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http://www.tellmehowto.net/answer/how_many_earths_can_fit_into_1919
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math
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How many earths can fit into Jupiters great red spot?
Question asked by: knowitall
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Why Do So Many Of The Planets Have Similar Rotational Patterns ?
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218190134.67/warc/CC-MAIN-20170322212950-00216-ip-10-233-31-227.ec2.internal.warc.gz
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CC-MAIN-2017-13
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http://www.archerschoicemedia.com/forum/showpost.php?p=22915&postcount=7
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math
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Yeah... I literally had no idea, but I thought that might be it. Lord knows I'm not afraid to ask the stupid question.
I need to find a cheap wench (.... I know.... how else am I gonna say it???) and a scale that will register 400 lbs. (again... refer to the previous parenthetical statement). I found a really good deal on jig, but of course funds are low... (I am perpetually cursed by right church, wrong pew) so I think I can make one. I found a chart that details the number of strands needed for any given draw weight...
I just didn't understand the 1/4# thing. I have a spool of Bohning serving thread I'm pretty happy with along with the bobbin. Just need a set of decent string splitters.
I like the numbers on that BCY. That was my primary target, but I looked at the Brownells too. Thanks guys!
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s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510267745.6/warc/CC-MAIN-20140728011747-00434-ip-10-146-231-18.ec2.internal.warc.gz
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CC-MAIN-2014-23
| 805 | 4 |
https://everything2.com/user/StrawberryFrog/writeups/BMI
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math
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Body Mass Index, a measure of human skinnyness or obesity. It is a way to measure if you are overweight or underweight.
Underweight: BMI of less than 18.5
Normal 18.5 - 24.9
Overweight 25.0 - 29.9
Obesity 30.0 - 39.9
Extreme Obesity 40.0 and greater
Just where to draw the line between normal and overweight is a judgement call. There are slight increases in risks of diabetes and heart disease with BMIs over 22. These risks become dramatically larger with BMIs over 30.
As noted over at ideal body weight, the following formula is an estimate that works for 90% of adults, but not for athletes, the aged or adolescents under 20 years of age. f you carry a lot of muscle then BMI won't work for you. If you think that you fall outside this formula's competence, then use a more accurate measurement technique to ascertain how much body fat you carry.
BMI = w / (h * h), where w is weight in kilograms, and h is height in meters.
Or a version with the conversion from imperial units built in:
BMI = w * 704.5 / (h * h), where w is weight in pounds and h is height in inches.
Worked example for my BMI:
I am 1.80m tall (just under six foot)
I weigh 72kg (147 pounds)
My BMI = 72 / (1.8 * 1.8) = 22.22
So now that I know that I am within the ideal weight range, how big is my range? Rearranging the equation for weight gives:
w = BMI * h * h
The ends of the ideal weight range correspond to a BMI of 18.5 and 25.0. Given my height, this gives
Low: w = 18.5 * 1.8 * 1.8 = 59.94 kg (131.9 pounds)
High: w = 25 * 1.8 * 1.8 = 81 kg (178 pounds)
Note that this calculation seems to be quite sensitive to small changes in height (using a height of 1.805 m instead yields a minimum weight of 60.27kg) so try to get that accurate.
Given that the input numbers of height and weight are only accurate to two digits, the output probably has the same degree of accuracy. Thus my ideal weight range is 60 to 81 kg.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084890874.84/warc/CC-MAIN-20180121195145-20180121215145-00621.warc.gz
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CC-MAIN-2018-05
| 1,899 | 22 |
https://startupeuropeclub.eu/coronavirus/in-response-to-the-crisis-caused-by-the-covid-19-pandemic-the-eib-group-will-rapidly-mobilise-up-to-eur-40-billion-and-calls-on-member-states-to-put-a-further-guarantee-in-place-for-sme-and-mid-cap-s/
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math
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news & open calls
In response to the crisis caused by the COVID-19 pandemic, the EIB Group will rapidly mobilise up to EUR 40 billion and calls on Member States to put a further guarantee in place for SME and mid-cap support from EIB and national promotional banks.
DIGITALEUROPE Summer Summit: Data and the Digital Decade
06/17/2021 11:00 am - 06/17/2021 1:00 pm
SERN Webinar SeriesBeyond Covid19 | Arts & entrepreneurship at the crossroads: boosting cooperation for sustainable fashion
06/06/2021 10:00 am - 06/02/2021 11:00 am
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s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988758.74/warc/CC-MAIN-20210506144716-20210506174716-00188.warc.gz
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CC-MAIN-2021-21
| 541 | 6 |
http://relativity.livingreviews.org/Articles/lrr-1998-13/articlesu1.html
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math
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Most of the lattice gauge formulations I will discuss below share some common features. The lattice geometry is hypercubic, defining a natural global coordinate system for labelling the lattice sites and edges. The gauge group is or its “Euclideanized” form , or a larger group containing it as a subgroup or via a contraction limit. Local curvature terms are represented by (the traces of) -valued Wilson holonomies around lattice plaquettes. The vierbeins are either considered as additional fields or identified with part of the connection variables. The symmetry group of the lattice Lagrangian is a subgroup of the gauge group , and does not contain any translation generators that appear when is the Poincaré group.
When discretizing conformal gravity (where ) or higher-derivative gravity in first-order form, the metricity condition on the connection has to be imposed by hand. This leads to technical complications in the evaluation of the functional integral.
The diffeomorphism invariance of the continuum theory is broken on the lattice; only the local gauge invariances can be preserved exactly. The reparametrization invariance re-emerges only at the linearized level, i.e., when considering small perturbations about flat space.
© Max Planck Society and the author(s)
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s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560279489.14/warc/CC-MAIN-20170116095119-00373-ip-10-171-10-70.ec2.internal.warc.gz
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CC-MAIN-2017-04
| 1,288 | 4 |
https://preply.com/en/question/the-side-of-square-is-a-10-metre-find-the-area-of-square-62481
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math
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The side of square is a 10 metre find the area of square
3 Answers3 from verified tutors
if the side of a square is 10 m it means all the other 3 sides they they are each 10 m.Area of a square its side times side which is 100 square metre.
Area of a square = side * side = 10*10 = 100
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662561747.42/warc/CC-MAIN-20220523194013-20220523224013-00331.warc.gz
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CC-MAIN-2022-21
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http://english.stackexchange.com/questions/113168/meaning-of-that-in-holomorphic-function-in-the-sector-s-that-is-continuous
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math
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I have encountered a confusing sentence in a math textbook:
Suppose F is a holomorphic function in the sector S that is continuous on the closure of S.
What does that mean in the above sentence? Does it mean the function F?
can be interpreted in two ways, because that can refer to the sector or the holomorphic function in the sector. Of course, from the context we know that it really refers to the latter.
You'll have to ask the author.
Grammatically, however, that is a restrictive relative pronoun that refers to "the sector S", and the relative clause means that sector S is continuous on the closure of sector S.
Knowing nothing about math, I can't tell you what this means, but that interpretation makes no semantic sense.
Because this makes no sense to me, I'd say that that is supposed to refer to "the holomorphic function F", as it would in a properly written sentence (but still a stylistically awkward kind of "read my mind, please, because I can't be bothered to express myself clearly" sentence):
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s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257823947.97/warc/CC-MAIN-20160723071023-00260-ip-10-185-27-174.ec2.internal.warc.gz
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CC-MAIN-2016-30
| 1,012 | 8 |
https://en.wikibooks.org/wiki/Statistical_Mechanics/Density_of_States
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math
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Statistical Mechanics/Density of States
Thermal Average Number of Particles Distribution Function[edit | edit source]
Now, since this is a distribution function, we can find thermal average quantities of other thermodynamic quantities:
Where n denotes the quantum orbital.
Now if the orbital step, n, is small, we can change the sum to an integral:
Here, this function is the function that mathematically allows us to transform the sum to the simplest possible integration (In the Thermal Radiation case, we will see that the D function is the Jacobian to spherical coordinate).
It is also better known as the...
Density of States[edit | edit source]
The mathematics of the DoS were explained in the previous section, all that remains of importance is to explain its significance. Here D(ε) is the number of orbitals of energy between ε and ε + dε. We can think of it as the number of orbitals per volume in the shell taken in the integration, in other words, the density of states.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323583423.96/warc/CC-MAIN-20211016043926-20211016073926-00436.warc.gz
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CC-MAIN-2021-43
| 986 | 9 |
https://core.ac.uk/display/2179730
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math
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Using the data from SNO NCD phase, SuperK, Borexino and KamLAND Solar phase, we derive in a model independent way, bounds on the possible components in the solar neutrino flux. We update the limits on the antineutrino ($\bar\nu_x$) flux and sterile ($\nu_s$) component and compare them with the previous results obtained using SNO Salt phase data and data from SuperKamiokande experiments. It is affirmed that the upper bound on $\bar\nu_x$ is independent of the $\nu_s$ component. We recover the $\nu_s$ and $\bar\nu_x$ upper bounds existing in the literature. We also obtain bounds on $f_B$, the SSM normalization factor and the common parameter range for $f_B$ and the $\nu_s$ components in the light of latest data. In summary, we update, in a model independent way, the previous results existing in literature in the light of latest solar neutrino data.Comment: 21 pages, 3 figures and 13 table
To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823228.36/warc/CC-MAIN-20181209232026-20181210013526-00538.warc.gz
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CC-MAIN-2018-51
| 1,007 | 2 |
http://ieor.columbia.edu/monte-carlo-simulation
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math
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IEORE4703 Monte Carlo Simulation
3 pts. Lect: 3. IEOR E4701: Stochastic Models for Financial Engineering, and IEOR E4706: Foundations of Financial Engineering, or instructor permission. This graduate course is only for MS Program in FE students. This course serves as an introduction to Monte Carlo stochastic simulation with its main focus on finance applications. Examples include simulating various random variables and then stochastic processes (random walks, point processes, geometric Brownian motion, other diffusions, binomial lattice model, etc.) for the purpose of numerically estimating quantities of interest (option prices, probabilities, other expected values and integrals, etc.) Methods to make the simulations more efficient (variance reduction methods), and statistical output analysis (confidence intervals) will be explored too. Although the main focus is on financial applications, other examples will sometimes be provided. Computer programming in MATLAB will be used. Students who have taken IEOR E4404 Simulation may not register for this course for credit.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917125841.92/warc/CC-MAIN-20170423031205-00519-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 1,081 | 2 |
https://betterworld2016.org/what-is-half-of-1-1-2-in-fraction-form/
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math
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You are watching: What is half of 1 1/2 in fraction form
2 1/2 = 2 1/2 = 2 · 2 + 1/2 = 4 + 1/2 = 5/2 = 2 1/2 = 2.5Spelled result in native is 5 halfs (or two and one half).
switch a mixed number 2 1/2 come a wrong fraction: 2 1/2 = 2 1/2 = 2 · 2 + 1/2 = 4 + 1/2 = 5/2To uncover a new numerator:a) multiply the entirety number 2 by the denominator 2. Whole number 2 same 2 * 2/2 = 4/2b) add the answer from previous action 4 to the molecule 1. New numerator is 4 + 1 = 5c) create a previous prize (new numerator 5) end the denominator 2.Two and one fifty percent is 5 halfs
Rules for expressions with fractions: Fractions - merely use a front slash between the numerator and also denominator, i.e., for five-hundredths, get in 5/100. If you room using combined numbers, be sure to leaving a single space between the whole and fraction part.The slash separates the molecule (number above a portion line) and denominator (number below).Mixed numerals (mixed fractions or combined numbers) compose as essence separated through one room and fraction i.e., 12/3 (having the very same sign). An instance of a negative mixed fraction: -5 1/2.Because cut is both indications for fraction line and division, we recommended use colon (:) as the operator of department fractions i.e., 1/2 : 3.Decimals (decimal numbers) enter with a decimal allude . and also they are instantly converted to fountain - i.e. 1.45.The colon : and also slash / is the price of division. Can be offered to divide blended numbers 12/3 : 43/8 or have the right to be offered for write complicated fractions i.e. 1/2 : 1/3.An asterisk * or × is the symbol because that multiplication.Plus + is addition, minus sign - is subtraction and ()<> is mathematics parentheses.The exponentiation/power symbol is ^ - because that example: (7/8-4/5)^2 = (7/8-4/5)2
Examples: • including fractions: 2/4 + 3/4• individually fractions: 2/3 - 1/2• multiply fractions: 7/8 * 3/9• splitting Fractions: 1/2 : 3/4• indexes of fraction: 3/5^3• fountain exponents: 16 ^ 1/2• adding fractions and mixed numbers: 8/5 + 6 2/7• splitting integer and also fraction: 5 ÷ 1/2• complicated fractions: 5/8 : 2 2/3• decimal come fraction: 0.625• fraction to Decimal: 1/4• portion to Percent: 1/8 %• to compare fractions: 1/4 2/3• multiplying a fraction by a totality number: 6 * 3/4• square source of a fraction: sqrt(1/16)• reducing or simple the fraction (simplification) - splitting the numerator and denominator that a portion by the very same non-zero number - equivalent fraction: 4/22• expression through brackets: 1/3 * (1/2 - 3 3/8)• compound fraction: 3/4 the 5/7• fractions multiple: 2/3 that 3/5• division to uncover the quotient: 3/5 ÷ 2/3The calculator follows renowned rules for order of operations. The most common mnemonics because that remembering this order of work are: PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction BODMAS - Brackets, that or Order, Division, Multiplication, Addition, Subtraction.
See more: On Her Third Attempt, Maya Angelou Husband, Paul Du Feu Three Times
GEMDAS - Grouping icons - base (), Exponents, Multiplication, Division, Addition, Subtraction. be careful, constantly do multiplication and division prior to addition and also subtraction. Part operators (+ and also -) and (* and also /) has actually the same priority and also then need to evaluate indigenous left to right.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662534773.36/warc/CC-MAIN-20220521014358-20220521044358-00379.warc.gz
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CC-MAIN-2022-21
| 3,514 | 7 |
https://slideplayer.com/slide/4999128/
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math
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RC Circuits Physics 102 Professor Lee Carkner Lecture 16.
