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# 737 grounded???

### Help Support HomeBuiltAirplanes.com:

#### pictsidhe

##### Well-Known Member
I was not referring to hand flying. I’m referring to the skill set that should have let the crew of Air France flight 447 recognize, and safely recover from, their stall. I’m referring to the skill set that would enable a flight crew to recognize that a trim system or a stick shaker is not operating properly. I’m assuming that if they recognize that, they will know what to do.

BJC
The pilot of 447 was unaware that the co-pilot had been holding back on the stick for the entire descent. He knew what to do when he discovered that. But, that came too late.

#### BJC

##### Well-Known Member
HBA Supporter
The pilot of 447 was unaware that the co-pilot had been holding back on the stick for the entire descent. He knew what to do when he discovered that. But, that came too late.
It’s my contention that both pilots in the front of a commercial air carrier should know how to fly.

BJC

#### Heliano

##### Well-Known Member
Opinions in several postings in this forum point to the right direction: Boeing has a more appropriate and more conservative approach to automation than Airbus; hand flying skill is still a must; Also situational awareness is critical: could have saved the Air France A330 over the Atlantic; etc.
However two topics must be clarified:
1 - The American Airlines A300 rudder failure: back then the airworthiness requirements in force (FAA, EASA, etc.) did NOT address rudder reversal, that is, full deflection to one side causing a pronounced sideslip angle then reversing the rudder deflection to the other side. What was required by then is full deflection to one side then back to neutral. This accident sent all the aircraft manufacturers scrambling to double check their designs for this weakness. The manufacturer I worked for by then was only producing regional jets with "T" tail ("T" tails require a stronger vertical tail anyhow, to withstand asymmetric vertical loads on the horizontal tail, and to be flutter-free) and found out their designs were OK.
2 - The 737 MAX history is not complete, and more information is needed to fully understand these accidents: The MAX series have, larger, bulkier engines. To keep using the same landing gear system Boeing had to move the engines forward and upward. This new arrangement seems to have caused changes in the aerodynamic behavior at high angles of attack. I - as most of the public - do not know the extent of these changes, i.e., if they cause longitudinal controlability problems or stability problems. May be the MCAS was added to correct these aerodynamic shortcomings. A big engine may in theory produce flow detachment on the wing or wake on the tail. Remember the little plate on the GE CF6 installations? The MCAS changes the stabilizer incidence, and it seems to change it at a much faster rate than a normal manual retrimming (I do not know if the wheel at the central console moves along with the MCAS actuation). Therefore, depending on how fast it actuates, if it happens inadvertently it may create an out-of-control situation before the crew can do anything.
I've read some comments comparing the MCAS to the MD11's LSAS but they are totally different, first because the LSAS actuates the elevator, not the stabilizer, and second because the LSAS, with limited authority, has nothing to do with controlability - its intent is to add longitudinal stability. I've flown the MD-11 for five years.

#### Vigilant1

##### Well-Known Member
The MCAS changes the stabilizer incidence, and it seems to change it at a much faster rate than a normal manual retrimming (I do not know if the wheel at the central console moves along with the MCAS actuation). Therefore, depending on how fast it actuates, if it happens inadvertently it may create an out-of-control situation before the crew can do anything.
The (large, painted with stripes) manual trim wheels do spin as the MCAS-directed trimming occurs.
The MCAS trimming can be stopped at any time by either turning off the electric trim or trimming in the opposite direction using the normal trim switches on the yoke. After approx 10 seconds, if excessively high AoA is still sensed by the active AoA vane, then the MCAS will again attempt to trim nose down (and it can again be countered with the trim switch). There's no limit to how often this cycle can be repeated.
The rate at which the MCAS directs the stab trim to occur is (reportedly) up to 0.27 degrees per second. This is not faster than the trim speed when activated by the switches on the yoke.

#### pictsidhe

##### Well-Known Member
It’s my contention that both pilots in the front of a commercial air carrier should know how to fly.

BJC
Yes. I think the Air France crash was partly due to the pilot assuming that the co-pilot knew what he was doing. It's well known what assumptions are the mother of...

#### BJC

##### Well-Known Member
HBA Supporter
The (large, painted with stripes) manual trim wheels do spin as the MCAS-directed trimming occurs.
The MCAS trimming can be stopped at any time by either turning off the electric trim or trimming in the opposite direction using the normal trim switches on the yoke.
I’ve heard that it is possible to stop the trimming action by holding the manual trim wheel.

BJC

#### Tiger Tim

##### Well-Known Member
If memory serves, the problem was that he went back and forth on the rudder a few times. It wasn't just one big stomp that did it.
I was at a talk by a well seasoned test pilot instructor who spent a good deal of time talking about this accident. IIRC he said afterward he took one of his school's two-seat jets up with the vertical fin instrumented to measure strain and got some data for himself. In stable cruise he pushed one rudder pedal to the floor and let it stabilize for a second at that yaw angle, then centred the pedals briefly, then put in some small amount of opposite rudder well before the plane had straightened out. I forget the units used, but the forces on the tail during that initial rudder input were quite a bit higher than I expected, then were an equal amount in the opposite direction just by centering the rudder, then went off the charts when he put in opposite input. I don't think any pilot had expected that prior to the accident as it was common to teach 'below maneuvering speed you can put in full control input without damaging the aircraft' when it turns out they really only mean elevator input.

Coincidentally, I used to employ the actor that played the First Officer who caused that accident in the episode of Mayday (or Air Crash Investigation depending on what country you're in). He's also a commercial pilot who now even flies for a national airline, possibly even on an Airbus by now.

#### davidb

##### Well-Known Member
It’s my contention that both pilots in the front of a commercial air carrier should know how to fly.
BJC
One well trained experienced pilot and one apprentice pilot works fine when everything is fine. History proves it is much better to have two trained and experienced pilots working together when unusual and critical things go wrong. Thankfully, the FAA has upped the minimum experience required in recent years and has mandated an emphasis on CRM.

History has also shown CRM skills are just as important as two experienced pilots because it enables the synergy.

#### BJC

##### Well-Known Member
HBA Supporter
I’ve heard that it is possible to stop the trimming action by holding the manual trim wheel.

BJC
A senior check pilot for all 737’s just confirmed that the trim can be stopped by holding the manual trim wheel.

BJC

#### Vigilant1

##### Well-Known Member
A senior check pilot for all 737’s just confirmed that the trim can be stopped by holding the manual trim wheel.

BJC
Thanks. One thing that apparently >doesn't< work when the MCAS is working is to apply opposite yoke pressure when the trim is running. This is one way that pilots in the 737 have learned (by habit) to disengage the trim, but it (reportedly) doesn't work that way in the 737MAX when MCAS is doing its thing (as it would largely defeat the purpose of MCAS--to force the nose down if a pilot is pulling back on the yoke and forcing the plane into an extreme nose-high AoA). This is one factor that has been cited as a reason the mishap crews thought they couldn't stop the trim from running--the technique they usually used (push the yoke in the opposite direction) wasn't working. Again--the memory procedure for trim anomalies doesn't say "apply opposite yoke," it says to turn off the autopilot, then it says to flip both cutout switches to "off" and use the manual trim wheel. And it doesn't say you should turn the switches back on, either.

#### Heliano

##### Well-Known Member
Thank you, Vigilant1. What you wrote is very good info. You've taught me a little more about the MAX. The thing I am still curious about is how much MCAS is crucial for stability/control at hi AOA's, and what the aerodynamic differences are between the MAX and the NG/Classic.

#### TXFlyGuy

##### Well-Known Member
Thanks. One thing that apparently >doesn't< work when the MCAS is working is to apply opposite yoke pressure when the trim is running. This is one way that pilots in the 737 have learned (by habit) to disengage the trim, but it (reportedly) doesn't work that way in the 737MAX when MCAS is doing its thing (as it would largely defeat the purpose of MCAS--to force the nose down if a pilot is pulling back on the yoke and forcing the plane into an extreme nose-high AoA). This is one factor that has been cited as a reason the mishap crews thought they couldn't stop the trim from running--the technique they usually used (push the yoke in the opposite direction) wasn't working. Again--the memory procedure for trim anomalies doesn't say "apply opposite yoke," it says to turn off the autopilot, then it says to flip both cutout switches to "off" and use the manual trim wheel. And it doesn't say you should turn the switches back on, either.
You might add this is not just 737 pilots that this applies to with regards of stopping a runaway trim with opposite yoke deflection, but ALL Boeing pilots.

As far as reengaging the trim switches after a situation has been stabilized...the checklist is your friend.

To follow up on a comment made by Heliano, about the landing gear / engines on the Max, Boeing wanted to modify the gear when they designed the 737-900, to give greater ground clearance for the engines. The argument was made as to why this was the proper course of action to the FAA. That idea was accepted by the Feds, however Boeing was advised that if they changed the landing gear a new type rating would be required for the -900.

Thus Boeing slapped yet another Band-Aid on the aging Fluf, making all of their customers happy with the common type.

Here is a post from an airline forum...
Replies: 18 | Views: 1,837 Time for Boeing to Replace the 737

The current "Max" version of the 737 is a 50+ year old design with a heavy slathering of lipstick. The 737 should have had a clean sheet replacement decades ago. Due to Boeing's continual laziness, lack of innovation and not enough competition, they have been content to keep re-heating a relic of the 60's.

