pixel shader ); but to a program, which is a pair vertex + pixel shader. It's probably not clear, but let's take an example. You have a vertex shader called VertexShader1 and a pixel shader called PixelShader1. VertexShader1 uses a constant called AtmosphereParams. To assign a value to this constant, you have to query the location of this constant in the program.. the location is an ID, so maybe it'll return 1. Now, let's say that you use the same vertex shader but a different pixel shader: PixelShader2. Well, here is the problem: if you query the location of the constant AtmosphereParams in VertexShader1, it might return another location ID. Fixing the issue required introducing the concepts of "virtual" constant IDs, and "real" constant IDs, and mapping one to another in real-time depending on which pair "vertex shader + pixel shader" is bound.. Once my GLSL implementation was complete, I started to experiment with the GLSL language, and so far no problem with it, it's pretty easy and much easier than coding everything in assembly. Regarding GLSL uniforms: The solution I used was to simply cache uniform name<->location pairs in real-time per-program. Whenever a program is re-linked, the cache would be emptied. This has the bonus of allowing me to lookup uniforms by name rather than by location, which makes the code much clearer. Yes, that's what I ended up doing, too. But it's a bit more complex when you have to maintain the same interface for ASM shaders and HLSL :) I don't know if anybody wondered.. imagine that a gas giant didn't have any cloud - just imagine a huge ball of gas in space. How would it look like ? Just like Neptune, I suppose ;) One big sphere of blue, in that case. Quote: Just like Neptune, I suppose ;) One big sphere of blue, in that case. I think you're wrong. Neptune is actually the opposite: it's completely made of very thick, opaque clouds. Neptune aparently has a rock center... not that any spacecraft could make in anywhere near it. It'd probably be crushed by the pressure or gravity or destroyed by the heat long before getting close to it. http://www.solarviews.com/eng/neptune.htm Our knowledge of the internal structure of Neptune is inferred from the planet's radius, mass, period of rotation, the shape of its gravitational field and the behavior of hydrogen, helium, and water at high pressure. This cut-away view shows Neptune composed of an outer envelope of molecular hydrogen, helium and methane roughly the mass of one to two Earths. Below this region Neptune appears to be composed of a mantle rich in water, methane, ammonia, and other elements. These elements are under high temperatures and pressures deep within the planet. The mantle is equivalent to 10 to 15 earth masses. Neptune's core is composed of rock and ice, and is likely no more than one Earth mass. I <3 GLSL Hello Flavien, I am an old university's relationship. I'm fallen on yours articles relating ShaderX2 programing (DirectX9). If you want to speak about our professional experience, i let you my Email adress: [email protected] I ll be happy to know what you become today !!! See you soon Seb D.
# Hairy ball theorem for odd-dimensional spheres Let $$\mathbb S^n$$ be the $$n$$-sphere: $$\mathbb S^n=\left\{x \in \mathbb R^{n+1}: \left\|x\right\|=1\right\}.$$The hairy ball theorem can be formulated as follows: If $$n$$ is even and $$f\,\colon\, \mathbb S^n \to \mathbb S^n$$ is a continuous function, then there exists at least one $$x \in \mathbb S^n$$ such that either $$f(x)=x$$ or $$f(x)=-x$$. This is not true for odd $$n=2k-1$$, with a counterexample being $$f(x_1,\,x_2,\,\dots,\,x_{2k-1},\,x_{2k})=(-x_2,\,x_1,\,\dots,\,-x_{2k},\,x_{2k-1}).$$ But what if remove the evenness condition for $$n$$ and demand $$f$$ to be even instead? Is the following statement true? Let $$n \in \mathbb N_0$$ and $$f\,\colon\, \mathbb S^n \to \mathbb S^n$$ be a continuous function such that $$f(x)=f(-x) \;\; \forall x \in \mathbb S^n$$. Then $$f$$ has a fixed point. This, of course, is true for even $$n$$-s, being a particular case of the hairy ball theorem. It is not hard to prove it also for $$n=1$$, but what about larger odd $$n$$-s? The Lefschetz fixed point theorem implies that any $$f: S^n \to S^n$$ without fixed points has degree $$(-1)^{n+1}$$. But an even map $$S^n \to S^n$$ has even degree, since it factors as $$S^n \xrightarrow{q} \mathbb{R}P^n \to S^n,$$ and for odd $$n$$, $$q$$ has degree $$2$$, while for even $$n$$, $$H_n(\mathbb{R}P^n; \mathbb{Z})=0$$. i think this type question do not have a certain conclusion and your example with $$n=1$$ is an only special case of it! however the outer semi-continuous define $$\limsup_{x \rightarrow \bar x} S(x) \subset S(\bar x)$$, its continuous condition is different from the Brouwer fixed point theorem, it needs an assumption in local domain. then relate this attainable least upper bound to continuum zero, you will get the condition of finite isolated zero point in Poincare-Hopf theorem. so the main condition for lager odd number is the restriction of infinite times $$C^{\infty}-$$ differentiable. this condition will lead your special example with $$n=1$$, but this is all the spares you can get!