Published byModified over 5 years ago
Presentation on theme: "RC Circuits Physics 102 Professor Lee Carkner Lecture 16."— Presentation transcript:
RC Circuits Physics 102 Professor Lee Carkner Lecture 16
Kirchhoff’s Rules Left loop: 6 - 6I 2 = 0 Right loop: 6I 2 - 6I 3 - 4I 3 = 0 Since I 2 = 1, 6 -10I 3 = 0, or 6 = 10I 3 or I 3 = 0.6 A I 1 = I 2 +I 3 Voltage: For battery V = 6 V, for 6 , V = 6I 2 = 6 V, for 2nd 6 , V = 6I 3 = 3.6 V, for 4 , V = 4I 3 = 2.4V + - V = 6 V 4 6 I1I1 I3I3 I2I2
Three light bulbs with resistance R 1 = 1 , R 2 = 2 and R 3 = 3 are connected in series to a battery. Which has the largest potential drop across it? A)R 1 B)R 2 C)R 3 D)All have the same potential drop E)It depends on the voltage of the battery
A string of Christmas trees lights are connected in series. If one light is removed and replaced with a normal wire, A)The other lights get dimmer B)The other lights get brighter C)The other lights don’t change D)It depends on the current in the wire E)It depends on the voltage across the wire
Kirchhoff Tips Current Each single branch has a current Voltage Only include batteries and resistors
Capacitance Remember that a capacitor stores charge: The value of C depends on its physical properties: C = 0 A/d How can we combine capacitors in circuits?
Simple Circuit Battery ( V) connected to capacitor (C) The capacitor experiences potential difference of V and has stored charge of Q = C V +- + - VV C Q
Capacitors in Parallel Potential difference across each is the same ( V) But: Q 2 = C 2 V The equivalent capacitance is: C eq = C 1 + C 2 +- VV C1C1 C2C2
Capacitors in Series Charge stored by each is the same (Q) Total V is the sum ( V = V 1 + V 2 ) Since V = Q/C: The equivalent capacitance is: 1/C eq = 1/C 1 + 1/C 2 +- VV C1C1 C2C2 + -- +
Capacitors in Circuits Can resolve every series or parallel group into one capacitor
Resistors and Capacitors After a certain amount of time, all the energy in the capacitor will go into heating the resistor A capacitor C paired with a resistor R will have a time constant ( ) = RC This is the time to charge a capacitor to about 63% of the final value
Charge Over Time If we charge a capacitor by connecting it to a battery of voltage , the charge and voltage on the capacitor is: Q C = CV C V C = [1-e (-t/ ) ] As you charge the capacitor you increase the repulsive force which makes adding more charge harder
Next Time Read: 20.1, 20.4 Homework: Ch 19 P 31, 50, Ch 20 P 10, 11 Quiz 2 next Friday
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http://www.amazon.co.uk/Gnomes-Fog-Reception-Intuitionism-Historical/dp/3764365366
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math
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This book is a revised version of the author's 1999 dissertation. It gives only a sketch Brouwer's views on the epistemology and ontology, and thus on the nature and boundaries, of mathematics. Hesseling writes: "I am here dealing with the genesis of his intuitionism as far as it is relevant to its reception. Since most reactions did not go deeply into intuitionistic mathematics, neither shall I. Instead I restrict myself to giving an impression of how Brouwer developed intuitionism by treating the main ideas of some of his papers." (67) In the last numbered chapter, Hesseling wanders off in a fanciful quest for cultural undertones to the debate.
Besides the lack of mathematical detail, the philosophical basis of Brouwer's views on mathematics is not presented with any depth. Brouwer's views on the criteria that certify what is legitimate mathematics arise from his philosophy. His philosophical claims require justification if they are to support a critique of mathematics. Furthermore, Kant's epistemology, certainly the most influential philosophical background to the debate, although for some participants filtered through Husserl's phenomenology, is given little attention. Hesseling hasn't gone into the intellectual depths of the controversy, and the result is a superficial presentation of ideas.
The debate resolved predominantly into the differences between Brouwer's Intuitionism, supported by Weyl, and Hilbert's Formalism, supported by Bernays. The Logicism of Frege, and of Russell and Whitehead is not discussed. Hesseling sees Weyl's 1921 essay "On the New Foundational Crisis of Mathematics" as a pivotal text in the debate.
Hesseling has surveyed the entire corpus of written, public reactions to Brouwer's Intuitionism from 1909 to 1933, and lists these texts by year in an appendix. Another appendix gives a chronology of the debate from 1897 to 1932. Brouwer lived until 1966, but Hesseling looks at the debate only up to 1933. He writes: "After 1933, Brouwer published some 30 more papers on intuitionism, some which were technical contributions to intuitionistic mathematics, others of a more expository nature. Compared to his ideas before 1930, no spectacular new insights were presented in the later papers." (86)
In 1928, Hilbert and Ackermann published their logic text. In 1930, Gödel announced his incompleteness proof and Heyting published a formalization of Intuitionistic logic. In 1932, Gödel began publishing on Intuitionistic logic. In 1934, Hilbert and Bernays published the first volume of their text on the foundations of mathematics. The features of the debate were changed.
Brouwer's position arises from the assertion that the ontology of mathematics is determined solely by epistemology, and thus a statement which has not been determined to be true or to be false cannot be determined to refer to a state of affairs or to anything which exists. If we cannot find it, then we cannot claim it exists and we also cannot claim it does not exist. Moreover, we cannot claim it is certainly either one or the other, because the limits of our epistemology are the limits of ontological fact. Moreover, knowledge is temporal and a process; and it is pre-linguistic. The negation of what is known is absurdity.
Brouwer claimed that mathematics is not in any sense linguistic and that mathematics precedes logic. Logic arises from mathematics via language. As Hesseling writes: "Mathematical language follows upon mathematical activity, and logic consists of looking at that language in a mathematical way." (39) Likewise: "Logical principles only hold for words that have mathematical meaning." (44)
Since mathematical meaning derives from emergent, epistemologically generated ontology, it follows that logic itself is not a formative and central structure of cognition, but rather is itself an emergent, structural overlay. It then follows that where mathematical meaning is indeterminate, so is logic.
The reductio ad absurdum method of proof involves the law of excluded middle. The dichotomy of either S or not-S (at least one and not both) ensures that reductio ad absurdum is valid. If the dichotomy fails, so does the justification for reductio ad absurdum. This is important to Brouwer because reductio ad absurdum allows for non-constructive proofs, which circumvent, overrun, and thwart his ontology.
In place of the law of excluded middle, in Intuitionism one has a logic where every proposition is either determined to be true or to be false or it is undetermined. One could then instate a logic, not of truth values, but of values of determination.
For a collection of fundamental texts from the debate, see Paulo Mancosu's From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s.
For a study devoted strictly to Brouwer's views on Intuitionism, see Walter P. van Stigt's Brouwer's Intuitionism.
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CC-MAIN-2013-20
| 4,887 | 12 |
https://www.coursehero.com/file/6788499/ST472-F10-Quiz-2-Solution/
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math
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This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Quiz 2 Math 490
September 14, 2010 1. You are given that mortality follows the Illustrative Life Table. Assume that deaths are uniformly
distributed between integral ages. Calculate 2qms. 2. You are given: a. Male mortality follows DeMoivre’s law with a) = 100.
b. Female mortality follows constant force of mortality based on ,u = 0.02. c. 5=5%. mfor males is equal to 21%] for females. X: For a given age x, .711 XI Calculate x. (x is not necessarily an integer.) ...
View Full Document
- Fall '11
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CC-MAIN-2017-51
| 628 | 7 |
https://slideplayer.com/slide/276966/
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math
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Presentation on theme: "20% In-house rental/New Third Party 21% TP upgrade & Resign potential 10% of our possible servicing customers That exposes 17% of our customers Approx."— Presentation transcript:
20% In-house rental/New Third Party 21% TP upgrade & Resign potential 10% of our possible servicing customers That exposes 17% of our customers Approx. 30% of our sales cant be plumbed in
What is it? 0.5 µm Absolute high efficiency depth filter cartridge Removes particles 0.5 micron and larger including but not limited to: Cryptosporidium, Giardia, E-Coli, Legionella >99.9% Retention Rating by ASTM F-795 Test KDF removes more than 95% of free chlorine Reduces water-soluble heavy metals such as Lead and Iron as well as scale Its redox method kills algae & bacteria Carbon removes volatile organics as well as taste and odor causing contaminants
What does all this mean? The AB-1 PLUS is an all in one water filter that utilizes multiple technologies to achieve a compact, efficient design.
So whats the Cost? 60c Service Frequency80c Service Frequency Current1/yr2/yr Current1/yr2/yr TwinAB-1Plus TwinAB-1Plus Initial$100.67$112.06 Initial$100.67$108.76 service /yr$11.09$16.80$35.00service /yr$11.09$16.10$33.50 3 year life$33.27$50.40$105.003 year life$33.27$48.30$100.50 total cost$133.94$162.46$217.06total cost$133.94$157.06$209.26 var on twin$0.00$28.52$83.12var on twin$0.00$23.12$75.32 variance /yr$0.00$9.51$27.71variance /yr$0.00$7.71$25.11 ext cost /mth $0.79$2.31ext cost /mth $0.64$2.09 *Twin filters pricing is about 70c to the dollar
Where will we be saved money? With its compact size the housing could be pre-attached to the back of a unit to save on expensive plumbing time Servicing time is cut down for our technicians – only 1 housing to sanitize & outlet lines after the filters will be clean. Waterways & taps will need minimal attention This financial year we would have saved about $1200 on replacement waterways This could save us about 5 minutes per refurb (@ avg 86 units /mth = 7hr /mth) This could save Rosco 3m 20sec per twin kit built (@ AVG 112 units per month = 6hr/mth) With an estimated 10% of coolers being returned having twins, we have to replace $1300 worth of housings – this number will increase as Office Spring was launched in 2006 Thats a saving of $317/mth (& any additional technician & plumbers hours) vs an extra cost of $260/mth (@ 60c exchange rate)
Can we apply it any where else? Clearwater exclusivity Commercial owned unit upgrade Customer retention Residential Applications Specification & Wholesale
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| 2,570 | 7 |
https://www.topperlearning.com/cbse-class-12-science-maths/matrices/introduction-to-matrices
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math
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CBSE Class 12-science Maths Introduction To Matrices
Polish your knowledge of CBSE Class 12 Science Mathematics Matrices – Introduction to Matrices at TopperLearning. In our video lessons, our Maths expert explains the steps to find the orders of a matrix with a given number of elements. Revise the different types of matrices by watching our online concept videos.
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https://www.physicsforums.com/threads/calculate-the-mass-of-co2-in-a-mixture.310156/
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I need to calculate the mass of CO2 in a mixture where there is 1.5kg of N2 and 1kg of O2 present. The total pressure of the mixture is 1.5bar, the volume is 2m^3 and the temperature is 293K. I also know the cv values for the constituents.
I know lots of equation but they none of them are for just one unknown.
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I have tried finding the volumetric analysis of the mixture but it all depends on knowing that one mass which I cant find?
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https://db0nus869y26v.cloudfront.net/en/Greeks_(finance)
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In mathematical finance, the Greeks are the quantities representing the sensitivity of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the most common of these sensitivities are denoted by Greek letters (as are some other finance measures). Collectively these have also been called the risk sensitivities, risk measures: 742 or hedge parameters.
|Definition of Greeks as the sensitivity of an option's price and risk (in the first row) to the underlying parameter (in the first column). First-order Greeks are in blue, second-order Greeks are in green, and third-order Greeks are in yellow. Note that vanna, charm and veta appear twice, since partial cross derivatives are equal by Schwarz's theorem. Rho, lambda, epsilon, and vera are left out as they are not as important as the rest. Three places in the table are not occupied, because the respective quantities have not yet been defined in the financial literature.|
The Greeks are vital tools in risk management. Each Greek measures the sensitivity of the value of a portfolio to a small change in a given underlying parameter, so that component risks may be treated in isolation, and the portfolio rebalanced accordingly to achieve a desired exposure; see for example delta hedging.
The Greeks in the Black–Scholes model are relatively easy to calculate, a desirable property of financial models, and are very useful for derivatives traders, especially those who seek to hedge their portfolios from adverse changes in market conditions. For this reason, those Greeks which are particularly useful for hedging—such as delta, theta, and vega—are well-defined for measuring changes in Price, Time and Volatility. Although rho is a primary input into the Black–Scholes model, the overall impact on the value of an option corresponding to changes in the risk-free interest rate is generally insignificant and therefore higher-order derivatives involving the risk-free interest rate are not common.
The most common of the Greeks are the first order derivatives: delta, vega, theta and rho as well as gamma, a second-order derivative of the value function. The remaining sensitivities in this list are common enough that they have common names, but this list is by no means exhaustive.
The use of Greek letter names is presumably by extension from the common finance terms alpha and beta, and the use of sigma (the standard deviation of logarithmic returns) and tau (time to expiry) in the Black–Scholes option pricing model. Several names such as 'vega' and 'zomma' are invented, but sound similar to Greek letters. The names 'color' and 'charm' presumably derive from the use of these terms for exotic properties of quarks in particle physics.
Delta, , measures the rate of change of the theoretical option value with respect to changes in the underlying asset's price. Delta is the first derivative of the value of the option with respect to the underlying instrument's price .
For a vanilla option, delta will be a number between 0.0 and 1.0 for a long call (or a short put) and 0.0 and −1.0 for a long put (or a short call); depending on price, a call option behaves as if one owns 1 share of the underlying stock (if deep in the money), or owns nothing (if far out of the money), or something in between, and conversely for a put option. The difference between the delta of a call and the delta of a put at the same strike is equal to one. By put–call parity, long a call and short a put is equivalent to a forward F, which is linear in the spot S, with unit factor, so the derivative dF/dS is 1. See the formulas below.