#### Vigilant1

##### Well-Known Member
The discussion at the link provides another in the chorus of "brilliant in hindsight" observations we are being treated to.
"Pleasing customers" (by maintaining the same type rating) is an important factor in being successful as a company. Boeing has done that. As far as "lack of competition", it is easy to find 10 more jabbering heads that claim Boeing chose to make the compromises needed to maintain the type rating >because < of competition from Airbus. And how many glitches (as big or bgiger than MCAS has proven to be) might have been lurking in a new clean-sheet design? We'll never know, but in the design of commercial airliners there is much to be said for the safety of evolution over revolution.
Boeing will make this plane better. I just hope the answer isn't some opaque
hardware/software voting monstrosity that a competent crew can't readily understand and fly around when needed. Boeing has been successful in part by avoiding this trap.

#### BBerson

##### Well-Known Member
HBA Supporter
Was a new Type rating really needed for the more suitable gear? Or just arbitrary Rule-making?

#### TXFlyGuy

##### Well-Known Member
I would be curious to know if Boeing's desire to modify the landing gear (make it a bit taller) on the -900 had been allowed by the FAA, and still maintaining the common type, would it have had a positive impact on the Max, making the obtuse MCAS program completely unneeded?

#### TXFlyGuy

##### Well-Known Member
Was a new Type rating really needed for the more suitable gear? Or just arbitrary Rule-making?
Only Boeing and the FAA can answer that.

I became aware of this development as my employer was one of the early customers for the -900, and these arguments were being thrown all over the place.

So Boeing made another compromise in the design, to keep the Fed's happy...and their customers.

Safety is considered important, up until it starts costing too many \$.

#### Tiger Tim

##### Well-Known Member
Any other free flight modelers sitting here thinking, "I'd have just made the stabilizer bigger," or is it just me?

(Obviously there's a huge difference when looking at engineering and weight and certification versus some balsa wood sticks being in a slightly different place)

#### davidb

##### Well-Known Member
Was a new Type rating really needed for the more suitable gear? Or just arbitrary Rule-making?
The Max 10 has the new gear and it is the same type rating. I don’t think the new gear affects the type rating. The new gear isn’t really needed until you stretch the fuselage a bit more. The new gear is quite complex (read expensive) because they had to design something taller that still fits in the old space.

#### BBerson

##### Well-Known Member
HBA Supporter
Yes, but the question was (see post 95) could Boeing have made a taller and a simpler modification than the MCAS, if the FAA had not threatened to impose the Type rating card?

#### TXFlyGuy

##### Well-Known Member
The Max 10 has the new gear and it is the same type rating. I don’t think the new gear affects the type rating. The new gear isn’t really needed until you stretch the fuselage a bit more. The new gear is quite complex (read expensive) because they had to design something taller that still fits in the old space.
Is the gear you reference taller than the previous landing gear? That was the main point of contention between Boeing and the FAA.

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# For Aslan pls. Why were people described as neighbourly and cheerful this season?

Ch. 11 The Chrysalids

##### Answers 1
Best Answer

The crops were unusually free of deviations that season. This meant that farmers did not have to destroy their harvests. This put people in a better mood. Old Jacob, who is usually pessimistic, admitted, “Merciful, the Lord is”, he said…..He then goes on to say something is bound to go wrong but I guess that was pretty optimistic for him!

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Q

Draw rough sketches of altitudes from A to BC for the following triangles (Fig 6.6):

2. Draw rough sketches of altitudes from A to $\small \overline{BC}$ for the following triangles (Fig $\small 6.6$):

altitudes from A to $\small \overline{BC}$ for the triangles are:


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# what happens when you add hcl to acetic acid?

because the surface area has been increased, making more dolomite available to the acid. In other words, if you treat the components separately, and then combine them, the following net reaction happens: $$\ce{CH3COO- + H+ -> CH3COOH}$$, I'll add that the point about significant figures is VERY important. It is easier than modelling with various calculations.

http://www.esm.psu.edu/wiki/_media/research:bas13:gamry_pstat_psu_2010_printerfriendly.ppt, Applied organic chemistry: Perfumery in daily life (in portuguese); Química orgânica aplicada: Perfumaria no cotidiano, Inorganic chemistry—An undeveloped resource in chemistry curricula. If you powder a small amount of magnesite on a streak plate and place a drop of acid on it, you might not see any action for several seconds. Why is the hydrolysis of the conjugate base of a weak acid neglected in buffer solutions? I will get water peak around 3500 region in broad peak, how can I remove the peak? For example, magnesite has a very weak All rights reserved. How do you put grass into a personification? Marble is a limestone or a dolostone that has been metamorphosed. In a mineral identification lab, barite is commonly confused with calcite because of contamination. Students will be investigating them with hardness tests, streak tests, acid tests and other experiments.
Acid dispensing bottles should be made of rigid plastic with a small opening which allows acid to be easily dispensed one-drop-at-a-time.

Calcite is a "ubiquitous" mineral. This is valuable information. answered  12/05/12. hydrochloric acid on a piece of dolomite, the reaction is weak or not observed. Calcite occurs in igneous, metamorphic, and sedimentary rocks and is the most commonly encountered carbonate mineral. If you are at an office or shared network, you can ask the network administrator to run a scan across the network looking for misconfigured or infected devices. Which New Zealander has won cycling medals? MathJax reference.

Why don't libraries smell like bookstores? The bubbling release of carbon dioxide gas can be so weak that you need a hand lens to observe single bubbles slowly growing in the drop of hydrochloric acid - or so vigorous that a flash of effervescence is produced. When testing Forecasting Prices vs Returns by Deep Learning. When acid begins to effervesce (fizz) on a specimen, a reaction Many shales were deposited in marine environments and contain enough calcium carbonate to produce a vigorous acid fizz.
I know HCl will split up into its ions since it is a strong acid. To avoid this problem scratch the rock across a streak plate and test the powder or the grains that are produced. To keep the acid test from fouling your Un compuesto quimico no es el fruto de una simple union, es mas que eso, representa una compatibilidad de cargas, electrones números de oxidación, valencias, cada uno en una debida proporción siempre y cuando estos tengan afinidad química, por lo que es importante, para el desarrollo del estudiante conocer como se forman como se componen como estan... Join ResearchGate to find the people and research you need to help your work. Another easy way to produce a small amount of mineral powder is to scratch the specimen with a nail.). reaction with cold HCl. It will have an acid reaction that is similar to the limestone or

And how can I prepare it from a 100% solution?

2 HCl + Na2SO4 ----> 2 NaCl + H2SO4. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. A few rocks can produce an extreme reaction with hydrochloric acid. Performance & security by Cloudflare, Please complete the security check to access. Your only clue might be that your skin feels slippery. cleavage and is not very hard, then many students will arrive at an incorrect identification. Magnesite: The mineral magnesite, which has a chemical composition of MgCO3, will effervesce weakly with warm hydrochloric acid and very weakly with cold acid. They are composed of How do you make the cool sound by touching the string with your index finger? Is there any way that you can separate sodium sulfate without adding heat to the system? taking place. They dispense the acid one-drop-at-a-time and will not spill if they are knocked over. Then, move on to those other reactions and the minor species. Universal indicator is added to the acetic acid solution and to the students observe the indicator in the acetic acid solution has a color corresponding to acidic. (Ubiquitous means that it is found almost everywhere.).

This occurs because the acid and rock react more vigorously at higher temperatures. Thanks for contributing an answer to Chemistry Stack Exchange! This behavior is encouraged if the classroom is equipped with large acid bottles that are filled to the top. You can write this equation, but it is an equilibrium reaction, which is more something formal. Small amounts of air escaping into a drop of acid from below can give the appearance of a

they are knocked over. frivolously. You would need to calculate the new amounts of acid and base present and then divide by the New volume. You are unlikely to be able to deconvolute useful data from complex mixtures of weak acids and bases.