These numbers are commonly presented as a percentage of the total number of shares represented by the option contract(s). This is convenient because the option will (instantaneously) behave like the number of shares indicated by the delta. For example, if a portfolio of 100 American call options on XYZ each have a delta of 0.25 (=25%), it will gain or lose value just like 2,500 shares of XYZ as the price changes for small price movements (100 option contracts covers 10,000 shares). The sign and percentage are often dropped – the sign is implicit in the option type (negative for put, positive for call) and the percentage is understood. The most commonly quoted are 25 delta put, 50 delta put/50 delta call, and 25 delta call. 50 Delta put and 50 Delta call are not quite identical, due to spot and forward differing by the discount factor, but they are often conflated.
Delta is always positive for long calls and negative for long puts (unless they are zero). The total delta of a complex portfolio of positions on the same underlying asset can be calculated by simply taking the sum of the deltas for each individual position – delta of a portfolio is linear in the constituents. Since the delta of underlying asset is always 1.0, the trader could delta-hedge his entire position in the underlying by buying or shorting the number of shares indicated by the total delta. For example, if the delta of a portfolio of options in XYZ (expressed as shares of the underlying) is +2.75, the trader would be able to delta-hedge the portfolio by selling short 2.75 shares of the underlying. This portfolio will then retain its total value regardless of which direction the price of XYZ moves. (Albeit for only small movements of the underlying, a short amount of time and not-withstanding changes in other market conditions such as volatility and the rate of return for a risk-free investment).
Main article: Moneyness
The (absolute value of) Delta is close to, but not identical with, the percent moneyness of an option, i.e., the implied probability that the option will expire in-the-money (if the market moves under Brownian motion in the risk-neutral measure). For this reason some option traders use the absolute value of delta as an approximation for percent moneyness. For example, if an out-of-the-money call option has a delta of 0.15, the trader might estimate that the option has approximately a 15% chance of expiring in-the-money. Similarly, if a put contract has a delta of −0.25, the trader might expect the option to have a 25% probability of expiring in-the-money. At-the-money calls and puts have a delta of approximately 0.5 and −0.5 respectively with a slight bias towards higher deltas for ATM calls. The actual probability of an option finishing in the money is its dual delta, which is the first derivative of option price with respect to strike.
Given a European call and put option for the same underlying, strike price and time to maturity, and with no dividend yield, the sum of the absolute values of the delta of each option will be 1 – more precisely, the delta of the call (positive) minus the delta of the put (negative) equals 1. This is due to put–call parity: a long call plus a short put (a call minus a put) replicates a forward, which has delta equal to 1.
If the value of delta for an option is known, one can calculate the value of the delta of the option of the same strike price, underlying and maturity but opposite right by subtracting 1 from a known call delta or adding 1 to a known put delta.
, therefore: and .
For example, if the delta of a call is 0.42 then one can compute the delta of the corresponding put at the same strike price by 0.42 − 1 = −0.58. To derive the delta of a call from a put, one can similarly take −0.58 and add 1 to get 0.42.
Vega measures sensitivity to volatility. Vega is the derivative of the option value with respect to the volatility of the underlying asset.
Vega is not the name of any Greek letter. The glyph used is a non-standard majuscule version of the Greek letter nu (), written as . Presumably the name vega was adopted because the Greek letter nu looked like a Latin vee, and vega was derived from vee by analogy with how beta, eta, and theta are pronounced in American English.
The symbol kappa, , is sometimes used (by academics) instead of vega (as is tau () or capital lambda (), : 315 though these are rare).
Vega is typically expressed as the amount of money per underlying share that the option's value will gain or lose as volatility rises or falls by 1 percentage point. All options (both calls and puts) will gain value with rising volatility.
Vega can be an important Greek to monitor for an option trader, especially in volatile markets, since the value of some option strategies can be particularly sensitive to changes in volatility. The value of an at-the-money option straddle, for example, is extremely dependent on changes to volatility.
Theta, , measures the sensitivity of the value of the derivative to the passage of time (see Option time value): the "time decay."
The mathematical result of the formula for theta (see below) is expressed in value per year. By convention, it is usual to divide the result by the number of days in a year, to arrive at the amount an option's price will drop, in relation to the underlying stock's price. Theta is almost always negative for long calls and puts, and positive for short (or written) calls and puts. An exception is a deep in-the-money European put. The total theta for a portfolio of options can be determined by summing the thetas for each individual position.
The value of an option can be analysed into two parts: the intrinsic value and the time value. The intrinsic value is the amount of money you would gain if you exercised the option immediately, so a call with strike $50 on a stock with price $60 would have intrinsic value of $10, whereas the corresponding put would have zero intrinsic value. The time value is the value of having the option of waiting longer before deciding to exercise. Even a deeply out of the money put will be worth something, as there is some chance the stock price will fall below the strike before the expiry date. However, as time approaches maturity, there is less chance of this happening, so the time value of an option is decreasing with time. Thus if you are long an option you are short theta: your portfolio will lose value with the passage of time (all other factors held constant).
Rho, , measures sensitivity to the interest rate: it is the derivative of the option value with respect to the risk-free interest rate (for the relevant outstanding term).
Except under extreme circumstances, the value of an option is less sensitive to changes in the risk-free interest rate than to changes in other parameters. For this reason, rho is the least used of the first-order Greeks.
Rho is typically expressed as the amount of money, per share of the underlying, that the value of the option will gain or lose as the risk-free interest rate rises or falls by 1.0% per annum (100 basis points).
Lambda, , omega, , or elasticity is the percentage change in option value per percentage change in the underlying price, a measure of leverage, sometimes called gearing.
It holds that .
Epsilon, (also known as psi, ), is the percentage change in option value per percentage change in the underlying dividend yield, a measure of the dividend risk. The dividend yield impact is in practice determined using a 10% increase in those yields. Obviously, this sensitivity can only be applied to derivative instruments of equity products.
Gamma, , measures the rate of change in the delta with respect to changes in the underlying price. Gamma is the second derivative of the value function with respect to the underlying price.
Most long options have positive gamma and most short options have negative gamma. Long options have a positive relationship with gamma because as price increases, Gamma increases as well, causing Delta to approach 1 from 0 (long call option) and 0 from −1 (long put option). The inverse is true for short options.
Gamma is greatest approximately at-the-money (ATM) and diminishes the further out you go either in-the-money (ITM) or out-of-the-money (OTM). Gamma is important because it corrects for the convexity of value.
When a trader seeks to establish an effective delta-hedge for a portfolio, the trader may also seek to neutralize the portfolio's gamma, as this will ensure that the hedge will be effective over a wider range of underlying price movements.
Vanna, also referred to as DvegaDspot and DdeltaDvol, is a second order derivative of the option value, once to the underlying spot price and once to volatility. It is mathematically equivalent to DdeltaDvol, the sensitivity of the option delta with respect to change in volatility; or alternatively, the partial of vega with respect to the underlying instrument's price. Vanna can be a useful sensitivity to monitor when maintaining a delta- or vega-hedged portfolio as vanna will help the trader to anticipate changes to the effectiveness of a delta-hedge as volatility changes or the effectiveness of a vega-hedge against change in the underlying spot price.
If the underlying value has continuous second partial derivatives, then ,
Charm or delta decay measures the instantaneous rate of change of delta over the passage of time.
Charm has also been called DdeltaDtime. Charm can be an important Greek to measure/monitor when delta-hedging a position over a weekend. Charm is a second-order derivative of the option value, once to price and once to the passage of time. It is also then the derivative of theta with respect to the underlying's price.
The mathematical result of the formula for charm (see below) is expressed in delta/year. It is often useful to divide this by the number of days per year to arrive at the delta decay per day. This use is fairly accurate when the number of days remaining until option expiration is large. When an option nears expiration, charm itself may change quickly, rendering full day estimates of delta decay inaccurate.
Vomma, volga, vega convexity, or DvegaDvol measures second order sensitivity to volatility. Vomma is the second derivative of the option value with respect to the volatility, or, stated another way, vomma measures the rate of change to vega as volatility changes.
With positive vomma, a position will become long vega as implied volatility increases and short vega as it decreases, which can be scalped in a way analogous to long gamma. And an initially vega-neutral, long-vomma position can be constructed from ratios of options at different strikes. Vomma is positive for long options away from the money, and initially increases with distance from the money (but drops off as vega drops off). (Specifically, vomma is positive where the usual d1 and d2 terms are of the same sign, which is true when d1 < 0 or d2 > 0.)
Veta or DvegaDtime measures the rate of change in the vega with respect to the passage of time. Veta is the second derivative of the value function; once to volatility and once to time.
It is common practice to divide the mathematical result of veta by 100 times the number of days per year to reduce the value to the percentage change in vega per one day.
Vera (sometimes rhova) measures the rate of change in rho with respect to volatility. Vera is the second derivative of the value function; once to volatility and once to interest rate.
The word 'Vera' was coined by R. Naryshkin in early 2012 when this sensitivity needed to be used in practice to assess the impact of volatility changes on rho-hedging, but no name yet existed in the available literature. 'Vera' was picked to sound similar to a combination of Vega and Rho, its respective first-order Greeks. This name is now in a wider use, including, for example, the Maple computer algebra software (which has 'BlackScholesVera' function in its Finance package).
This partial derivative has a fundamental role in the Breeden-Litzenberger formula, which uses quoted call option prices to estimate the risk-neutral probabilities implied by such prices.
For call options, it can be approximated using infinitesimal portfolios of butterfly strategies.
Speed measures the rate of change in Gamma with respect to changes in the underlying price.
This is also sometimes referred to as the gamma of the gamma: 799 or DgammaDspot. Speed is the third derivative of the value function with respect to the underlying spot price. Speed can be important to monitor when delta-hedging or gamma-hedging a portfolio.
Zomma measures the rate of change of gamma with respect to changes in volatility.
Zomma has also been referred to as DgammaDvol. Zomma is the third derivative of the option value, twice to underlying asset price and once to volatility. Zomma can be a useful sensitivity to monitor when maintaining a gamma-hedged portfolio as zomma will help the trader to anticipate changes to the effectiveness of the hedge as volatility changes.
Color, gamma decay or DgammaDtime measures the rate of change of gamma over the passage of time.
Color is a third-order derivative of the option value, twice to underlying asset price and once to time. Color can be an important sensitivity to monitor when maintaining a gamma-hedged portfolio as it can help the trader to anticipate the effectiveness of the hedge as time passes.
The mathematical result of the formula for color (see below) is expressed in gamma per year. It is often useful to divide this by the number of days per year to arrive at the change in gamma per day. This use is fairly accurate when the number of days remaining until option expiration is large. When an option nears expiration, color itself may change quickly, rendering full day estimates of gamma change inaccurate.
Ultima measures the sensitivity of the option vomma with respect to change in volatility.
Ultima has also been referred to as DvommaDvol. Ultima is a third-order derivative of the option value to volatility.
If the value of a derivative is dependent on two or more underlyings, its Greeks are extended to include the cross-effects between the underlyings.
Correlation delta measures the sensitivity of the derivative's value to a change in the correlation between the underlyings. It is also commonly known as cega.
Cross gamma measures the rate of change of delta in one underlying to a change in the level of another underlying.
Cross vanna measures the rate of change of vega in one underlying due to a change in the level of another underlying. Equivalently, it measures the rate of change of delta in the second underlying due to a change in the volatility of the first underlying.
Cross volga measures the rate of change of vega in one underlying to a change in the volatility of another underlying.
See also: Black–Scholes model
The Greeks of European options (calls and puts) under the Black–Scholes model are calculated as follows, where (phi) is the standard normal probability density function and is the standard normal cumulative distribution function. Note that the gamma and vega formulas are the same for calls and puts.
For a given:
|fair value ()|
Under the Black model (commonly used for commodities and options on futures) the Greeks can be calculated as follows:
|fair value ()|
(*) It can be shown that
Then we have:
Some related risk measures of financial instruments are listed below.
Main articles: Bond duration and Bond convexity
In trading bonds and other fixed income securities, various measures of bond duration are used analogously to the delta of an option. The closest analogue to the delta is DV01, which is the reduction in price (in currency units) for an increase of one basis point (i.e. 0.01% per annum) in the yield (the yield is the underlying variable). See also Bond duration § Risk – duration as interest rate sensitivity.
Analogous to the lambda is the modified duration, which is the percentage change in the market price of the bond(s) for a unit change in the yield (i.e. it is equivalent to DV01 divided by the market price). Unlike the lambda, which is an elasticity (a percentage change in output for a percentage change in input), the modified duration is instead a semi-elasticity—a percentage change in output for a unit change in input. See also Key rate duration.
Bond convexity is a measure of the sensitivity of the duration to changes in interest rates, the second derivative of the price of the bond with respect to interest rates (duration is the first derivative); it is then analogous to gamma. In general, the higher the convexity, the more sensitive the bond price is to the change in interest rates. Bond convexity is one of the most basic and widely used forms of convexity in finance.
For a bond with an embedded option, the standard yield to maturity based calculations here do not consider how changes in interest rates will alter the cash flows due to option exercise. To address this, effective duration and effective convexity are introduced. These values are typically calculated using a tree-based model, built for the entire yield curve (as opposed to a single yield to maturity), and therefore capturing exercise behavior at each point in the option's life as a function of both time and interest rates; see Lattice model (finance) § Interest rate derivatives.
Main article: Beta (finance)
The beta (β) of a stock or portfolio is a number describing the volatility of an asset in relation to the volatility of the benchmark that said asset is being compared to. This benchmark is generally the overall financial market and is often estimated via the use of representative indices, such as the S&P 500.
An asset has a Beta of zero if its returns change independently of changes in the market's returns. A positive beta means that the asset's returns generally follow the market's returns, in the sense that they both tend to be above their respective averages together, or both tend to be below their respective averages together. A negative beta means that the asset's returns generally move opposite the market's returns: one will tend to be above its average when the other is below its average.
Main article: Fugit
The fugit is the expected time to exercise an American or Bermudan option. Fugit is usefully computed for hedging purposes — for example, one can represent flows of an American swaption like the flows of a swap starting at the fugit multiplied by delta, and then use these to compute other sensitivities.
((cite journal)): Cite journal requires
Step-by-step mathematical derivations of option Greeks
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https://link.springer.com/article/10.1007/s00454-017-9948-x?error=cookies_not_supported&code=c95e8411-68bc-4c3f-b851-861523d775a1
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We introduce the notion of local spectral expansion of a simplicial complex as a possible analogue of spectral expansion defined for graphs. We then show that the condition of local spectral expansion for a complex yields various spectral gaps in both the links of the complex and the global Laplacians of the complex.
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Ballmann, W., Świątkowski, J.: On \(L^2\)-cohomology and property (T) for automorphism groups of polyhedral cell complexes. Geom. Funct. Anal. 7(4), 615–645 (1997)
Borel, A.: Cohomologie de certains groupes discretes et laplacien \(p\)-adique (d’après H. Garland). In: Séminaire Bourbaki, 26e année (1973/1974), Exp. No. 437. Lecture Notes in Mathematics, Vol. 431, pp. 12–35. Springer, Berlin (1975)
Garland, H.: \(p\)-Adic curvature and the cohomology of discrete subgroups of \(p\)-adic groups. Ann. Math. 97(3), 375–423 (1973)
Gromov, M.: Singularities, expanders and topology of maps. Part 2: From combinatorics to topology via algebraic isoperimetry. Geom. Funct. Anal. 20(2), 416–526 (2010)
Horak, D., Jost, J.: Spectra of combinatorial Laplace operators on simplicial complexes. Adv. Math. 244, 303–336 (2013)
Linial, N., Meshulam, R.: Homological connectivity of random 2-complexes. Combinatorica 26(4), 475–487 (2006)
Lubotzky, A.: Expander graphs in pure and applied mathematics. Bull. Am. Math. Soc. (N.S.) 49(1), 113–162 (2012)
Lubotzky, A.: Ramanujan complexes and high dimensional expanders. Jpn. J. Math. 9(2), 137–169 (2014)
Lubotzky, A., Meshulam, R., Mozes, S.: Expansion of building-like complexes. Groups Geom. Dyn. 10(1), 155–175 (2016)
Meshulam, R., Wallach, N.: Homological connectivity of random \(k\)-dimensional complexes. Random Struct. Algorithms 34(3), 408–417 (2009)
Parzanchevski, O.: Mixing in high-dimensional expanders. Comb. Probab. Comput. 26(5), 746–761 (2017)
Parzanchevski, O., Rosenthal, R., Tessler, R.J.: Isoperimetric inequalities in simplicial complexes. Combinatorica 36(2), 195–227 (2016)
The author would like to thank Matthew Kahle for many useful discussions and Alex Lubotzky for the inspiration to pursue this subject.
Editor in Charge: János Pach
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Cite this article
Oppenheim, I. Local Spectral Expansion Approach to High Dimensional Expanders Part I: Descent of Spectral Gaps. Discrete Comput Geom 59, 293–330 (2018). https://doi.org/10.1007/s00454-017-9948-x
- High dimensional expanders
- Graph Laplacian
- Simplicial complexes
- Spectral gap
Mathematics Subject Classification
- Primary 05E45
- Secondary 05A20
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An antiproportionality is a correlation with constant product.
What is an antiproportionality?
An antiproportionality is a correlation which satisfies the following condition: If one value gets higher, the other one gets lower. For example, assume that 6 excavators need 12 hours to dig a hole. Then, 3 excavators would need 24 hours.
How to calculate with antiproportionalities?
It's easy to see that the product of the values is always the same. This product is called the factor of antiproportionality. In our example, that product equals 72. Knowing that, one can easily calculate that 72 excavators would need 1 hour or one excavator would need 72 hours.
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Post hoc tests a common follow up for both manova and anova. Furthermore, you do not have to select a transformation in a proc mixed analysis. Difference between anova and ancova with comparison chart. This approach allows researchers to examine the main effects of discipline and gender on grades, as well as the interaction between them, while statistically controlling for parental income. A multivariate analysis of variance manova could be used to test this hypothesis. The data is from an experiment to test the similarity of two testing methods. A research group wants to study the effectiveness of three. For example, if vocabulary size is measured at 2, 4, 6.
The obvious difference between anova and a multivariate analysis of variance manova is the m, which stands for multivariate. First, convert the data to long format and make sure subject is a factor, as shown above. Multivariate analysis of variance manova is simply an anova with several. The term twoway gives you an indication of how many independent variables you have in. Anova is the analysis of variation between two or more samples while regression is the analysis of a relation between two or more variables. The second line specifies the variables in the data editor. In anova, differences among various group means on a singleresponse variable are studied. A mixed model analysis of variance or mixed model anova is the right data. The first two words before and after are the repeated measures variables and these words are the words used in the data editor. Use and interpret manova in spss hire a professional. In statistics, when two or more than two means are compared simultaneously, the statistical method used to make the comparison is called anova.
An analysis of their anova, manova and ancova analyses by. Oct 11, 2017 difference between ttest and anova last updated on october 11, 2017 by surbhi s there is a thin line of demarcation amidst ttest and anova, i. Verma msc statistics, phd, mapsychology, masterscomputer application professorstatistics lakshmibai national institute of physical education, gwalior, india deemed university email. Is a manova an anova with two or more continuous response variables. Simple effects in mixed designs discovering statistics. Twoway mixed anova analysis of variance comes in many shapes and sizes.
This is because the methods of drying are three nonrandomly chosen industrial processes, but the. That is to say, anova tests for the difference in means between two or more groups. In one of the repeated measures rm manova studies, the. For detailed information we refer to the reference manual. An anova analysis of variance is used to determine whether or not there is a statistically significant difference between the means of three or more independent groups. For example, in brown 2007, i used an example anova to demonstrate how to. First, an anova is different from both a manova and mancova because an anova has only one dependent variable, while both a manova and mancova have multiple dependent variables.
In basic terms, a manova is an anova with two or more continuous response variables. The mixed factor model given here is called the restricted version. While manova is the classical approach, the mixedmodel methodology, although by now implemented in all major statistical software packages, still is a relatively. Methods for testing omnibus overall hypotheses could include the anova test or an alternative to the. Jan 12, 2018 understand the difference between anova, ancova, manova and mancova in less than 4 minutes. Subjects will experience significantly greater sleep disturbances in the. Manova method for analyzing repeated measures designs. Mancova assumes that the observations are independent of one another, there is not any pattern for the selection of the sample, and that the sample is completely. Two factor mixed anova real statistics using excel. For example, we may conduct a study where we try two different textbooks.
It sounds like you need to perform a posthoc test to determine which groups are significantly different from the others for variable a. I think that mixed anova is something of a special case of multilevel modeling. These distinctions are important because the test statistics used to test. Manova models several dependent variables simultaneously and you can include a variety of independent variables. The default approach to missing data in nearly all statistical packages is listwise. Analysis of the variance is a method of investigating the differences between two samples, or populations. Thus, in a mixeddesign anova model, one factor a fixed effects factor is a betweensubjects variable and the other a random effects factor is a withinsubjects variable.
Five advantages of running repeated measures anova as a mixed. Estimates of the population variances and confidence intervals corresponding to the random effects, and, are calculated as in the two random factor model example 1. The distinctions between anova, ancova, manova, and. A mixed betweenwithin subjects analysis of variance was conducted to compare scores on the criminal social identity between violent and nonviolent offenders across three time periods time 1, time 2, and time 3. Nov 23, 2012 what is the difference between regression and anova.
The manova sscp matrices require estimation of many bits, which can also eat up your power. A mixed model analysis of variance or mixed model anova is the right data analytic approach for a study that contains a a continuous dependent variable, b two or more categorical independent variables, c at least one independent variable that. This leads to factorial anova models, as for example discussed in 26. Difference between ttest and anova with comparison chart. Difference between regression and anova compare the. Repeated measures anova with spss oneway withinsubjects anova with spss one between and one within mixed design with spss repeated measures manova with spss how to interpret spss outputs how to report results 2 when the same measurement is made several. So, for example, a oneway anova might look at three classes of stu. Jan 11, 2017 knowing the difference between anova and ancova, will help you identify, which one should be used to compare the mean values of the dependent variable associated as a result of controlled independent variables, subsequent to the consideration of the affect of uncontrolled independent variables. In the concrete drying example, if analyzed as a twoway anova with interaction, we would have a mixed e. Repeated measures anova with spss oneway withinsubjects anova with spss one between and one within mixed design with spss repeated measures manova with spss. How can i test the assumptions for a mixed design manova, and how robust is it to. Twoway mixed anova with one withinsubjects factor and one betweengroups factor. Introduction to manova, manova vs anova n manova using r. Twofactor mixed manova with spss linkedin slideshare.
Six differences between repeated measures anova and linear. While manova is the classical approach, the mixed model methodology, although by now implemented in all major statistical software packages, still is a relatively. One thing that makes the decision harder is sometimes the results are exactly the same from the two models and sometimes the results are vastly different. So whenever it says the univariate or multivariate mixed model in the. There is an unrestricted version where the test for factor b is done via. Difference between ancova and anova difference wiki. Manova before after by treat0 4 this initialises the anova command in spss. Spss procedure for mixed betweenwithin subjects anova click on plots click on withingroup factor time and move it into horizontal axis box click on betweengroup factor typcrim and move it into separate lines box click on add continue and ok. Twoway mixed anova using spss as we have seen before, the name of any anova can be broken down to tell us the type of design that was used. Mixedmultilevel multivariate models can also be run, for example, via mcmcglmm. This tutorial explains the differences between the statistical methods anova, ancova, manova, and mancova anova. Mixed design anova labcoat lenis real research the objection of desire problem bernard, p. So, it is a 2 x 2 x 2 x 2 mixed design manova, for which i have 2 betweensubject variables sex of the speaker and language and 2 withinsubject variables target sex and target attractiveness. There is a concern that images that portray women as sexually desirable objectify them.
Power and sample size for manova and repeated measures. Anova approaches to repeated measures univariate repeatedmeasures anova chapter 2 repeated measures manova chapter 3 assumptions interval measurement and normally distributed errors homogeneous across groups transformation may help group comparisons estimation and comparison of group means. Multivariate models are a generalization of manova. Aug 11, 2014 the distinctions between anova, ancova, manova, and mancova can be difficult to keep straight. Comparing the sas glm and mixed procedures for repeated. The mixed model for multivariate repeated measures mediatum. That is to say, anova tests for the difference in means between two or more groups, while manova tests for the difference in two or more. In this tutorial some of the features of the bionumerics manova window will be illustrated using a sample data set see2. As mixed models are becoming more widespread, there is a lot of confusion about when to use these more flexible but complicated models and when to use the much simpler and easiertounderstand repeated measures anova. Again, we are especially interested in balanced and unbalanced manova models as extension. Multivariate models which your intended case is an example of can be run in r. However, the socalled mixed model approach is a viable alternative to analyzing this type of data, because its underlying statistical assumptions are equivalent to the manova model. The two most common types of anovas are the oneway anova and twoway anova.
You simply determine the entire mean model and place all fixed effects on the model statement. Like anova, manova has both a oneway flavor and a twoway flavor. Anova theory is applied using three basic models fixed effects model, random effects model, and mixed effects model while regression is. The twoway part of the name simply means that two independent variables have been manipulated in the experiment. For example, we may conduct a study where we try two different textbooks, and we. It allows to you test whether participants perform differently in different experimental conditions. What to do if levenes test is significant in a mixed anova in spss. Anova one dv only manova 2 or more dvs intervalratio, 1 or more iv categorical anova determines the difference in means manova determines if the dvs get significantly affected by changes in the ivs. I am trying to do an anova anaysis in r on a data set with one within factor and one between factor. In multivariate analysis of covariance mancova, all assumptions are the same as in manova, but one more additional assumption is related to covariate. The manova extends this analysis by taking into account multiple continuous dependent variables, and bundles them together into a weighted linear combination or composite variable. Anova and manova are two different statistical methods used to compare means.
What is the difference between a 2way anova and a manova. Is there any difference between manova and mixed anova. In statistics, a mixeddesign analysis of variance model, also known as a splitplot anova, is used to test for differences between two or more independent groups whilst subjecting participants to repeated measures. In this case, to be consistent with example 1, the target variable has been renamed from trans1 to newb.
Anova and manova 1 introduction the central goal of an analysis of variance anova is to investigate the differences between the means of a set of quantitative variables across a number of groups. Effect size and eta squared university of virginia. Mixed multilevel multivariate models can also be run, for example, via mcmcglmm. Anova and manova are two statistical methods used to check for the differences in the two samples or populations. The different tests and plots present in the manova window will not be covered in detail in this tutorial. Manova to mancova when one or more more covariates are added to the mix. There are four multivariate test statistics, which can also complicate matters if you are not certain which one is the best for you to use. You can also use random effects anova in which you let each subject have his, or her, own intercept or intercept and slope. Eta2 is most often reported for straightforward anova designs that a are balanced i. The manova will compare whether or not the newly created combination differs by the different groups, or levels, of the independent variable. With twoway anova, you have one continuous dependent variable and two categorical grouping variables for the independent variables. Here, a mixed model anova with a covariatecalled a mixed model analysis of covariance or mixed model ancovacan be used to analyze the data. Difference between anova and manova compare the difference. However, the socalled mixedmodel approach is a viable alternative to analyzing this type of data, because its underlying statistical assumptions are equivalent to the manova model.
Multivariate analysis of variance manova multiplegroup manova contrast contrast a contrast is a linear combination of the group means of a given factor. Comparing the sas glm and mixed procedures for repeated measures. The proc mixed mean specification is actually more general than the one in proc glm in two ways. Multivariate analysis of variance manova is simply an anova with several dependent variables. Multivariate analysis of variance manova introduction multivariate analysis of variance manova is an extension of common analysis of variance anova.