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# Contextual Approach to Quantum Formalism / Edition 1

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• Used (2) from $215.58 ## More About This Textbook ### Overview The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model. By taking into account the dependence of (classical) probabilities on contexts (i.e. complexes of physical conditions), one can reproduce all distinct features of quantum probabilities such as the interference of probabilities and the violation of Bell’s inequality. Moreover, by starting with a formula for the interference of probabilities (which generalizes the well known classical formula of total probability), one can construct the representation of contextual probabilities by complex probability amplitudes or, in the abstract formalism, by normalized vectors of the complex Hilbert space or its hyperbolic generalization. Thus the Hilbert space representation of probabilities can be naturally derived from classical probabilistic assumptions. An important chapter of the book critically reviews known no-go theorems: the impossibility to establish a finer description of micro-phenomena than provided by quantum mechanics; and, in particular, the commonly accepted consequences of Bell’s theorem (including quantum non-locality). Also, possible applications of the contextual probabilistic model and its quantum-like representation in complex Hilbert spaces in other fields (e.g. in cognitive science and psychology) are discussed. Read More Show Less ### Editorial Reviews ##### From the Publisher From the reviews: “In this book the author presents an unorthodox account of quantum probability theory according to which all the latter’s key features can be reproduced and brought under a common formalism (known as the ‘Växjö model’) with classical statistical mechanics by using a formalism based on contextual probability … . the ideas contained in this book are of potentially very high importance.” (Dean Rickles, Mathematical Reviews, Issue 2011 i) Read More Show Less ### Product Details • ISBN-13: 9781402095924 • Publisher: Springer Netherlands • Publication date: 5/18/2009 • Series: Fundamental Theories of Physics Series , #160 • Edition description: 2009 • Edition number: 1 • Pages: 354 • Product dimensions: 9.21 (w) x 6.14 (h) x 0.88 (d) ### Meet the Author Prof. Andrei Khrennikov is the director of International center for mathematical modeling in physics, engineering and cognitive science, University of Växjö, Sweden, which was created 8 years ago to perform interdisciplinary research. Two series of conferences on quantum foundations (especially probabilistic aspects) were established on the basis of this center: "Foundations of Probability and Physics" and "Quantum Theory: Reconsideration of Foundations". These series became well known in the quantum community (including quantum information groups). Hundreds of theoreticians (physicists and mathematicians), experimenters and even philosophers participated in these conferences presenting a huge diversity of views to quantum foundations. Contacts with these people played the crucial role in creation of the present book. Prof. Andrei Khrennikov published about 300 papers in internationally recognized journals in mathematics, physics and biology and 9 monographs – in p-adic and non-Archimedean analysis with applications to mathematical physics and cognitive sciences as well as foundations of probabilityu theory. Read More Show Less ### Table of Contents Part I: Quantum and Classical Probability Chapter 1: Quantum Mechanics: Postulates and Interpretations1.1 Quantum Mechanics 1.1.1 Mathematical Basis 1.1.2 Postulates 1.2 Projection Postulate, Collapse of Wave Function, Schr\"odinger's Cat 1.2.1 Von Neumann's Projection Postulate 1.2.2 Collapse of Wave Function 1.2.3 Schr\"odinger's Cat 1.2.4 L\"uders Projection Postulate 1.3 Statistical Mixtures 1.4 Von Neumann's and L\"uders' Postulates for Mixed States1.5 Conditional Probability1.6 Derivation of Interference of Probabilities Chapter 2: Classical Probability Theories2.1 Kolmogorov Measure-Theoretic Model 2.1.1 Formalism 2.1.2 Discussion 2.2 Von Mises Frequency Model 2.2.1 Collective (Random Sequence) 2.2.2 Difficulties with Definition of Randomness 2.2.3$S$-sequences 2.2.4 Operations for Collectives 2.3 Combining and Independence of Collectives Part I I: Contextual Probability and\\ Quantum-Like Models Chapter 1: Contextual Probability and Interference1.1 V\"axj\"o model: Contextual Probability 1.1.1 Contexts 1.1.2 Observables 1.1.3 Contextual Probability Space and Model 1.1.4 V\"axj\"o Models Induced by the Kolmogorov Model 1.1.5 V\"axj\"o Models Induced by QM 1.1.6 V\"axj\"o Models Induced by the von Mises Model 1.2 Contextual Probabilistic Description of Double Slit Experiment 1.3 Formula of Total Probability and Measures of Supplementarity 1.4 Supplementary Observables 1.5 Principle of Supplementarity 1.6 Supplementarity and Kolmogorovness 1.6.1 Double Shasticity as the Law of Probabilistic Balance 1.6.2 Probabilistically Balanced Observables 1.6.3 Symmetrically Conditioned Observables 1.7 Incompatibility, Supplementarity and Existence of Joint Probability Distribution 1.7.1 Joint Probability Distribution 1.7.2 Incompatible and Supplementary Observables 1.7.3 Compatibility and Probabilistic Compatibility 1.8 Interpretational Questions 1.8.1 Contextuality 1.8.2 Realism 1.9 Historical Remark: Comparing with Mackey's Model1.10 Subjective and Contextual Probabilities in Quantum Theory Chapter 2: Quantum-Like Representation of Contextual Probabilistic Model 2.1 Trigonometric, Hyperbolic, and Hyper-Trigonometric Contexts 2.2 Quantum-Like Representation Algorithm — QLRA 2.2.1 Probabilistic Data about Context 2.2.2 Construction of Complex Probabilistic Amplitudes 2.3 Hilbert Space Representation of$b$-Observable 2.3.1 Born's Rule 2.3.2 Fundamental Physical Observable: Views of De Broglie and Bohm 2.3.3$b$-Observable as Multiplication Operator2.3.4 Interference 2.4 Hilbert Space Representation of$a$-Observable2.4.1 Conventional Quantum and Quantum-Like Representations2.4.2$a$-Basis from Interference2.4.3 Necessary and Sufficient Conditions for Born's Rule2.4.4 Choice of Probabilistic Phases 2.4.5 Contextual Dependence of$a$-Basis2.4.6 Existence of Quantum-Like Representation with Born's Rule for Both Reference Observables 2.4.7 &'grave;Pathologies'' 2.5 Properties of Mapping of Trigonometric Contexts into Complex Amplitudes 2.5.1 Classical-Like Contexts 2.5.2 Non Injectivity of Representation Map 2.6 Non-Double Shastic Matrix: Quantum-Like Representations 2.7 Noncommutativity of Operators Representing Observables 2.8 Symmetrically Conditioned Observables 2.8.1$b$-Selections are Trigonometric Contexts 2.8.2 Extension of Representation Map 2.9 Formalization of the Notion of Quantum-Like Representation 2.10 Domain of Application of Quantum-Like Representation Algorithm Chapter 3: Ensemble Representation of Contextual Statistical Model 3.1 Systems and Contexts 3.2 Interference of Probabilities: Ensemble Derivation 3.3 Classical and Nonclassical Probabilistic Behaviors 3.3.1 Classical Probabilistic Behavior 3.3.2 Quantum Probabilistic Behavior 3.3.3 Neither Classical nor Quantum Probabilistic Behavior 3.4 Hyperbolic probabilistic behavior Chapter 4: Latent Quantum-Like Structure in the Kolmogorov Model 4.1 Contextual Model with &'grave;Continuous Observables'' 4.1.1 Measure-Theoretic Representation of V\"axj\"o Model 4.2 Measure-Theoretic Derivation of Interference 4.3 Quantum-Like Representation of Kolmogorov Model 4.4 Example of Quantum-Like Representation of Contextual Kolmogorovian Model4.4.1 Contextual Kolmogorovian Probability Model 4.4.2 Quantum-Like Representation 4.5 Features of Quantum-Like Representation of Contextual Kolmogorovian Model 4.6 Dispersion-Free States 4.7 Complex Amplitudes of Probabilities: Multi-Valued Variables Chapter 5: Interference of Probabilities from Law of Large Numbers 5.1 Kolmogorovian Description of Quantum Measurements 5.2 Limit Theorems and Formula of Total Probability with Interference Term Part III: Bell's Inequality Chapter 1: Probabilistic Analysis of Bell's Argument 1.1 Measure-Theoretic Derivations of Bell-Type Inequalities 1.1.1 Bell's Inequality 1.1.2 Wigner's Inequality 1.1.3 Clauser-Horne-Shimony-Holt's Inequality 1.2 Correspondence between Classical and Quantum Statistical Models 1.3 Von Neumann Postulates on Classical$\to $Quantum Correspondence 1.4 Bell-Type No-Go Theorems 1.5 Range of Values (&'grave;Spectral'') Postulate 1.6 Contextuality 1.6.1 Non-Injectivity of Classical$\to \$ Quantum Correspondence 1.6.2 Bell's Inequality and Experiment 1.7 Bell-Contextuality and Action at Distance

Chapter 2 : Bell Inequality for Conditional Probabilities 2.1 Measure-Theoretic Probability Models 2.1.1 Conventional Probability Model and Classical Statistical Mechanics 2.1.2 Bell's Probability Model and Classical Statistical Mechanics 2.1.3 Confronting Bell's Classical Probabilistic Model and Quantum Mechanics 2.2 Wigner-Type Inequality for Conditional Probabilities 2.3 Impossibility of Classical Probabilistic description of Spin Projections of Single Electron

Chapter 3: Frequency Probabilistic Analysis of Bell-type Considerations 3.1 Frequency Probabilistic Description of Models with Hidden Variables for EPR-Bohm Experiment 3.2 Bell Locality (Bell-Clauser-Horne Factoribility) Condition 3.3 Chaos of Hidden Variables does not Contradict to Stabilization of Frequencies for Macro-Observables 3.4 Fluctuating Distributions of Hidden Variables 3.5 Generalized Bell's Inequality 3.6 Transmission of Information with the Aid of Dependent Collectives

Chapter 4: Local Realistic Representation for Correlations in the EPR-experiment for Position and Momentum 4.1 Space and Arguments of Einstein, Podolsky, Rosen, and Bell 4.1.1 Bell's Local Realism 4.1.2 Einstein's Local Realism 4.1.3 Local Realist Representation for Quantum Spin Correlations 4.1.4 EPR versus Bohm and Bell 4.2 Bel&lgrave;s Theorem and Ranges of Values of Observables 4.3 Correlation Functions in EPR Model 4.4 Space-Time Dependence of Correlation Functions and Disentanglement 4.4.1 Modified Bel&lgrave;s Equation 4.4.2 Disentanglement 4.5 Role of Space-Time in EPR Argument Part IV: Interrelation between Classical and Quantum Probabilities

Chapter 1: Discrete Time Dynamics 1.1 Discrete Time in Newton's Equations 1.2 Diffraction Pattern in a Single Slit Scattering 1.3 Interference in the Two Slit Experiment for Deterministic Particles 1.4 Physical Interpretation of Results of Computer Simulation 1.5 Discrete Time Dynamics 1.6 Motion in Central Potential 1.7 Energy Levels of Hydrogen Atom 1.8 Spectrum of Harmonic Oscillator 1.9 General Case of Arbitrary Spectrum 1.10 Energy Spectrum in Various Potentials 1.11 Discussion and Conclusion

Chapter 2: Noncommutative Probability in Classical Disordered Systems 2.1 Noncommutative Probability and Time Averaging 2.2 Noncommutative Probability and Disordered Systems

Chapter 3: Derivation of Schr\"odinger's Equation in the Contextual Probabilistic Framework 3.1 Representation of Contextual Probabilistic Dynamics in the Complex Hilbert Space 3.2 Characterization of Schr\"odinger Dynamics through Dynamics of the Coefficients of Supplementarity Part V Hyperbolic Quantum Mechanics 297

Chapter 1: Representation of Contextual Statistical Model by Hyperbolic Amplitudes 1.1 Hyperbolic Algebra 1.2 Hyperbolic Version of Quantum-like Representation Algorithm 1.2.1 Hyperbolic Probability Amplitude, Hyperbolic Born's Rule 1.2.2 Hyperbolic Hilbert Space 1.2.3 Hyperbolic Hilbert Space Representation 1.3 Hyperbolic Quantization 1.4 Experimental Verification of Hyperbolic Quantum Mechanics

Chapter 2: Hyperbolic Quantum Mechanics as Deformation of Conventional Classical Mechanics2.1 On the Classical Limit of Hyperbolic Quantum Mechanics 2.2 Ultra-distributions and Pseudo-differential Operators over the Hyperbolic Algebra 2.3 The Classical Limit of the Hyperbolic Quantum Field Theory 2.4 Hyperbolic Fermions and Hyperbolic Supersymmetry

References

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text:
# Optimal stopping for diffusion with discontinuous coefficients

 Dia 2019-05-10 10:30:00-03:00 Hora 2019-05-10 10:30:00-03:00 Lugar Salón de seminarios del piso 14, CMAT

### Optimal stopping for diffusion with discontinuous coefficients

#### Ernesto Mordecki(Centro de Matemática -- Facultad de Ciencias)

We show through examples that simple discontinuity of the coefficients of a diffusion produce non connected optimal stopping regions for simple payoffs.

Our examples comprise the broken drift diffusion (i.e. a diffusion with piecewise constant drift coefficient changing at zero) and a linear payoff and the oscillating brownian motion (i.e. a diffusion with piecewise constant diffusion coefficient changing at zero) with a quadratic payoff.

Both examples show the same behaviour. This is joint work with Paavo Salminen.

References

1) Optimal stopping of Brownian motion with broken drift. Ernesto Mordecki Paavo Salminen
High Frequency. Pages: 113-120. First Published: 11 April 2019

2) Optimal stopping of oscillating Brownian motion. Ernesto Mordecki, Paavo Salminen.
arXiv:1903.01457 [math.PR]


text:
# Decomposition of formyl fluoride on the lowest triplet state surface

Sumathi, R and Chandra, AK (1992) Decomposition of formyl fluoride on the lowest triplet state surface. In: Chemical Physics, 165 (2-3). pp. 257-263.

 PDF DcompositionJuly15th.pdf Restricted to Registered users only Download (578Kb) | Request a copy

## Abstract

Decomposition of formyl fluoride on the lowest triplet potential energy hypersurface is studied using ab initio quantum chemical methods. Dissociation energies and the barrier to dissociation from the lowest triplet HFCO into $H(^2S)$ and $FCO(^2A')$ are reported. Results reveal that the barrier to dissociation into $F(^2P) + HCO (^2A')$ is very high. The triatomic radical, $FCO(^2A')$ decomposes into $F(^2P) +CO(^1\sum)$ from the high vibrational levels of the C-F stretch.

Item Type: Journal Article Copyright of this article belongs to Elsevier. Division of Chemical Sciences > Inorganic & Physical Chemistry 22 Aug 2006 19 Sep 2010 04:30 http://eprints.iisc.ernet.in/id/eprint/8082


text:
# Engineering Handbook/Mathematics/Derivative

## Derivative

In calculus, Leibniz's notation, named in honor of the 17th-century German philosopher and mathematician Gottfried Wilhelm Leibniz, uses the symbols dx and dy to represent "infinitely small" (or infinitesimal) increments of x and y, just as Δx and Δy represent finite increments of x and y.[1] For y as a function of x, or

$y=f(x) \,,$

the derivative of y with respect to x, which later came to be viewed as

$\lim_{\Delta x\rightarrow 0}\frac{\Delta y}{\Delta x} = \lim_{\Delta x\rightarrow 0}\frac{f(x + \Delta x)-f(x)}{(x + \Delta x)-x},$

was, according to Leibniz, the quotient of an infinitesimal increment of y by an infinitesimal increment of x, or

$\frac{dy}{dx}=f'(x),$

where the right hand side is Lagrange's notation for the derivative of f at x. From the point of view of modern infinitesimal theory, $\Delta x$ is an infinitesimal x-increment, $\Delta y$ is the corresponding y-increment, and the derivative is the standard part of the infinitesimal ratio:

$f'(x)={\rm st}\Bigg( \frac{\Delta y}{\Delta x} \Bigg)$.

Equivalently, $f'(x)$ is the real number adequal to the infinitesimal ratio $\frac{\Delta x}{\Delta y}$. Then one sets $dx=\Delta x$, $dy = f'(x) dx\,$, so that by definition, $f'(x)\,$ is the ratio of dy by dx.

Similarly, although mathematicians sometimes now view an integral

$\int f(x)\,dx$

as a limit

$\lim_{\Delta x\rightarrow 0}\sum_{i} f(x_i)\,\Delta x,$

where Δx is an interval containing xi, Leibniz viewed it as the sum (the integral sign denoting summation) of infinitely many infinitesimal quantities f(x) dx. From the modern viewpoint, it is more correct to view the integral as the standard part of, or adequal to, an infinite sum of such quantities.

## History

The Newton-Leibniz approach to infinitesimal calculus was introduced in the 17th century. While Newton did not have a standard notation for integration, Leibniz began using the $\int$ character. He based the character on the Latin word summa ("sum"), which he wrote ſumma with the elongated s commonly used in Germany at the time. This use first appeared publicly in his paper De Geometria, published in Acta Eruditorum of June 1686,[2] but he had been using it in private manuscripts at least since 1675.[3]

In the 19th century, mathematicians ceased to take Leibniz's notation for derivatives and integrals literally. That is, mathematicians felt that the concept of infinitesimals contained logical contradictions in its development. A number of 19th century mathematicians (Cauchy, Weierstrass and others) found logically rigorous ways to treat derivatives and integrals without infinitesimals using limits as shown above. Nonetheless, Leibniz's notation is still in general use. Although the notation need not be taken literally, it is usually simpler than alternatives when the technique of separation of variables is used in the solution of differential equations. In physical applications, one may for example regard f(x) as measured in meters per second, and dx in seconds, so that f(x) dx is in meters, and so is the value of its definite integral. In that way the Leibniz notation is in harmony with dimensional analysis.

In the 1960s, building upon earlier work by Edwin Hewitt and Jerzy Łoś, Abraham Robinson introduced ways of treating infinitesimals both literally and logically rigorously, as a foundation for both calculus and analysis. Robinson's methods are used by only a minority of mathematicians. Jerome Keisler wrote a first-year-calculus textbook based to Robinson's approach.