Whether the data were analysed using univariate anova, manova, or mma. Cross validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. An obvious choice is mma also known as linear mixed models or. Manova and anova tell you that there is a significant effect while the post hoc tests help you map out the nature of those effectswhich groups. This idea was tested in an inventive study by philippe bernard. In manova, the number of response variables is increased to two or more. The core component of all four of these analyses anova, ancova, manova, and mancova is the first in the list, the anova.419 814 667 1561 401 725 448 621 148 321 416 774 1445 1173 285 514 623 466 1001 894 1118 587 1471 216 407 837 1544 1108 1447 1468 896 1070 1025 992 595 1167 321 75 215 478 485 1042 610 944 1185 291 189 1340 1435 1061
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https://www.thermal-engineering.org/what-is-thermodynamic-processes-in-otto-cycle-definition/
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math
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Otto Cycle – Processes
In an ideal Otto cycle, the system executing the cycle undergoes a series of four internally reversible processes: two isentropic (reversible adiabatic) processes alternated with two isochoric processes:
- Isentropic compression (compression stroke) – The gas (fuel-air mixture) is compressed adiabatically from state 1 to state 2, as the piston moves from bottom dead center to top dead center. The surroundings do work on the gas, increasing its internal energy (temperature) and compressing it. On the other hand the entropy remains unchanged. The changes in volumes and its the ratio (V1 / V2) is known as the compression ratio.
- Isochoric compression (ignition phase) – In this phase (between state 2 and state 3) there is a constant-volume (the piston is at rest ) heat transfer to the air from an external source while the piston is at rest at top dead center. This process is intended to represent the ignition of the fuel–air mixture injected into the chamber and the subsequent rapid burning. The pressure rises and the ratio (P3 / P2) is known as the “explosion ratio”.
- Isentropic expansion (power stroke) – The gas expands adiabatically from state 3 to state 4, as the piston moves from top dead center to bottom dead center. The gas does work on the surroundings (piston) and loses an amount of internal energy equal to the work that leaves the system. Again the entropy remains unchanged. The volume ratio (V4 / V3) is known as the isentropic expansion ration, but for Otto cycle, it is equal to the compression ratio.
- Isochoric decompression (exhaust stroke) – In this phase the cycle completes by a constant-volume process in which heat is rejected from the air while the piston is at bottom dead center. The working gas pressure drops instantaneously from point 4 to point 1. The exhaust valve opens at point 4. The exhaust stroke is directly after this decompression. As the piston moves from bottom dead center (point 1) to top dead center (point 0) with the exhaust valve opened, the gaseous mixture is vented to the atmosphere and the process starts anew.
During the Otto cycle, work is done on the gas by the piston between states 1 and 2 (isentropic compression). Work is done by the gas on the piston between stages 3 and 4 (isentropic expansion). The difference between the work done by the gas and the work done on the gas is the net work produced by the cycle and it corresponds to the area enclosed by the cycle curve. The work produced by the cycle times the rate of the cycle (cycles per second) is equal to the power produced by the Otto engine.
An isentropic process is a thermodynamic process, in which the entropy of the fluid or gas remains constant. It means the isentropic process is a special case of an adiabatic process in which there is no transfer of heat or matter. It is a reversible adiabatic process. The assumption of no heat transfer is very important, since we can use the adiabatic approximation only in very rapid processes.
Isentropic Process and the First Law
For a closed system, we can write the first law of thermodynamics in terms of enthalpy:
dH = dQ + Vdp
dH = TdS + Vdp
Isentropic process (dQ = 0):
dH = Vdp → W = H2 – H1 → H2 – H1 = Cp (T2 – T1) (for ideal gas)
Isentropic Process of the Ideal Gas
The isentropic process (a special case of adiabatic process) can be expressed with the ideal gas law as:
pVκ = constant
p1V1κ = p2V2κ
in which κ = cp/cv is the ratio of the specific heats (or heat capacities) for the gas. One for constant pressure (cp) and one for constant volume (cv). Note that, this ratio κ = cp/cv is a factor in determining the speed of sound in a gas and other adiabatic processes.
An isochoric process is a thermodynamic process, in which the volume of the closed system remains constant (V = const). It describes the behavior of gas inside the container, that cannot be deformed. Since the volume remains constant, the heat transfer into or out of the system does not the p∆V work, but only changes the internal energy (the temperature) of the system.
Isochoric Process and the First Law
The classical form of the first law of thermodynamics is the following equation:
dU = dQ – dW
In this equation dW is equal to dW = pdV and is known as the boundary work. Then:
dU = dQ – pdV
In isochoric process and the ideal gas, all of heat added to the system will be used to increase the internal energy.
Isochoric process (pdV = 0):
dU = dQ (for ideal gas)
dU = 0 = Q – W → W = Q (for ideal gas)
Isochoric Process of the Ideal Gas
The isochoric process can be expressed with the ideal gas law as:
On a p-V diagram, the process occurs along a horizontal line that has the equation V = constant.
See also: Guy-Lussac’s Law
We hope, this article, Thermodynamic Processes in Otto Cycle, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about thermal engineering.
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https://askthetask.com/1245/form-the-vertices-triangle-abc-and-calculate-length-rounded
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math
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The length of BC is 22.7
What is a right angled triangle?
A right angled triangle is one in which of the the angles is 90 degrees.
in the triangle AB = adjacent, BC = hypotenuse Ac = opposite
cos 66 = 9.2/BC
BC = 9.2/cos 66 = 9.2/0.406 = 22.7
In conclusion, the length of side BC is 22.7
Learn more about right-angled triangles: 64787
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https://plazgetti.gq/105.html
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math
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On interpreting the statistical significance of R squared up vote 0 down vote favorite I have performed a linear regression analysis to two series of data, each of which has 50 values.
How can the answer be improved? Rsquared evaluates the scatter of the data points around the fitted regression line. It is also called the coefficient of determination, or the coefficient of multiple determination for multiple regression. For the same data set, higher Rsquared values represent smaller differences between the observed data and the fitted values.
Testing for the significance of the correlation coefficient, r. When the test is against the null hypothesis: The simplest formula for computing the appropriate t value to test significance of a correlation coefficient employs the t distribution: Coefficient of determination rsquared.
25; How High Should Rsquared Be in Regression Analysis? How High Should Rsquared Be in Regression Analysis? The Minitab Blog. Search for a blog post: Analytics. Data Analysis; Machine Significance of r squared value Predictive Analytics This interpretation is correct regardless of whether the Rsquared value is 25 or 95! When an intercept is included, then r 2 is simply the square of the sample correlation coefficient (i. e.r) between the observed outcomes and the observed predictor values.
If additional regressors are included, R 2 is the square of the coefficient of multiple correlation. In both such cases, the coefficient of determination ranges from 0 to 1. With enough power, Rsquared values very close to zero can be statistically significant, but that doesn't mean they have practical significance.
It is a statistical artifact. Specifically, adjusted Rsquared is equal to 1 minus (n 1) (n k 1) times 1minusRsquared, where n is the sample size and k is the number of independent variables. Join Wayne Winston for an indepth discussion in this video, Interpreting the Rsquared value, part of Excel Data Analysis: Forecasting. Determining significance. 3m 49s. How to Interpret a Regression Model with Low Rsquared and Low P values. How to Interpret a Regression Model with Low Rsquared and Low P values.
The Minitab Blog. Search for a blog post: Analytics. Data Analysis; How do you pull out the pvalue (for the significance of the coefficient of the single explanatory variable being nonzero) and Rsquared value from a simple linear regression model? For example. Plotting fitted values by observed values graphically illustrates different Rsquared values for regression models. The regression model on the left accounts for 38. 0 of the variance while the one on the right accounts for 87.
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https://dominicantoday.com/dr/economy/2017/12/01/gasoline-propane-rise-natural-gas-unchanged/
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Gasoline, propane rise, natural gas unchanged
Visit Santiago, it's closer than you think....
Santo Domingo.- The Industry and Commerce Ministry on Friday posted the fuel prices for the week from December 2 to 9, when premium gasoline will cost RD$221.80, or RD$2.00 more, and regular will cost RD$207.20, an increase of RD$3.50 per gallon.
Regular diesel will cost RD$167.50, an increase of RD$1.00, and optimum diesel will cost RD$180.60, or RD$1.00 less per gallon.
Avtur will cost RD$131.90; kerosene will cost RD$158.30 and fuel oil RD$109.85, all RD$1.00 higher per gallon.
Propane will cost RD$119.30 per gallon, an increase of RD$1.00 and natural gas remains at RD$28.97 per cubic meter.
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https://www.mopedarmy.com/forums/read.php?6,1632642,1632642
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math
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I just got a puch magnum mk 2 the 2 hp one 2 speed. The clutch on it seems to be going. I also have a 2hp 1 speed puch maxi i use for parts.
I was curious if the clutch from the 1 speed would go on the puch magnum mk2?
Also how much tranny fluid do i put in the MK2 and what type?
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https://mstdn.io/@codewiz/107511282018296306
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math
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@sektor My interest in math also died around the time I dropped out of college, particularly this stuff that was taught only in abstract terms...
...but now I need basic control theory and linear algebra in my code, and suddenly it's become super fascinating! 🤩
@codewiz I think it was the graphing that drew me away in the end. I couldn't wrap my head around the revolution integrals, and the pictures seem to be quite intricate to represent in Braille fassion. My precalc professor had the awesome idea to use 3D printed graphs, which I think will win out in the end.
@sektor Not sure why US college math has this weird emphasis on graphing functions, actually. And I was very surprised when I found that all college students
have to buy those stupid calculators. So anachronistic! 😂
Italian calculus, on the other hand, was very heavy on definitions and proofs...
@codewiz I didn't get it either, but then again I never saw the practicality of anything past Calc II. But that is just me.
@sektor Yeah, i agree. Even quantum field theory seems to be within reach of calculus 2 (plus group theory and statistics?)
But people, please try to prove us wrong with counterexamples?
The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!
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https://physics.stackexchange.com/questions/351240/how-can-a-magnetic-field-exist-outside-a-capacitor-where-the-electric-flux-is-no
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math
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I came across a line stating that a magnetic field exists in a region outside a circular plate capacitor that is being charged. I am not able to understand this as there is no change in electric flux and according to Maxwell's law of induction, magnetic field can't be induced without a change in electric flux. I've attached photos of the diagram and the statements (enclosed within brackets). Am I missing something here?
As the capacitor is being charged, the electric field between its plates is increasing with time. There is therefore a time varying electric flux aka a displacement current and, by Ampère's Law (which is, I believe, what you mean by "Maxwell's law of induction"), an MMF around the loop in your drawing.
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http://www.ques10.com/p/1269/electronic-instruments-and-measurements-questio-12/
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math
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Electronic Instruments and Measurements - May 2013
Electronics Engineering (Semester 3)
TOTAL MARKS: 80
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks.
Answer any four of the following :-
1 (a) How CRO is applicable for component testing? Justify.(5 marks) 1 (b) What is Lissajous pattern? How measurement of frequency can be done it with?(5 marks) 1 (c) How power factor meter works?(5 marks) 1 (d) What is back emf voltage equation?(5 marks) 1 (e) What is hybrid stepper motor?(5 marks) 2 (a) What is dual trace, multi-trace, dual beam and sampling storage oscilloscope? (10 marks) 2 (b) With the neat diagram and waveform explain the working of phase meter using Flip-Flop.(10 marks) 3 (a) What are the Essentials of indicating instrument? Explain it in details.(10 marks) 3 (b) Explain the measurement of inductance by Maxwell's Hay's method.(10 marks) 4 (a) List various types of DVMs and explain in detail.(10 marks) 4 (b) What are the Requirements of a good laboratory type signal generator? Explain A.F. signal generator.(10 marks) 5 (a) Explain construction ans working principle of stepper motor.(10 marks) 5 (b) Explain Kelvin's double bridge.(10 marks) 6 (a) List various methods of analog to digital and digital to analog conversion and explain any one in detail.(10 marks) 6 (b) What is beat Frequency oscillator and explain its advantages.(10 marks) 7 (a) Describe the panel layout of CRO.(10 marks) 7 (b) How to Measure medium, low and high resistance?(10 marks)
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https://www.projecteuclid.org/euclid.ejp/1464819838
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math
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Electronic Journal of Probability
- Electron. J. Probab.
- Volume 15 (2010), paper no. 53, 1645-1681.
On Some non Asymptotic Bounds for the Euler Scheme
We obtain non asymptotic bounds for the Monte Carlo algorithm associated to the Euler discretization of some diffusion processes. The key tool is the Gaussian concentration satisfied by the density of the discretization scheme. This Gaussian concentration is derived from a Gaussian upper bound of the density of the scheme and a modification of the so-called "Herbst argument" used to prove Logarithmic Sobolev inequalities. We eventually establish a Gaussian lower bound for the density of the scheme that emphasizes the concentration is sharp.
Electron. J. Probab., Volume 15 (2010), paper no. 53, 1645-1681.
Accepted: 26 October 2010
First available in Project Euclid: 1 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H35: Computational methods for stochastic equations [See also 65C30]
Secondary: 65C30: Stochastic differential and integral equations 65C05: Monte Carlo methods 60E15: Inequalities; stochastic orderings
This work is licensed under aCreative Commons Attribution 3.0 License.
Menozzi, Stéphane; Lemaire, Vincent. On Some non Asymptotic Bounds for the Euler Scheme. Electron. J. Probab. 15 (2010), paper no. 53, 1645--1681. doi:10.1214/EJP.v15-814. https://projecteuclid.org/euclid.ejp/1464819838
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https://jestineyong.com/testing-capacitor-value/
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math
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Testing Capacitor Value
I have Question about how to test this type of component if they are bad or good (.15j100) (1j63)
Test with digital capacitance meter. The first one is .15uf 100v or 150 nanofarad and the second one is 1uf 63 volt. You can easily get a digital capacitance meter from any local electronics shop or from ebay dot com. If the value that you get is less than the rated value (more than 10% tolerance) then you need to replace the capacitor. If possible replace with the same type of capacitor because in certain circuit it only work fine with the same type and not other type.
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https://www.nagwa.com/en/videos/834191694564/
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math
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The current in the circuit shown is 100 milliamperes. What is the current in the 50Ω resistor to the nearest milliampere?