## Leibniz's notation for differentiation

In Leibniz's notation for differentiation, the derivative of the function f(x) is written:

$\frac{d\bigl(f(x)\bigr)}{dx}\,.$

If we have a variable representing a function, for example if we set

$y=f(x) \,,$

then we can write the derivative as:

$\frac{dy}{dx}\,.$

Using Lagrange's notation, we can write:

$\frac{d\bigl(f(x)\bigr)}{dx} = f'(x)\,.$

Using Newton's notation, we can write:

$\frac{dx}{dt} = \dot{x}\,.$

For higher derivatives, we express them as follows:

$\frac{d^n\bigl(f(x)\bigr)}{dx^n}\text{ or }\frac{d^ny}{dx^n}$

denotes the nth derivative of ƒ(x) or y respectively. Historically, this came from the fact that, for example, the third derivative is:

$\frac{d \left(\frac{d \left( \frac{d \left(f(x)\right)} {dx}\right)} {dx}\right)} {dx}\,,$

which we can loosely write as:

$\left(\frac{d}{dx}\right)^3 \bigl(f(x)\bigr) = \frac{d^3}{\left(dx\right)^3} \bigl(f(x)\bigr)\,.$

Now drop the parentheses and we have:

$\frac{d^3}{dx^3}\bigl(f(x)\bigr)\ \mbox{or}\ \frac{d^3y}{dx^3}\,.$

The chain rule and integration by substitution rules are especially easy to express here, because the "d" terms appear to cancel:

$\frac{dy}{dx} = \frac{dy}{du_1} \cdot \frac{du_1}{du_2} \cdot \frac{du_2}{du_3}\cdots \frac{du_n}{dx}\,,$

etc., and:

$\int y \, dx = \int y \frac{dx}{du} \, du.$

## Notations for differentiation

Main page: Notation for differentiation

### Leibniz's notation

Main page: Leibniz's notation

The notation for derivatives introduced by Gottfried Leibniz is one of the earliest. It is still commonly used when the equation y = ƒ(x) is viewed as a functional relationship between dependent and independent variables. Then the first derivative is denoted by

$\frac{dy}{dx},\quad\frac{d f}{dx}(x),\;\;\mathrm{or}\;\; \frac{d}{dx}f(x),$

and was once thought of as an infinitesimal quotient. Higher derivatives are expressed using the notation

$\frac{d^ny}{dx^n}, \quad\frac{d^n f}{dx^n}(x), \;\;\mathrm{or}\;\; \frac{d^n}{dx^n}f(x)$

for the nth derivative of y = ƒ(x) (with respect to x). These are abbreviations for multiple applications of the derivative operator. For example,

$\frac{d^2y}{dx^2} = \frac{d}{dx}\left(\frac{dy}{dx}\right).$

With Leibniz's notation, we can write the derivative of y at the point x = a in two different ways:

$\left.\frac{dy}{dx}\right|_{x=a} = \frac{dy}{dx}(a).$

Leibniz's notation allows one to specify the variable for differentiation (in the denominator). This is especially relevant for partial differentiation. It also makes the chain rule easy to remember:[4]

$\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}.$

### Lagrange's notation

Sometimes referred to as prime notation,[5] one of the most common modern notations for differentiation is due to Joseph-Louis Lagrange and uses the prime mark, so that the derivative of a function ƒ(x) is denoted ƒ′(x) or simply ƒ′. Similarly, the second and third derivatives are denoted

$(f')'=f''\,$   and   $(f'')'=f'''.\,$

To denote the number of derivatives beyond this point, some authors use Roman numerals in superscript, whereas others place the number in parentheses:

$f^{\mathrm{iv}}\,\!$   or   $f^{(4)}.\,\!$

The latter notation generalizes to yield the notation ƒ (n) for the nth derivative of ƒ — this notation is most useful when we wish to talk about the derivative as being a function itself, as in this case the Leibniz notation can become cumbersome.

### Newton's notation

Main page: Newton's notation

Newton's notation for differentiation, also called the dot notation, places a dot over the function name to represent a time derivative. If y = ƒ(t), then

$\dot{y}$   and   $\ddot{y}$

denote, respectively, the first and second derivatives of y with respect to t. This notation is used exclusively for time derivatives, meaning that the independent variable of the function represents time. It is very common in physics and in mathematical disciplines connected with physics such as differential equations. While the notation becomes unmanageable for high-order derivatives, in practice only very few derivatives are needed.

### Euler's notation

Euler's notation uses a differential operator D, which is applied to a function ƒ to give the first derivative Df. The second derivative is denoted D2ƒ, and the nth derivative is denoted Dnƒ.

If y = ƒ(x) is a dependent variable, then often the subscript x is attached to the D to clarify the independent variable x. Euler's notation is then written

$D_x y\,$   or   $D_x f(x)\,$,

although this subscript is often omitted when the variable x is understood, for instance when this is the only variable present in the expression.

Euler's notation is useful for stating and solving linear differential equations.

Table of Derivatives
${d \over dx} c = 0$
${d \over dx} x = 1$
${d \over dx} cx = c$
${d \over dx} |x| = {x \over |x|} = \sgn x,\qquad x \ne 0$
${d \over dx} x^c = cx^{c-1}$ where both xc and cxc-1 are defined.
${d \over dx} \left({1 \over x}\right) = {d \over dx} \left(x^{-1}\right) = -x^{-2} = -{1 \over x^2}$
${d \over dx} \left({1 \over x^c}\right) = {d \over dx} \left(x^{-c}\right) = -{c \over x^{c+1}}$
${d \over dx} \sqrt{x} = {d \over dx} x^{1\over 2} = {1 \over 2} x^{-{1\over 2}} = {1 \over 2 \sqrt{x}}$ x > 0
${d \over dx} c^x = {c^x \ln c}$ c > 0[/itex]
${d \over dx} e^x = e^x$
${d \over dx} \log_c x = {1 \over x \ln c}$ c > 0, $c \ne 1$
${d \over dx} \ln x = {1 \over x}$
${d \over dx} \sin x = \cos x$
${d \over dx} \cos x = -\sin x$
${d \over dx} \tan x = \sec^2 x$
${d \over dx} \sec x = \tan x \sec x$
${d \over dx} \cot x = -\csc^2 x$
${d \over dx} \csc x = -\csc x \cot x$
${d \over dx} \arcsin x = { 1 \over \sqrt{1 - x^2}}$
${d \over dx} \arccos x = {-1 \over \sqrt{1 - x^2}}$
${d \over dx} \arctan x = { 1 \over 1 + x^2}$
${d \over dx} \arcsec x = { 1 \over |x|\sqrt{x^2 - 1}}$
${d \over dx} \arccot x = {-1 \over 1 + x^2}$
${d \over dx} \arccsc x = {-1 \over |x|\sqrt{x^2 - 1}}$
${d \over dx} \sinh x = \cosh x$
${d \over dx} \cosh x = \sinh x$
${d \over dx} \tanh x = \mbox{sech}^2 x$
${d \over dx} \mbox{sech} x = - \tanh x \mbox{sech} x$
${d \over dx} \mbox{coth} x = - \mbox{csch}^2 x$
${d \over dx} \mbox{csch} x = - \mbox{coth} x \mbox{csch} x$
${d \over dx} \mbox{arcsinh} x = { 1 \over \sqrt{x^2 + 1}}$
${d \over dx} \mbox{arccosh} x = { 1 \over \sqrt{x^2 - 1}}$
${d \over dx} \mbox{arctanh} x = { 1 \over 1 - x^2}$
${d \over dx} \mbox{arcsech} x = { 1 \over x\sqrt{1 - x^2}}$
${d \over dx} \mbox{arccoth} x = { 1 \over 1 - x^2}$
${d \over dx} \mbox{arccsch} x = {-1 \over |x|\sqrt{1 + x^2}}$

## References

1. Stewart, James (2008). Calculus: Early Transcendentals (6th ed.). Brooks/Cole. ISBN 0-495-01166-5.
2. Mathematics and its History, John Stillwell, Springer 1989, p. 110
3. Early Mathematical Manuscripts of Leibniz, J. M. Child, Open Court Publishing Co., 1920, pp. 73–74, 80.
4. In the formulation of calculus in terms of limits, the du symbol has been assigned various meanings by various authors. Some authors do not assign a meaning to du by itself, but only as part of the symbol du/dx. Others define "dx" as an independent variable, and define du by du = dx•ƒ′ (x). In non-standard analysis du is defined as an infinitesimal. It is also interpreted as the exterior derivative du of a function u. See differential (infinitesimal) for further information.
5. [1]


text:
# Luatex and unicode math without unicode-math

I'm using fontspec in lualatex to get a OTF main font, but I'd like to use one of the good old math fonts (like the default TeX one). After trying different packages, I didn't manage to make it work with utf-8 input:

\documentclass{minimal}
\usepackage{fontspec}
\setmainfont{TeX Gyre Pagella}
\begin{document}
Test for $\alpha$ and $α$.
\end{document}

This renders only the first math symbol correctly. What do I miss exactly?

-

You must declare the alpha. E.g. in fontmath.ltx the command \alpha is set up this way:

\DeclareMathSymbol{\alpha}{\mathord}{letters}{"0B}

You need the same declaration for the alpha (the ^^^^03b1 are only ascii substitutes for the alpha, you can replace them):

\documentclass{minimal}
\usepackage{fontspec}
\setmainfont{TeX Gyre Pagella}
\DeclareMathSymbol{^^^^03b1}{\mathord}{letters}{"0B}
\begin{document}
Test for $\alpha$ and $^^^^03b1$.
\end{document}

-
Ok. Is there any package that include these definitions for the most common symbols? –  Stéphane Gimenez Nov 16 '11 at 10:25
I don't know such a package. –  Ulrike Fischer Nov 16 '11 at 10:35
Ok thank you! Maybe I'll make mine :-) –  Stéphane Gimenez Nov 16 '11 at 10:54
@StéphaneGimenez In case you did, would you mind publishing it? –  Tobias Kienzler Dec 14 '12 at 11:06
@StéphaneGimenez, Did you make yours? :) or find an alternative (within pdflatex). It would be very useful. –  alfC Dec 24 '12 at 10:18

use the Latin Modern Math font:

\documentclass{minimal}
\usepackage{unicode-math,fontspec}
\setmainfont{TeX Gyre Pagella}
\setmathfont{lmmath-regular.otf}
\begin{document}
Test for $\alpha$ and $α$.
\end{document}

-
@Hebert, So fontspec or unicode-math} needs xelatex or lualatex. Once you use one of them, the document compiles and generates the expected output, even with the the two lines \setmainfont{... lines. It even works without the fontspec package. (in TeXLive 2012 at least) –  alfC Dec 24 '12 at 10:17
@alfC: sure it loads Latin Modern by default but I wanted to use Pagella! –  Herbert Dec 24 '12 at 11:36


text:
This week in Pre-Calc 11, we learned how to graph absolute values. These can be applied to both linear and quadratic functions. This task is very easy to complete.