We want to know the current in the 50Ω resistor. These resistors are all in series because there’s only one path for the current to take. So before we answer this question, let’s review how voltage and current behave across resistors that are in series. This circuit shows two resistors in series with a voltage 𝑉 and a current 𝐼. Since the same current flows through the entire circuit, the current across both resistors is the same. Since the current across each resistor is the same, according to Ohm’s law which says that the voltage is equal to the current times the resistance, the voltage across each resistor will not be the same. But it will be proportional to the resistance. Though the voltages across each resistor will be different, they will add to the total voltage of the circuit.
Now that we’ve reviewed how current and voltage behave across resistors in series, we know that the current in the 50Ω resistor must be the same as the current in the whole circuit because all of the resistors in this circuit are in series. So the current in the 50Ω resistor to the nearest milliampere is 100 milliamperes.
What is the voltage across the 40Ω resistor to two significant figures?
Now we want the voltage across the 40Ω resistor, which we’ll be able to find using Ohm’s law. As we’ve already established, the current in each resistor in this circuit is the same, 100 milliamperes. And the resistance of the 40Ω resistor is 40Ω. Before we can solve for the voltage, we need to convert the current from milliamperes to amperes. There are 1000 milliamperes in an ampere. So to convert from milliamperes to amperes, we should divide by 1000. Now we can solve for the voltage, which is 4.00 volts, rounding to two significant figures. We’ll find the voltage across the 40Ω resistor is 4.0 volts.
What is the total resistance in this circuit to the nearest ohm?
We can find the total resistance of resistors in series by adding together the resistances of the individual resistors in the circuit. So, we can find the total resistance of this circuit by summing the 30, 40, and 50Ω resistances together. Adding everything together, we’ll find that the total resistance in this circuit is 120Ω.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107875980.5/warc/CC-MAIN-20201021035155-20201021065155-00455.warc.gz
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CC-MAIN-2020-45
| 2,355 | 7 |
https://www.astm.org/stp16317s.html
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math
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This paper describes the application of the reference stress approach and probabilistic methods to the determination of creep crack growth based on the time-dependent fracture mechanics parameter, C(t), where t is time. This parameter is defined as the simple sum of a transient component, C(t → 0), which is applicable to short times and a steady-state component, C*. The reference stress approach enables a relatively simple expression for C* to be derived. A scheme is developed that optimizes the fit of the reference stress approach to published computed solutions for Jp, the fully plastic component of the J-integral. The optimization scheme involves the derivation of an engineering parameter, V. An expression for C* is readily derived from an expression for Jp by invoking the creep-plastic analogy. Values of V are derived from the analysis of 189 sets of computed solutions. These values are statistically analyzed and used to derive a distribution function describing the uncertainty in V. This function is used together with distribution functions for other random variables (such as the creep strain rate coefficient and crack growth law coefficient) in example probabilistic analyses of flaws in welded internally pressurized pipes operating in the creep regime. Probability sensitivity factors are generated as part of the probabilistic analyses.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947475833.51/warc/CC-MAIN-20240302152131-20240302182131-00162.warc.gz
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CC-MAIN-2024-10
| 1,365 | 1 |
http://openstudy.com/updates/566e60d7e4b0d639d63d4ac8
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math
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So I have two questions I really need help if someone could explain how to do it. It would mean a lot. I'm swamped with Homework and Math is my worst subject.
mAngleBAC = 3x + 9, mAngleABC = 8x + 11, and mAngleBCA = 5x - 8
I understand that I have to solve for X but how do I go about doing it?
b. Find the measures of Angle 1, Angle 2, and Angle 3.
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
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Do those angles form a triangle? Do you know anything about the sum of the angles of a triangle?
I also forgot to add this. If you could all around explain it to me so I can understand it that would be great.
Yeah, those are the interior angles of a triangle. The interior angles of a triangle always add to 180 degrees, just like the interior angles of a rectangle always add to 360 degrees. Use that information to write an equation involving \(x\) and solve for \(x\). Then substitute the value you found for \(x\) into the formula for the size of each angle. If you find that \(x=10\), for example, angle BAC \(= 3x + 9\) would have value \(3*10+9 = 39\)
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s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084886939.10/warc/CC-MAIN-20180117122304-20180117142304-00138.warc.gz
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CC-MAIN-2018-05
| 1,922 | 13 |
https://www.businessinsider.com/oracle-sued-google-for-6-billion-and-wound-up-owing-4-million-2012-7
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math
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\n \n \n \n \n \n \n <img src="https://i.insider.com/4fcf965feab8ea9879000003?width=600&format=jpeg&auto=webp" />\n \n \n \n \n \n \n Twitter\n \n \n \nEarlier this year Oracle was battling Google in court, claiming Android was violating its patents.At the start of the suit, Oracle was looking to take $6 billion from Google for damages.\n\n\n\nThe case is over. Oracle lost.Instead of getting $6 billion, it could end up owing Google $4 million for legal expenses, Groklaw reports.The judge told Oracle that its damages claim was ridiculous and so Oracle's expert witness had to keep coming up with new damages estimates. On the third try, the Judge said that if Oracle lost the case, Oracle would have to pay for Google's legal fees.So Google just handed Oracle the bill.Amazingly, Oracle actually hasn't completely given up. It did win on two minor incidents of copyright infringement. Oracle is still trying to get something out of those wins (which should amount to $300,000 at most, we previously reported.)\n\n\n\nBut Google thinks that this is Oracle's attempt to slither itself into a new trial and along with the bill for legal expenses, it asked the court to deny its latest motion.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251783342.96/warc/CC-MAIN-20200128215526-20200129005526-00087.warc.gz
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CC-MAIN-2020-05
| 1,194 | 1 |
http://doctord.webhop.net/Courses/BEI/EE301/EE235/EE235/Project/lesson8/lesson8.html
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math
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The Step Response is the response of an LTI system to a unit step function. In other words, the input to the system is simply the unit step function: x(t) = u(t).
This is equivalent to simply integrating the input from the infinite past up to time t.
Superposition (or Divide-and-Conquer):
We can directly apply superposition to find the output of LTI systems if x(t) can be expressed as a linear combination of basis functions Φk(t).
The Φk(t) are some convenient set of functions, for example unit impulses, unit step functions, or complex exponentials.
|Example 2 If an input is written as: |
using superposition, we can write its output as:
Ψk(t) = S[Φk(t)] = h(t) * Φk(t) = Φk(t) * h(t)
Again, using superposition, we can write:
Find the output of the system where
x(t) = 2u(t) - u(t - 1) -
u(t - 2) and
h(t) = e-at [ u(t) - u(t - 2) ].
Convolution is commutative, associative, and distributive. Keeping this in mind may simplify some convolutions for you.
w(t) = x(t) * h1(t), y(t) = w(t) * h2(t)
= [ x(t) * h1(t) ] * h2(t)
= x(t) * [h1(t) * h2(t)], by associativity of convolution
Therefore the impulse response h(t) for this overall system is h1(t) * h2(t).
We can change the order in which the convolutions are performed due to commutativity. For a cascade of M systems there are M! possible system orderings.
Parallel systems is a large area of research today.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100942.92/warc/CC-MAIN-20231209170619-20231209200619-00728.warc.gz
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CC-MAIN-2023-50
| 1,376 | 20 |
https://www.kopykitab.com/Complex-Variables-And-Special-Functions-by-Patra-Baidyanath
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math
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About The Book Complex Variables And Special Functions
Authors aim is to make the readers easily understand the theory of complex variables. He explains this subject matter from a rudimentary to advanced level in a very simple manner.
Organized in two parts, this book explains exact definitions of different terms used by supplying worked-out examples wherever found necessary. A large number of examples have been solved in the book to acquaint the readers with different techniques. Furthermore, a large number of problems have been supplied with answers at the end of each chapter.
The first part of the book (Chapters 1 through 11) containing analysis of complex variables will be useful for the undergraduate students of engineering and science.
The second part of the book (Chapters 12 through 20) is written in complex domain and is targeted towards advanced level readers who are either pursuing postgraduate studies in Mathematics or research in Applied Mathematics. The first part is prerequisite for this section of the book.
Table of Contents:
1. Complex Numbers
2. Complex Variables and Regions of Complex Plane
5. Elementary and Multivalued Functions
7. Complex Sequence and Series
8. Zeros, Singularities and Residues
9. Application of Residues
10. Meromorphic Functions and Some Special Topics
11. Mapping or Transformation
12. The Gamma Function and Related Functions
13. Homogeneous Linear Ordinary Differential Equation
14. Fuchsian Type of ODE
15. The Hypergeometric Equation
16. Legendre Equation
17. Bessel Functions
18. Hermite Functions and Polynomials
19. Laguerre Polynomials
20. Chebyshev Polynomials
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CC-MAIN-2020-10
| 1,628 | 23 |
http://vcsp.info/Chapter_5/Influences_on_Motion_in_Earth_Atmosphere/Reynolds_Number_Ballistics.aspx
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math
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Last Revision March, 2011
Influences on Motion in Earth's Atmosphere
An excerpt from a 2006 textbook, "Classical Mechanics" by R. Douglas Gregory, Cambridge University Press, sets up the challenge for this and the previous topic. It is:
Although it is not known how to obtain analytical solutions for the differential equations that apply to a body encountering resistance that is proportional to the square of its velocity, it is quite possible to obtain practical computer assisted numerical solutions to such equations.
The object is now to consider elements to be taken into account to model both horizontal and vertical motion of bodies in Earth's Atmosphere, 2-dimensional motion.
Does the Atmosphere have much Effect?
Imagine that a cannon projects a spherical maple wood ball vertically upward with a muzzle velocity v. Presume that maple wood has a density of ~755 kg/cubic metre. See
for wood densities.
The ball will encounter a drag force and a slight buoyant force due to the atmosphere as well as the force due to gravity just as did the falling body of the previous topic. The major difference between the two cases is that there is an initial velocity v and effect of buoyancy is now included.
The downward force equation is:
m * a = m * g - m' * g - Drag
where m' is the mass of the displaced fluid
The effect of the buoyancy is
taken into account as a modification to g in the differential equation:
a = g * (1-m'/m) - Drag/m or
a = g' - Drag/m
. Assume a radius of 4 centimetres, g =9.82022, and the mass of a ball as ~ 0.2024. Provide an upward velocity of 100 metres per second. Without air drag or buoyancy how high will the ball rise? This is a mechanics question to which the analytic answer is most often expressed as:
v ^ 2 / (2 * g) ~= 509.15 metres.
This analytic expression presumes that the force of gravity is uniform and does not include buoyancy, which is reasonable as in this case these effects are quite small.
The 2D calculator, described and made available for use by the viewer in the last topic of Chapter 6 or on the upper row of tabs, provides an answer of ~ 509.95 metres without drag but with buoyancy included.
With small air drags
of 0.1 and 0.4 in this same case the calculator provides corresponding heights of ~ 309 metres and 163 metres, buoyancy included. Each height a far cry from the other and both well distanced from the case of no resistance.
Drag Versus Reynolds Number
Some values of the drag coefficient versus the Reynolds number are given in a document by H. Edward Donley
That source provides numerical values for R and for its logarithm, log(R, 10), and then uses the logarithms for the plot. This writer noted an instance where R and its logarithm were not in agreement. The error appears to clearly be a typing error that has been corrected by this author to produce the plot following:
Two additional points have been added to the chart, the diamond shape points. These are said to be average values where the lower value, 0.1, is said to apply to smooth spheres and the higher value, 0.4, is said to be suitable for rough spheres. The position of the lower diamond suggests that the Donley values apply to smooth spheres.
For many purposes the drag coefficient for a sphere is taken to be sufficiently constant for Reynolds numbers in the range 1000 < R < 100,000.
For a given radius of sphere the Reynolds number R is directly proportional to the velocity of the body and inversely proportional to the kinematic viscosity of the medium. The latter is quite dependent on the temperature of the medium. See
Aside from the drag coefficient do we need to consider changes in air density, gravity, wind, spin and the like to get it right?
Following is a quote from "Guns of World War II", available on the Web at the time of writing but since vanished.
Even if, for centuries, ballistics was considered as a science, in (sic) facts, it is all but impossible, even today, to forecast the end-result of a fired shell.
A projectile fired at an angle to the direction of gravitational force can be described as having two orthogonal components of velocity, one in the direction of the gravitational force and one at 90
In the absence of other forces such as wind, these components are presumed to remain in a plane.
Only the first component will be influenced by gravity.
Both components will encounter air resistance. Too determine the amount of resistance affecting each; the resistance due to their combined velocity must be distributed between them in accord with the ratio of their individual velocities to the combined velocity.
Call the vertical component the y component and the horizontal component the x component.
At the beginning of a numerical calculation step an object may have velocity components v
with a combined velocity:
V = (v
The atmospheric resistance factor is presumed to have the form K * V^2 where K is determined by the shape of the object and the density of the atmosphere.
In constructing a spreadsheet, the increments to v
for an increment of time Dt become:
= -Dt * (v
/ V) *K * V^2 and
= -Dt * (v
/ V) *K * V^2 - Dt * g'
Elevation and Maximum Range
At the beginning of a projectile flight, the initial velocity v
is resolved into its x, y components, employing radian measure:
*sin(θ*π/180) and v
The elevation angle θ is with respect to the horizontal.
As time progresses these components will change in value as gravity and the resistance of the medium take their toll on the motion.
Use the 2D calculator link given in the last topic of Chapter 6, to choose the elevation that will provide maximum range for a 4.0 cm. wooden ball projected at 100 metres per second. Do this for drag coefficients of 1E-10, 0.1, and 0.4. Use a step size of 0.02
, ~1020 m); (42.5
, ~530 m); (42
Once again, air resistance matters. The smoothness of the ball plays a very significant role!
In the next topic further reality is added to model motion through Earth's atmosphere by introducing the Standard Atmosphere and the variation in gravitational attraction with altitude.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817670.11/warc/CC-MAIN-20240420153103-20240420183103-00221.warc.gz
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CC-MAIN-2024-18
| 6,055 | 57 |
https://inventively.com/search/trademarks/85809117
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math
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The mark consists of the stylized wording "POLITICAL" above the stylized word "COM". Each of the letters of the word "COM" appears within a circle. There are two horizontal lines on either side of the word "COM" and under the word "POLITICAL".
100, 101, 102
Design plus words, letters, and/or numbers
Color is not claimed as a feature of the mark.
Circles, exactly three circles , Circles that are totally or partially shaded., Bands, straight , Bands, horizontal
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s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463612069.19/warc/CC-MAIN-20170529091944-20170529111944-00442.warc.gz
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CC-MAIN-2017-22
| 463 | 5 |
https://www.thefreelibrary.com/3D+Simulation+of+Self-Compacting+Concrete+Flow+Based+on+MRT-LBM-a0576377421
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math
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3D Simulation of Self-Compacting Concrete Flow Based on MRT-LBM.
As a highly flowable concrete, the self-compacting concrete does not require any vibration during casting processes and has been considered as "the most revolutionary development in concrete construction for several decades" . Although SCC has been successful in plenty of applications, many problems are encountered during construction because of aggregate segregation, air voids, and the improper filling of formworks, and most of these problems are closely related to the flowability of SCC. Therefore, it is important to well understand and accurately predict the flow characteristics for the success of SCC casting. However, the accurate prediction of the SCC flowing behavior is a big challenge, especially in the case of heavy reinforcement, complex formwork shapes, and large size of aggregates. In this regard, the numerical modeling of SCC is an indispensable and inexpensive approach, not only as a tool for form filling prediction but also in terms of determination of fresh concrete properties, mix design, and casting optimization. Nowadays, the numerical modeling of fresh concrete flow has gained importance, and it is becoming an important tool for the prediction and optimization of casting processes [2, 3].
The modeling of fresh SCC is not a trivial task because it involves a free-surface flow of a dense suspension with a wide range of particle sizes and shows non-Newtonian flow behavior. A complete description of SCC from the cement particles to coarse aggregates is impossible with any computer model since accounting for broad particle size and shape distributions exceeds the computational limits of even the best supercomputers . The fresh SCC can be treated as a one-phase fluid and simulated using CFD because it is flowable and the amount of coarse particles is lower than that in conventional concrete. In terms of rheology, the fresh SCC can be approximated as one of the known non-Newtonian materials such as the Bingham or Herschel-Bulkley fluid. In case if the high shear rates are likely to occur in the casting processes, the shear-thickening behavior can happen, and the Herschel-Bulkley model could be a more suitable one. At the end of the casting process, the shear rates are rather low and the yield stress practically dominates the flow. Therefore, the material can be modeled as a Bingham fluid to predict the final shape.
At present, many numerical techniques have been developed to model the SCC flow by assuming it as a homogeneous viscous fluid and using either the mesh-based methods such as the finite volume method (FVM) and the finite element method (FEM) or the meshless methods like the smoothed particle hydrodynamics (SPH) and the lattice Boltzmann method (LBM). Due to the fact that the flow of SCC is a typical free-surface flow, the treatment of the interface and its position represents another important numerical modeling issue. In this regard, the meshless methods have an advantage over the mesh-based methods. As a meshless Lagrangian method, the SPH method is good at modeling Newtonian and non-Newtonian flows with a free surface and has been chosen for simulating the SCC flow by Kulasegaram et al. , Lashkarbolouk et al. , Qiu , Abo Dhaheer et al. , and Wu et al. . However, the SPH method has difficulties in solving problems with complex solid boundary conditions. For these reasons, many researchers have made much effort to develop an alternative method called LBM for modeling the SCC flow due to the fact that it is easy for coding, intrinsically parallelizable, and applicable to complex geometries straightforwardly. For example, Svec et al. and Leonardi et al. simulated the fresh SCC as the non-Newtonian fluid based on the singlerelaxation-time (SRT) LBM. Although the single-relaxationtime (SRT) model has been successful in many applications, it is prone to numerical instability in complex flows . To overcome these difficulties, the multiple-relaxation-time (MRT) model proposed by d'Humieres et al. is useful to stabilize the solution and to obtain satisfactory results because the MRT model allows the usage of an independently optimized relaxation time for each physical process . Therefore, Chen et al. solved Bingham fluids by using the MRT model, but the free surface is not considered in their model. In the present work, we will develop a 3D multiple-relaxation-time LBM with a mass tracking algorithm representing the free surface to simulate the flow of fresh SCC.
2. Mathematical Formulations
2.1. Multiple-Relaxation-Time LBM. In this paper, the SCC flow is solved based on the lattice Boltzmann method which is considered as a very attractive alternative to the traditional CFD, especially in problems with complex boundary conditions. In the LBM, a finite number of velocity vectors [e.sub.[alpha]] are used to discretize the velocity space, and the fluid motion is described by a particle distribution functionf(x, [e.sub.[alpha]], t) which is the probability density of finding particles with velocity [e.sub.[alpha]] at a location x and at a given time t. The LB equations can recover the continuum Navier-Stokes equations by means of the Chapman-Enskog expansion if a proper set of discrete velocities was employed [17, 19]. The D3Q27 (3 dimensions and 27 velocities) discrete velocity model illustrated in Figure 1 was used in this study. The particle velocity vectors [e.sub.[alpha]] for this lattice model are given by
[mathematical expression not reproducible], (1)
where c = [delta]x/[delta]t, with [delta]x and [delta]t being the lattice spacing and the time step, respectively.
A discretization of the Boltzmann equation in time and space leads to the lattice Boltzmann equation [20, 21]:
[f.sub.[alpha]] (x + [e.sub.[alpha]][delta]t, t + [delta]t) - [f.sub.[alpha]] (x, t) = [[LAMBDA].sub.[alpha]j][[f.sub.j](x, t) - [f.sup.eq.sub.j] (x, t)] + [F.sub.[alpha]][delta]t, (2)
where [f.sub.[alpha]] is the distribution function of particles moving with velocity [e.sub.[alpha]], [[LAMBDA].sub.[alpha]j] is the collision matrix, [f.sup.eq] is the equilibrium distribution function, and [F.sub.[alpha]] is the external force.
The equilibrium distribution function [f.sup.eq] is obtained using the Taylor series expansion of the Maxwell-Boltzmann distribution function with velocity u up to second order. It can be written as
[mathematical expression not reproducible], (3)
where [rho] is the fluid density, u is the fluid velocity, and the sound speed is [c.sub.s] = c/[square root of (3)]. The weight coefficients for D3Q27 are given by
[mathematical expression not reproducible]. (4)
The components of F are given as
[F.sub.[alpha]] = [w.sub.[alpha]][rho][[e.sub.[alpha]] x a/[c.sup.2.sub.s]], (5)
where a is the acceleration.
The relaxation process has major influence on the physical fidelity as well as numerical stability. For the single-relaxation-time (SRT) model, the collision matrix is [[LAMBDA].sub.[alpha]j] = -1/[tau][[delta].sub.[alpha]j], where [[delta].sub.[alpha]j] is the Kronecker symbol and t is the relaxation time which is related to the kinetic viscosity by v = [c.sup.2.sub.s]([tau] - 1/2)[delta]t. For the multiple-relaxation-time LBM, the collision matrix A can be written as
[LAMBDA] = -[M.sup.-1]SM, (6)
where the linear transform matrix M is a 27 x 27 matrix. The diagonal matrix S may be written as S = diag (0, 0, 0, 0, s4, s5, s5, s7, s7, s7, s10, s10, s10, s13, s13, s13, s16, s17, s18, s18, s20, s20, s20, s23, s23, s23, s26) with s4 = 1.54, s5 = s7 = 1/t, s10 = 1.5, s13 = 1.83, s16 = 1.4, s17 = 1.61, s18 = s20 = 1.98, and s23 = s26 = 1.74.
The macroscopic density [rho] and velocity u are computed by
[mathematical expression not reproducible]. (7)
The pressure p is related to the density by
p = [rho][c.sup.2.sub.s] (8)
2.2. Free Surface Modeling. For the modeling of the liquid-gas interface, the most straightforward way is to track all the phases, for example, liquid and gas. Such a method has the highest accuracy at the expense of high computational costs. The mass tracking algorithm without considering the gas phase is employed in the present study due to the fact that it is simple, fast, and accurate. In this algorithm, the fluid domain is divided into liquid, interface, and gas nodes (Figure 2). The liquid and interface nodes are active and solved by the LBM, and the remaining gas nodes are inactive without evolution equation. Liquid and gas nodes are never directly connected but through an interface node. The adopted mass tracking algorithm is applied directly at the level of the LBM, so the algorithm mimics the free surface by modifying the particle distributions. An additional macroscopic variable for the mass m (x, t) stored in a node is required and defined as
[mathematical expression not reproducible]. (9)
The mass is calculated by
m(x, t + [delta]t) = m(x, t) + [summation over ([alpha])][k.sub.[alpha]] [f.sub.[bar.[alpha]]](x + [e.sub.[alpha]] [delta]t, t) - [f.sub.[alpha]](x, t)], (10)
where [f.sub.[bar.[alpha]]] and [f.sub.[alpha]] are the particle distributions with opposite directions and
[mathematical expression not reproducible]. (11)
The interface node becomes a fluid node when the mass reaches its density with m (x, t) = [rho] (x, t) and vice versa; the interface node becomes a gas node when the mass drops down to zero with m (x, t) = 0.
2.3. Modified Herschel-Bulkley Model. In this study, the fresh SCC is assumed as viscoplastic fluids to consider its non-Newtonian behavior. Among the constitutive relations of viscoplastic fluids, the Herschel-Bulkley model is probably the most commonly used because of its simplicity and flexibility. The standard Herschel-Bulkley model is described by
[mathematical expression not reproducible], (12)
where [??] is the shear rate ([s.sup.-1]), a is the stress (Pa), [[sigma].sub.y] is the yield stress (Pa), and k is the consistency index (Pa x [s.sup.n]); n is a measure of the deviation of the fluid from Newtonian (the power-law index). For a fluid with n > 1, the effective viscosity increases with shear rate, and the fluid is called shear-thickening or dilatant fluid. For a fluid with 0 < n < 1, the effective viscosity decreases with shear rate, and the fluid is called shear-thinning or pseudoplastic fluid.
The standard Hershel-Bulkley model becomes discontinuous at less shear rates and causes instability during numerical solution due to the fact that the non-Newtonian viscosity becomes unbounded at small shear rates. In order to overcome such discontinuity, the standard Herschel-Bulkley model can be modified as
[mathematical expression not reproducible], (13)
where [mu] is the apparent viscosity of fluid, and the yielding viscosity [[mu].sub.y] can be estimated from experimental rheological curves and can be assumed to be the slope of the line of shear stress versus shear rate curve before yielding. The modified Herschel-Bulkley model combines the effects of Bingham and power-law behavior in a fluid. For low strain rates, the material acts like a very viscous fluid with yield viscosity [[mu].sub.y]. As the strain rate increases and the yield stress threshold [[sigma].sub.y] is passed, the fluid behavior is described by a power law.
3. Numerical Examples and Validation
In this section, the developed MRT-LBM is applied to simulate the slump flow of fresh SCC to validate the capability of the proposed model in modeling SCC flow. And the model is also used to simulate the passing ability and the filling ability of SCC by using an enhanced L-box test.
3.1. Slump Test. The slump flow is the most commonly used test in SCC technology. It measures flow spread and optionally the flow time [t.sub.50]. The numerical simulation of the slump test in our study is based on a laboratory experiment by Huang , Figure 3(a). The dimensions of the cone are 300 mm height, 200 mm lower diameter, and 100 mm upper diameter, Figure 3(b). The SCC used in this study has the following properties: yield stress = 100 Pa, plastic viscosity = 50 Pa x s, and density = 2300 kg/[m.sup.3]. In the standard form of the slump test, only the final spread value of the slump is measured to evaluate the flowing behavior of the SCC.
The numerical simulation of the slump flow is performed based on the developed MRT-LBM. In our simulation, the lattice spacing is set to 0.01 m for the LBM discretization, Figure 3(c). The value of the yielding viscosity was chosen to be 1000 times higher than the value of the yield stress, with the power-law index being n = 1. Figure 4 presents some snapshots at different instants of the material shape with the velocity magnitude. In Figure 5, experimental and numerical results for the material shape at the end of the flow are compared. It can be seen from this figure that the calculated slump flow spread diameter is about 624 mm which shows a perfect match between the experimental and simulated flow distance that can be observed in terms of the maximum spread distance. This proves the correctness of the proposed model and its ability to simulate the free surface flow of fresh SCC.
3.2. Enhanced L-Box Test. The L-box test is generally used for assessing the passing ability and filling ability of fresh SCC in confined spaces. In this section, a laboratory experiment of an enhanced L-box test by Huang was simulated using the developed MRT-LBM. The enhanced L-box consists of the concrete reservoir, slide gate, and horizontal test channel with four ball obstacles (Figure 6(a)). The vertical section is filled with concrete, and subsequently, the gate is lifted to allow concrete to flow into the horizontal section. When the flow stops, one measures the reached height of fresh SCC after passing through the specified gaps of balls and flowing within a defined flow distance. With this reached height, the passing or blocking behavior of SCC can be estimated. The dimensions of the enhanced L-box test are shown in Figure 6(b).
In our simulation, the SCC is placed at the middle upper part of the vertical container, which is then suddenly released, and the concrete begins to spread under the gravity loading, Figure 6(c). The numerical simulation is performed based on the developed MRT-LBM and the lattice spacing is set to 0.01 m for the LBM discretization. The value of the yielding viscosity was chosen to be 1000 times higher than the value of the yield stress, with the power-law index being n = 1. SCC used for this study was the same concrete as in the slump test with the following properties: yield stress = 50 Pa, plastic viscosity = 50 Pa x s, and density = 2300 kg/[m.sup.3]. The total volume of the material is V = 13 L. Some snapshots of the SCC shape with the velocity magnitude at different instants are presented in Figure 7. Figure 8 compares the experimental and numerical results for the final spread of the SCC flow. The simulated flow spread agrees well with the experimental results. This in turn further validates the proposed model in modeling the passing ability and filling ability of fresh SCC in confined spaces. A slight discrepancy in the shape of the SCC can be noted which may be due to the fact that the balls are perfectly touched by the lateral wall in simulation but there are existing gaps between them in the experiment.