First we will do a linear function.

y= |x+2|

We know that our y-int. is 2, our slope is 1 up, 1 over

First we will graph the function

So we know that it will go past the zero, but we know that the function is an absolute value, which means it can’t go past zero, which means we will have to go back up so it will stay positive.

So for a quadratic it is also very simple.

Our equation will be $y= |x^2 -2|$

Since our vertex is (0,-2) we need to keep the quadratic positive

so all we do is move the part that is negative to the positive side.

Week 12 – Graphing Absolute Values


text:
# A 100 V carrier peak changes from 160 V to 40 V by a modulating signal. The modulation factor is

This question was previously asked in
ESE Electrical 2014 Paper 2: Official Paper
View all UPSC IES Papers >
1. 0.3
2. 0.5
3. 0.6
4. 0.7

Option 3 : 0.6
Free
CT 3: Building Materials
2962
10 Questions 20 Marks 12 Mins

## Detailed Solution

Concept:

For an Amplitude modulated wave with carrier amplitude AC, the maximum and minimum amplitude is given by:

Amax = Ac(1 + μ)

Amin = Ac(1 - μ)

$$\frac{{{A_{max}}}}{{{A_{min}}}} = \frac{{1 + μ}}{{1 - μ}}$$

The above can be written as:

$$μ = \frac{{{A_{max}} - {A_{min}}}}{{{A_{max}} + {A_{min}}}}$$

Calculation:

Given Amax = 160 V and Amin = 40 V

The modulation index will be:

$$μ = \frac{{{160} - 40}}{{160 + 40}}=\frac{120}{200}$$

μ = 0.6


text:
# Tag Info

Contrary to what @user21's answer, I don't think that you need to do anything special for point loads. Let's see why. A point load can be represented as a Dirac delta "function". So, in your case it would be something like $$R = \rho \delta(x - x_i)\, ,$$ where $\rho$ is the intensity of the source and $x_i$ is the position. If we use a weighted ...
Seen that you also have an account over at mathematica stackexchange I am going to show an implementation using Mathematica. This is certainly not the only way you can do it but hopefully gets you started. We start by creating a 1D mesh Needs["NDSolveFEM"] region = Line[{{0}, {1}}]; includePoints = {{1/3}, {2/3}}; mesh = ToElementMesh[region, &...


text:
# Confusion about partial and total derivatives.

I stumbled upon this:

And there is something that specifically bothers me. Say $$L(q(t),\dot{q}(t),t)$$

Then I claim it makes no sense that $\frac{\partial L}{\partial t}$ only differentiates the explicit dependencies of $L$ on $t$ without also differentiating the contributions of $q(t)$ and $\dot{q}(t)$.

Why do I claim this? Well suppose we have a function such that $$f(x(r,\theta),y(r,\theta))$$

Then the operator $\frac{\partial}{\partial r}$ does act on the functions and not only on "explicit dependences".

What is going on here?

It might look as if I'm an advanced student because of the image I've posted, but I really am not, so don't be misguided (if that were to be the case).

Thanks.

• The notation for partial derivatives is awful. Your doubt is 200% reasonable. EDIT: One way to go around this is by adopting Rudin's PMA notation for partial derivative: $D_1f=\frac{\partial f}{\partial x}$, for example. EDIT2: In fact, I think this notation is one of the worst of mathematics. – Aloizio Macedo Sep 24 '15 at 7:30

Suppose the variables were named $(a,b,c)$ to begin with (instead of $(q,\dot q,t)$), so that you simply have a function $L(a,b,c)$. Then there's nothing strange about computing the partial derivative $\frac{\partial L}{\partial c}(a,b,c)$, right? And there is also nothing strange about inserting values $$a=q(t), \quad b=\dot q(t), \quad c=t$$ after you have computed this derivative: $\frac{\partial L}{\partial c}(q(t),\dot q(t),t)$. And this is exactly what is meant by the notation $$\frac{\partial L}{\partial t}(q(t),\dot q(t),t).$$
For comparison, if instead you first insert these values into $L(a,b,c)$, so that you get a function of $t$ alone, and then take the (ordinary) derivative of this function (with respect to $t$ of course, since it's now the only variable in sight), then you get the "total derivative" which is denoted by $$\frac{dL}{dt}(q(t),\dot q(t),t).$$
• Sorry to comment a thread far from now! But I really wonder what is $\frac{dL}{dq}$ in your example – FaDA Aug 17 at 0:16
• @FaDA: I don't understand your question. $dL/dq$ doesn't make much sense. – Hans Lundmark Aug 17 at 9:58
• Thanks for your reply! It doesn't have too much physical meaning, but when performing integration over a space of (q,p,t) it is useful when doing integration by parts. Here is my question math.stackexchange.com/questions/3325649/… In this thread which gives two links, the second link is the case where $dL/dq$ is useful in the integration by parts like I mentioned – FaDA Aug 17 at 10:57
• @FaDA: I still don't understand. You would have to clarify what you mean by $dL/dq$ to begin with. – Hans Lundmark Aug 17 at 13:45


text:
# Show information only once in footnotes

I am using citestyle=authortitle-ibid, but I have to make it work according to these rules:

1. The first time a reference is made, there should be all the information in the footnote (including publisher, author, editor, containing book, year etc.).
2. The second time the same reference is used, even on another page, the footnote should contain author, year and page, unless the information is ambigious without the title. In the latter case, the title should be contained as well.

I am wondering how one could achieve this. Personally, I think putting all the information in footnotes is a bad idea, however, I was told to do so.

• In which cases are the informations ambiguous? May 16, 2014 at 14:19
• In other words, you want to combine the authortitle style with an authordate style? Normally, when the year alone doesn't disambiguate, you add a letter. Smith 2001a vs Smith 2001b vs Smith 2002 --- no one is going to be confused as to which is which. When you use titles, you disambiguate via the shorttitle field, which is what gets printed in subsequent citations.
– jon
May 16, 2014 at 14:19
• Also when John Smith published something in 2000, and Robert Smith published something in 2000, then you usually want to have J. Smith 2000 vs R. Smith 2000: Smith 2000 + title won't (directly) tell you whether John or Robert was the author...
– jon
May 16, 2014 at 14:21
• @jon As far as I know, I'll have to use the whole name (or at least last name + initial) anyway. I don't like this style, but my teacher enforces it for some reason. May 16, 2014 at 14:24
• Well many teachers, especially those who type out all their own references by hand, can have odd preferences. Just to be clear: in the subsequent references where the title is necessary, the full title must be used, or the shorttile field?
– jon
May 16, 2014 at 14:29

My original answer used chicago, because it's a highly developed style which I thought came close to what was wanted. However, a comment in response indicated that the questioner has developed his/her own custom .bbx style based on authortitle-ibid, and I think there are likely to be conflicts there.

Frankly, I don't think authortitle-ibid is the place to start: a key feature of the style you want is (a) full citations at first and (b) short citations on subsequent use. The standard style that comes close to this is verbose-ibid, and that is probably the right place to start. It's still more likely to be compatible with your custom adjustments, since it won't be far from authortitle-ibid as far as full citations is concerned, and it will certainly be closer than chicago. If you start from authortitle you are going to have to recreate all the structure for full citations and so forth that is already present in verbose, which is pointless.

Within the verbose-ibid style, the typesetting of shortened citations is handled by the bibmacro cite:short, and so we redefine that.

\documentclass{article}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@book{author1,
author    = {Author, A.},
title     = {First Work},
date      = {2010},
publisher = {Publisher},
}
@book{author2,
author    = {Author, A.},
title     = {Second Work},
date      = {2010},
publisher = {Publisher},
}
@book{author3,
author    = {Author, A.},
title     = {Third Work},
date      = {2011},
publisher = {Publisher},
}
\end{filecontents}
\setlength{\textheight}{2in}

\usepackage[style=verbose-ibid,labeldate=true]{biblatex}
\makeatletter
\renewbibmacro*{cite:short}{%
\printnames{labelname}%
\iffieldundef{extrayear}%
\mkbibparens{\printdatelabel}}}
{\setunit*{\nametitledelim}%
\printfield[citetitle]{labeltitle}%
\printtext{\mkbibparens{\printdatelabel}}}}}
\makeatother

\begin{document}

We use \texttt{verbose-ibid} as our style, setting \texttt{labeldate}
true so as to have a hook to decide if we have multiple works by the
same author(s) in the same year.

We revise the \texttt{cite:short} macro. On the first occasion
something is printed, we will have full citations.\footcite{author1,
author2, author3} On subsequent occasions they will be shortened,
with titles added only if necessary for
disambiguation.\footcite{author1, author2, author3}

\end{document}

Producing:

The effect you want is nearly the default with the biblatex-chicago style, with the notes option: it is loaded (unusually) as a free-standing package not a style, but it makes full use of biblatex. The documentation is extensive.

Indeed, I first thought that this just did what you want: but I was reading too quickly -- the default is to have an author/title style on subsequent citations, not the mixture of author/year and title you suggest. That can, however, be fairly easily accomplished by redefining one bibmacro: we also need to add the labeldate option, not because we add any additional labels this way, but because it's a handy way of getting biber to tell us if there is more than one relevant citation in a given year. The basic technique could, I think, be easily adapted to the standard styles.

A brief example follows:

\documentclass{article}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@book{author1,
author = {Author, A.},
title  = {First Work},
date   = {2010},
}
@book{author2,
author = {Author, A.},
title  = {Second Work},
date   = {2010},
}
@book{author3,
author = {Author, A.},
title  = {Third Work},
date   = {2011},
}
\end{filecontents}

\usepackage[notes,labeldate=true]{biblatex-chicago}
\makeatletter
\renewbibmacro*{cite:short}{%
\ifthenelse{\ifnameundef{labelname}\OR%
\ifentrytype{inreference}\OR%
\ifentrytype{reference}\OR%
\ifentrytype{mvreference}}%
{\iffieldequalstr{entrysubtype}{magazine}% Simplify .bib creation
{\ifuseauthor%
{\printfield[journaltitle]{journaltitle}\isdot\newcunit}%
{}}%
{\ifentrytype{manual}%
{\printlist{organization}\isdot\newcunit}%
{}}}%
{\iffieldequalstr{authortype}{anon}%
{\bibleftbracket\printnames{labelname}%
\bibrightbracket\classicpunct}%
{\iffieldequalstr{authortype}{anon?}%
{\bibleftbracket\printnames{labelname}?%
\bibrightbracket\classicpunct}%
{\usebibmacro{choose+labelname}%\printnames{labelname}%
\isdot\classicpunct}}}%
\iffieldundef{extrayear}% Is the reference unique?
{\printfield[citetitle]{labeltitle}% Yes: print the title
\ifboolexpr{%
togl {cms@allshort}%
or
test {\ifbibliography}
}%
{\printtext[bibhyperref]{%
\mkbibparens{\printdatelabel}}}% We want the date label not the title
\mkbibparens{\printdatelabel}}}% We want the date label not the title
}%:\thefield{entrytype}?
\makeatother

\begin{document}

With \texttt{biblatex-chicago} with the \texttt{notes} option, the
default is for citation to appear in footnotes, with a full citation
on the first occasion and an abbreviated citation on subsequent occasions.

So the first citation is full,\footcite{author1} an immediately
following citation will use \emph{ibid}\footcite[Thus:][]{author1},
(unless \texttt{ibidtracker} is set false) but otherwise later
citations will be abbreviated.

We do, however, have to make minor modifications to one macro, because
by default the package assumes author/title citations, but we have to
provide author/year citations, with the date printed only if there is
more than one work in the relevant year. We thus get all our full
citations out,\footcite{author1, author2, author3} and then
demonstrate that happening.\footcite{author1, author2, author3}

\end{document}

• I don't think this is quite true: the point is that the year is always included in the subsequent citations, and, when that is not enough, then the title is added as well in order to disambiguate. (The year only partially disambiguates on its own --- that's what makes it weird!)
– jon
May 16, 2014 at 16:04
• @jon You are right: I read too quickly. May 16, 2014 at 17:17
• @PaulStanley This looks great, can't wait to try it! I already wrote a custom bbx file for my bibliography, can I still use it with the biblatex-chicago package? May 17, 2014 at 12:54
• Well, I doubt a custom bbx file will work smoothly with chicago; but if you look at the bibmacro above, I doubt you will have much difficulty in converting it to your package. The useful "trick" is the use of extrayear to do your disambiguation, and that should be adaptable to the standard package. But if you are trying to customize towards this result, it would be easier to start with verbose-ibid anyway, since that gets closer to what you want .... May 17, 2014 at 14:19
• @just.kidding I have updated my answer to use the same technique but with a standard style, which you will probably find easier to work with. May 17, 2014 at 15:05


text:
## Differentiation of cot inverse x

Here you will learn differentiation of cot inverse x or arccotx x by using chain rule. Let’s begin – Differentiation of cot inverse x or $$cot^{-1}x$$ : The differentiation of $$cot^{-1}x$$ with respect to x is $$-1\over {1 + x^2}$$. i.e. $$d\over dx$$ $$cot^{-1}x$$ = $$-1\over {1 + x^2}$$. Proof using chain rule : Let …


text:
# Standard deviation of a population

Calculate the standard deviation of a population.
You might need: Calculator

### Problem

A group of kids just finished trick-or-treating. The number of pieces of candy collected by each of the 5 kids is listed below.
31, comma, 33, comma, 36, comma, 41, comma, 34
Find the standard deviation of the data set.


text:
## virtus Group Title Question attached below one year ago one year ago

1. virtus Group Title

|dw:1345271219374:dw|

2. virtus Group Title

prove that triangle OTM is similar to triangle TPM

3. mukushla Group Title

|dw:1345271392740:dw|

4. dpaInc Group Title

since both are right triangles and <TOM is congruent to <TOP, those two triangles are similar by AAA

5. dpaInc Group Title

^^^ that is assuming PT is tangent to the circle....

6. virtus Group Title

Yes PT is a tangent to the circle, but can you elaborate on why it is similar by AAA. i don't get it thanks

7. mukushla Group Title

PT is a tangent to the circle so OT is perpendicular to PT and PTO=90 is that right?

both are right triangles and one angle O is common

|dw:1345271947198:dw|

10. virtus Group Title

umm we are proving OTM is similar to triangle TPM

11. virtus Group Title

not OTM is similar to triangle OTP

first step we are proving OTM ~ OPT next we gona prove OPT ~ TPM and conclude OTM ~ TPM

did you understand why OTM ~ OPT ?

|dw:1345272356748:dw|

|dw:1345272694033:dw|

its just a simple game with $$\alpha$$ , $$90-\alpha$$, and seeing which triangles have same set of angles

17. virtus Group Title

ohhh sorry @rsadhvika i understand thanks!


text:
Question

# A man grows into a giant such that his linear dimensions increase by a factor of $$9$$. Assuming that his density remains same, the stress in the leg will change by a factor of :

A
181
B
9
C
19
D
81

Solution

## The correct option is D $$9$$$$Stress =\dfrac{force}{Area}$$Let linear dimensions be $$l, b, h$$.$$Stress = \dfrac{Force}{l\times b}$$Now, dimensions increase by facror of g.So, Now $$S'= \dfrac{Force}{9l\times 9b}=\dfrac{ma}{81 lb}$$$$S' = \dfrac{\rho Va}{81\times lb}$$$$\therefore$$ $$\dfrac{S'}{S} = \dfrac{9^3V}{81\times lb}\times \dfrac{lb}{V}$$$$S'=9S$$Hence stress in leg will change by factor of $$9$$Physics

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text:
Deepak Scored 45->99%ile with Bounce Back Crack Course. You can do it too!

# Two positive charges of magnitude 'q' are placed at the ends of a side (side 1 ) of a square of side '2a'.

Question:

Two positive charges of magnitude ' $q$ ' are placed at the ends of a side (side 1 ) of a square of side '2a'. Two negative charges of the same magnitude are kept at the other corners. Starting from rest, if a charge $\mathrm{Q}$ moves from the middle of side 1 to the centre of square, its kinetic energy at the centre of square is :-

1. $\frac{1}{4 \pi \epsilon_{0}} \frac{2 \mathrm{qQ}}{\mathrm{a}}\left(1-\frac{1}{\sqrt{5}}\right)$

2. Zero

3. $\frac{1}{4 \pi \in_{0}} \frac{2 \mathrm{qQ}}{\mathrm{a}}\left(1+\frac{1}{\sqrt{5}}\right)$

4. $\frac{1}{4 \pi \in_{0}} \frac{2 \mathrm{qQ}}{\mathrm{a}}\left(1-\frac{2}{\sqrt{5}}\right)$

Correct Option: 1

Solution:


text:
Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals → CMB
Abstract view

Determination of Hauptmoduls and Construction of Abelian Extensions of Quadratic Number Fields

Published:2007-09-01
Printed: Sep 2007
• Hung-Jen Chiang-Hsieh
• Yifan Yang
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
 Format: HTML LaTeX MathJax PDF PostScript

Abstract

We obtain Hauptmoduls of genus zero congruence subgroups of the type $\Gamma_0^+(p):=\linebreak\Gamma_0(p)+w_p$, where $p$ is a prime and $w_p$ is the Atkin--Lehner involution. We then use the Hauptmoduls, along with modular functions on $\Gamma_1(p)$ to construct families of cyclic extensions of quadratic number fields. Further examples of cyclic extension of bi-quadratic and tri-quadratic number fields are also given.
 MSC Classifications: 11F03 - Modular and automorphic functions 11G16 - Elliptic and modular units [See also 11R27] 11R20 - Other abelian and metabelian extensions

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/


text:
# Dominant (music)

(Redirected from Dominant chord)
Tonic and dominant in C  Play. C major and G major chords.
The second to last chord in this example is built on the dominant (V) and found here in the circle progression on C: I-IV-viio-iii-vi-ii-V-I  Play

In music, the dominant is the fifth scale degree of the diatonic scale, called "dominant" because it is next in importance to the tonic,[1] and a dominant chord is any chord built upon that pitch, using the notes of the same diatonic scale. The dominant function (diatonic function) has the role of creating instability that requires the tonic for resolution.

In very much conventionally tonal music, harmonic analysis will reveal a broad prevalence of the primary (often triadic) harmonies: tonic, dominant, and subdominant (i.e., I and its chief auxiliaries a 5th removed), and especially the first two of these.
—Berry (1976)[2]
The scheme I-x-V-I symbolizes, though naturally in a very summarizing way, the harmonic course of any composition of the Classical period. This x, usually appearing as a progression of chords, as a whole series, constitutes, as it were, the actual "music" within the scheme, which through the annexed formula V-I, is made into a unit, a group, or even a whole piece.
—Rudolph Reti, (1962)[3] quoted in[4]

For example, in the C major scale (white keys on a piano, starting with C), the dominant is the note G; and the dominant triad consists of the notes G, B, and D.

## Dominant chords

In music theory, the dominant triad (3-note chord) is a major triad, symbolized by the Roman numeral V, if it is within the major diatonic scale (for example G-B-D in C major). It is, however, a minor triad, denoted v, if it is within the minor diatonic scale (for example G-B-D in C minor). In the minor scale, the dominant triad is often substituted with a major triad, by sharpening the second note, which is a minor third from the dominant note, into a major third, since the major third from the dominant is the leading tone for the minor scale. For instance, in G-B-D, the B is sharpened to B natural (B), since B is the leading tone for the C minor scale.

### Seventh chord

A dominant seventh chord is a chord built upon the dominant of a major diatonic scale, containing a dominant (major) triad and an additional minor seventh (for example G-B-D-F in C major). It is typically denoted G7.

As defined by the 19th century musicologist Joseph Fétis the dominante was a seventh chord over the first note of a descending perfect fifth in the basse fondamentale or root progression, the common practice period dominant seventh he named the dominante tonique.[5]

Dominant chord (V) in the ii-V-I cadence on C  Play

### Dominant chord in authentic cadence

A cadential dominant chord followed by a tonic chord (the chord of the key of the piece) is denominated as authentic cadence. If the roots are in the bass and the tonic is in the highest voice, it is called a perfect authentic cadence.

## Dominant key in tonal modulation

The movement to the dominant was part of musical grammar, not an element of form. Almost all music in the eighteenth century went to the dominant: before 1750 it was not something to be emphasized; afterward, it was something that the composer could take advantage of. This means that every eighteenth century listener expected the movement to the dominant in the sense that [one] would have been puzzled if [one] did not get it; it was a necessary condition of intelligibility.
—Charles Rosen (1972)[6]

"Dominant" also refers to a relationship of musical keys. For example, relative to the key of C major, the key of G major is the dominant key. Music which modulates (changes key) often modulates into the dominant. Modulation into the dominant key often creates a sense of increased tension; as opposed to modulation into subdominant (fourth note of the scale), which creates a sense of musical relaxation.

The vast majority of harmonies designated as "essential" in the basic frame of structure must be I and V–the latter, when tonal music is viewed in broadest terms, an auxiliary support and embellishment of the former, for which it is the principal medium of tonicization.
—Berry (1976)[2]

The dominant chord itself is composed of the dominant (sol), the leading-tone (ti), and the supertonic (re) scale degrees. According to the rules of tonal resolution, both the leading-tone and the supertonic primarily resolve to the tonic. These two tones resolving to the tonic are strengthened by the dominant scale degree, which is a common tone between the tonic and dominant chords. The dominant may also be considered the result of a transformational operation applied to the tonic that most closely resembles the tonic by some clear-cut criteria such as common tones.[7]

## In non-Western music

The dominant is an important concept in Middle Eastern music. In the Persian Dastgah, Arabic maqam and the Turkish makam, scales are made up of trichords, tetrachords and pentachords (each called a jins in Arabic), with the tonic of a maqam being the lowest note of the lower jins and the dominant being that of the upper jins. The dominant of a maqam is not always the fifth, however; for example, in Kurd and Bayati, the dominant is the fourth, and in maqam Saba, the dominant is the minor third. A maqam may have more than one dominant.


text:
Narrow resonances revisited: Simplifying multidimensional constraints
Open Access Publications from the University of California

## Narrow resonances revisited: Simplifying multidimensional constraints

• Author(s): Chivukula, R Sekhar
• Ittisamai, Pawin
• Osborne, James
• Simmons, Elizabeth H
• et al.

## Published Web Location

https://doi.org/10.1103/PhysRevD.103.095008
Abstract

As we amass more LHC data, we continue to search for new and improved methods of visualizing search results, in ways that are as model-independent as possible. The simplified limits framework is an approach developed to recast limits on searches for narrow resonances in terms of products of branching ratios (BRs) corresponding to the resonance's production and decay modes. In this work, we extend the simplified limits framework to a multidimensional parameter space of BRs, which can be used to unfold an ambiguity in the simplified parameter $\zeta$ introduced when more than one channel contributes to the production of the resonance. It is also naturally applicable to combining constraints from experimental searches with different observed final states. Constraints can be visualized in a three-dimensional space of branching ratios by employing ternary diagrams, triangle plots which utilize the inherent unitarity of the sum of the resonance's BRs. To demonstrate this new methodology, we recast constraints from recent ATLAS searches in diboson final states for spin-0, 1, and 2 narrow resonances into constraints on the resonance's width-to-mass ratio and display them in the space of relevant branching ratios. We also demonstrate how to generalize the method to cases where more than three branching ratios are relevant by using N-simplex diagrams, and we suggest a broader application of the general method to digital data sets.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.


text:
I am trying to upload a paper and its giving me error. i checked the tex file and its compiling perfectly on my computer. I wonder if any one had the same issue and knows how to fix it.

``````Package pdftex.def Error: File `ZurekD.pdf' not found.

See the pdftex.def package documentation for explanation.
Type H <return> for immediate help.
...

l.309 \includegraphics[width=4 in]{ZurekD.pdf}

?
! Emergency stop.
...

l.309 \includegraphics[width=4 in]{ZurekD.pdf}

! ==> Fatal error occurred, no output PDF file produced!
Transcript written on EmergentEntanglementGeometry.log.

[verbose]: pdflatex 'EmergentEntanglementGeometry.tex' failed.
[verbose]: Removing (La)TeX AUX file called 'EmergentEntanglementGeometry.aux' (1549483535 >= 1549483535)
[verbose]: 'htex' is not a valid TeX format; will ignore.
[verbose]: TEXMFCNF is unset.
[verbose]: ~~~~~~~~~~~ Running htex for the first time ~~~~~~~~
[verbose]: Running: "(export HOME=/tmp PATH=/texlive/2016/bin/arch:/bin; cd /submissions/2567556/ && tex 'EmergentEntanglementGeometry.tex' < /dev/null)" 2>&1
[verbose]: This is TeX, Version 3.14159265 (TeX Live 2016) (preloaded format=tex)
(./EmergentEntanglementGeometry.tex
! Undefined control sequence.
l.1 \documentclass
[11pt]{amsart}
?
! Emergency stop.
l.1 \documentclass
[11pt]{amsart}
No pages of output.
Transcript written on EmergentEntanglementGeometry.log.

[verbose]: tex 'EmergentEntanglementGeometry.tex' failed.
[verbose]: TEXMFCNF is unset.
[verbose]: ~~~~~~~~~~~ Running tex for the first time ~~~~~~~~
[verbose]: Running: "(export HOME=/tmp PATH=/texlive/2016/bin/arch:/bin; cd /submissions/2567556/ && tex 'EmergentEntanglementGeometry.tex' < /dev/null)" 2>&1
[verbose]: This is TeX, Version 3.14159265 (TeX Live 2016) (preloaded format=tex)
(./EmergentEntanglementGeometry.tex
! Undefined control sequence.
l.1 \documentclass
[11pt]{amsart}
?
! Emergency stop.
l.1 \documentclass
[11pt]{amsart}
No pages of output.
Transcript written on EmergentEntanglementGeometry.log.

[verbose]: tex 'EmergentEntanglementGeometry.tex' failed.
[verbose]: We failed utterly to process the TeX file 'EmergentEntanglementGeometry.tex'
[error]: Unable to sucessfully process tex files.
*** AutoTeX ABORTING ***

[verbose]: AutoTeX returned error: Unable to sucessfully process tex files.

[verbose]: \$autotex->process failed \$@: \$?: 0 \$!: Inappropriate ioctl for device
[verbose]: Error running AutoTeX process:
``````
• the error seems quite clear you are including the file `ZurekD.pdf` but it can not be found, are you sure it's in the right place in your submission? – David Carlisle Feb 6 at 20:13
• Welcome to TeX.SE! There are two errors, apparenlty: The first is the `ZurekD.pdf` which was not found. The second is that the system is running (plain) `tex 'EmergentEntanglementGeometry.tex'`, but the file starts with a LaTeX command. Try to have the system run `pdflatex` instead of `tex`. – Phelype Oleinik Feb 6 at 20:14