In this paper, a multiple-relaxation-time LBM with a D3Q27 discrete velocity model for modeling the flow behavior of fresh SCC was proposed. The rheology of the fresh SCC was approximated as a non-Newtonian material using the modified Herschel-Bulkley fluid model. The free surface was modeled based on the mass tracking algorithm which is a simple and fast algorithm that conserves the mass precisely. The numerical simulation of slump flow of fresh SCC was first performed to validate the capability of the proposed model in modeling SCC flow. And then, the model was further used to simulate the passing ability and the filling ability of fresh SCC in confined spaces based on an enhanced L-box test. The simulated results agree well with the corresponding experimental data in the published literature. This proves that the proposed MRT-LBM is suitable for numerical simulations of the fresh SCC flows. It should be noted that the main problem for the application of the present model to real engineering problems is its high computational cost. Therefore, further investigations might be needed to consider hardware acceleration and parallel computing to make the proposed model more useful and versatile.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
The authors are grateful for funding from the National Natural Science Foundation of China (Grant nos. 11772351 and 51509248) and the Scientific Research and Experiment of Regulation Engineering for the Songhua River Mainstream in Heilongjiang Province, China (Grant no. SGZL/KY-12).
EFNARC, Specification and Guidelines for Self-Compacting Concrete, Scientific Research Publishing, Surrey, UK, 2002.
N. Roussel, M. R. Geiker, F. Dufour, L. N. Thrane, and P. Szabo, "Computational modeling of concrete flow: general overview," Cement and Concrete Research, vol. 37, no. 9, pp. 1298-1307, 2007.
N. Roussel and A. Gram, Simulation of Fresh Concrete Flow, State-of-the Art Report of the RILEM Technical Committee 222-SCF, RILEM State-of-the-Art Reports, vol. 15, Springer, Netherlands, 2014.
K. Vasilic, M. Geiker, J. Hattel et al., "Advanced Methods and Future Perspectives," in Simulation of Fresh Concrete Flow, N. Roussel and A. Gram, Eds., vol. 15pp. 125-146, Springer, Netherlands, 2014.
N. Roussel, "Correlation between yield stress and slump: comparison between numerical simulations and concrete rheometers results," Materials and Structures, vol. 39, no. 4, pp. 501-509, 2006.
B. Patzak and Z. Bittnar, "Modeling of fresh concrete flow," Computers and Structures, vol. 87, no. 15, pp. 962-969, 2009.
S. Shao and E. Y. M. Lo, "Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface," Advances in Water Resources, vol. 26, no. 7, pp. 787-800, 2003.
S. Kulasegaram, B. L. Karihaloo, and A. Ghanbari, "Modelling the flow of self-compacting concrete," International Journal for Numerical and Analytical Methods in Geomechanics, vol. 35, no. 6, pp. 713-723, 2011.
H. Lashkarbolouk, M. R. Chamani, A. M. Halabian, and A. R. Pishehvar, "Viscosity evaluation of SCC based on flow simulation in L-box test," Magazine of Concrete Research, vol. 65, no. 6, pp. 365-376, 2013.
L.-C. Qiu, "Three dimensional GPU-based SPH modelling of self-compacting concrete flows," in Proceedings of the third international symposium on Design, Performance and Use of Self-Consolidating Concrete, pp. 151-155, RILEM Publications S.A.R.L, Xiamen, China, June 2014.
M. S. Abo Dhaheer, S. Kulasegaram, and B. L. Karihaloo, "Simulation of self-compacting concrete flow in the J-ring test using smoothed particle hydrodynamics (SPH)," Cement and Concrete Research, vol. 89, pp. 27-34, 2016.
J. Wu, X. Liu, H. Xu, and H. Du, "Simulation on the self-compacting concrete by an enhanced Lagrangian particle method," Advances in Materials Science and Engineering, vol. 2016, Article ID 8070748, 11 pages, 2016.
O. Svec, J. Skocek, H. Stang, M. R. Geiker, and N. Roussel, "Free surface flow of a suspension of rigid particles in a non-Newtonian fluid: a lattice Boltzmann approach," Journal of Non-Newtonian Fluid Mechanics, vol. 179-180, pp. 32-42, 2012.
A. Leonardi, F. K. Wittel, M. Mendoza, and H. J. Herrmann, "Coupled DEM-LBM method for the free-surface simulation of heterogeneous suspensions," Computational Particle Mechanics, vol. 1, no. 1, pp. 3-13, 2014.
K. N. Premnath and S. Banerjee, "On the three-dimensional central moment Lattice Boltzmann method," Journal of Statistical Physics, vol. 143, no. 4, pp. 747-794, 2011.
D. d'Humieres, I. Ginzburg, M. Krafczyk, P. Lallemand, and L.-S. Luo, "Multiple-relaxation-time lattice Boltzmann models in three dimensions," Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 360, no. 1792, pp. 437-451, 2002.
P. Lallemand and L.-S. Luo, "Theory of the lattice Boltzmann method: dispersion, isotropy, Galilean invariance, and stability," Physical Review E, vol. 61, no. 6, pp. 6546-6562, 2000.
S. G. Chen, C. H. Zhang, Y. T. Feng, Q. C. Sun, and F. Jin, "Three-dimensional simulations of Bingham plastic flows with the multiple-relaxation-time lattice Boltzmann model," Science China Physics Mechanics and Astronomy, vol. 57, no. 3, pp. 532-540, 2014.
S. Chen and G. D. Doolen, "Lattice Boltzmann method for fluid flows," Annual Review of Fluid Mechanics, vol. 30, no. 1, pp. 329-364, 1998.
S. Succi, H. Chen, and S. Orszag, "Relaxation approximations and kinetic models of fluid turbulence," Physica A: Statistical Mechanics and its Applications, vol. 362, no. 1, pp. 1-5, 2006.
Z. Guo, C. Zheng, and B. Shi, "Discrete lattice effects on the forcing term in the lattice Boltzmann method," Physical Review E, vol. 65, no. 4, p. 046308, 2002.
C. Korner, M. Thies, T. Hofmann, N. Thurey, and U. Rude, "Lattice Boltzmann model for free surface flow for modeling foaming," Journal of Statistical Physics, vol. 121, no. 1-2, pp. 179-196, 2005.
P. Prajapati and F. Ein-Mozaffari, "CFD investigation of the mixing of yield pseudo plastic fluids with anchor impellers," Chemical Engineering & Technology, vol. 32, no. 8, pp. 1211-1218, 2009.
M. S. Huang, The Application of Discrete Element Method on Filling Performance Simulation of Self-Compacting Concrete in RFC, Ph.D. thesis, Tsinghua University, Beijing, China, 2010, in Chinese.
Liu-Chao Qiu and Yu Han
College of Water Resources and Civil Engineering, China Agricultural University, Beijing 100083, China
Correspondence should be addressed to Liu-Chao Qiu; [email protected] and Yu Han; [email protected]
Received 21 June 2017; Accepted 2 November 2017; Published 28 January 2018
Academic Editor: Ying Li
Caption: Figure 1: Three-dimensional twenty-seven particle velocity (D3Q27) lattice.
Caption: Figure 2: Mass tracking algorithm scheme.
Caption: Figure 3: Slump test. (a) Experiment setup , (b) model size, and (c) LBM discretization.
Caption: Figure 4: The velocity distribution during the slump test. (a) t = 0.1s, (b) t = 0.2 s, (c) t = 0.3 s, (d) t = 0.5 s, (e) t = 1.0 s, and (f) t = 2.0 s.
Caption: Figure 5: Final spread of the slump test. (a) Experiment and (b) simulation.
Caption: Figure 6: The enhanced L-box test. (a) Experiment setup , (b) model size, and (c) LBM discretization.
Caption: Figure 7: The velocity distribution of the enhanced L-box test. (a) t = 0 s, (b) t = 25 s, (c) t = 50 s, (d) t = 75 s, (e) t = 100 s, (f) t = 125 s, (g) t = 150 s, (h) t = 175 s, (i) t = 200 s, (j) t = 225 s, (k) t = 250 s, and (l) final shape.
Caption: Figure 8: Final shape of SCC in the enhanced L-box test. (a) Experiment and (b) simulation.
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|Title Annotation:||Research Article|
|Author:||Qiu, Liu-Chao; Han, Yu|
|Publication:||Advances in Materials Science and Engineering|
|Date:||Jan 1, 2018|
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posted by chase
A fixed quantity of gas at 27°C exhibits a pressure of 729 torr and occupies a volume of 5.70 L.
(a) Use Boyle's law to calculate the volume the gas will occupy if the pressure is increased to 1.75 atm while the temperature is held constant.
(b) Use Charles's law to calculate the volume the gas will occupy if the temperature is increased to 154°C while the pressure is held constant.
see other post.
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http://www.mathisfunforum.com/post.php?tid=18275&qid=236332
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Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
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Topic review (newest first)
Bob bundy's way is the best way since it is only one step. Here is another neat way to do it but it takes a bit longer (it's how I did it though);
I still prefer the one-step method though, haha. So this post is a little redundant...
Anyway start with the left hand side:
Divide top and bottom by
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https://www.physicsforums.com/threads/rotational-dynamics-rod.385449/
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rotational dynamics rod--plz help! 1. The problem statement, all variables and given/known data A thin rod of length l and mass m is fixed at a far ends by a free pivot and held from rotating with a string attached at 3/4l and fixed toa ceiling. The moment of inertia of a thin rod about a far end is ml2/3 a) what is the pivot point exerting on the rod The rope is cut at t =0 seconds. at t =0 seconds find: b) the angular acceleration of the rod. c) the transverse acceleration of the rod's center of mass. d) the transverse aceleration of point A (the far end of the rod) e) the force exerted by the pivot point picture is attached.
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math
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Here you will find our range of challenging math problem worksheets which are designed to give children the opportunity to apply their skills and knowledge to solve a range of longer problems. These problems are also a great way of developing perseverance and getting children to try different approaches in their math. Children will enjoy completing these Math games and Free 4th Grade Math worksheets whilst learning at the same time.
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He separated 5 boxes of 24 away from the original 12 boxes, and made new packages with six highlighters in each package.
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https://www.pagalguy.com/t/advance-maths-for-beginners-concepts-and-doubts/3048171
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math
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to discuss advance maths topics in detail
wat is mid pt of triangle?
@SujataPatil @caemento When the question comes asking for maximum possiblities and minimum possibilities and includes variables, concentrate on two things 1. boundary conditions 2. which variables has to be considered or varied (this part comes only with practise)....... When too many variables are there, use options rather than solving and check if it satisfies the boundary conditions......
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@vishiac bro hav to ask few ques.... i too hav solved those... but having some confusion!!!
a)4 b)8 c)1 d)2
options 11, 83/9 7 13/9
if a^2=by+cz, b^2=cz+ax, and c^2=ax+by, then value of x/(a+x) +y/(b+y)+z/(c+z) is
options 1 a+b+c 1/a+1/b+1/c 0
The least number that must be substracted from 63520 to make the result a perfect square is
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http://www.wyzant.com/resources/answers/quadratic_equations?userid=7042039
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math
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-2(+ or -) 2i(square root 3) ------------------------------- 2 It is steps off of a quadratic formula.
solve the quadratic equation by completing the squares:3x^2-2x+1=5
solve using factor method
Are there any quadratic equations that cannot be solved by factoring? Why or why not?
This is a general question
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How do I write this equation in standard form? ax^2+bx+C
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9 x 2 - 9x + 2 = 0 x=
a cement walk of constant width is built around a 20-ft by 40-ft rectangular pool. The total area of the pool and the walk is 1500ft sq. Find the width of walk
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This is what i am supposed to do: -introduce the angry bird level that you are using -picture of level with the best possible opening shots graphed in geogebra -explanation of why this...
I'm solving a quadratic equation which is 2x^2-x-10=0 and I know that a=2 b=-1 and c=-10 ans with the problem put it into the formula which is -(-10 +- √ -1^2-4(2)(-10) and when I get my answer...
How to find the solution set by factoring and using the zero product rule or by quadractic formula
7x2-4x. How do you factor completely?
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I keep getting the wrong answer and I dont know what step im missing.
I'm not sure if I have the right answer so I hope one of you can answer this and see for me. I came up with x^2+3x+2=0
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https://www.allinterview.com/interview-questions/80-255/civil-engineering.html
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math
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How much concreat we make by 1 bag cement? (ratio- 1:1.5:3 or 1:2:4)2 2695
How much cost will come for 900 sq ft cement plastering630
how ratio is calculated for any grade of concrete. for e.g. sppose M20 requires(x;y:z) quantity of cememt sand and aggregate.527
How much 1sqft area reinforce formula properly define1 1851
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how many cement bags required for one cum of brick work the brick size is 20x10x10.1 2091
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silt%= silt volume/ silt+sand volume is this right?
pile load testing procedure
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if dia of inner circle is 42 m and depth is 1.5 m and width is 1 m ,then whait is the quantity of steel?
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it is a corrected question." make a list of engineering property(properties) of soil.
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Before casting a basement roof slab which is connected with retaining wall surcharge load (i.e. sand or earth filling) outside the retaining wall is prohibited because of––
from one meter cube of stone masonry structure how much cubic meter of cement mortar we use as our estimation 25-30% is that correct for estimation of quantity of sand and cement(2:1) proportion of mortar
what is the cost difference of a same structure when it is constructed with brick masonary and when it is constructed with block masonary and concrete as a frame structure????????????????????????
Please Clear My doubt . We Can Design the size of the beam by manually by the Length of the beam...What is the technique adopted
what does the grad of cement shows (denotes)?
cement, sand, aggregate,reinforcement & concrete consumption per square feet in multi storeyed building
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https://db0nus869y26v.cloudfront.net/en/Theorem_of_the_gnomon
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The theorem of the gnomon states that certain parallelograms occurring in a gnomon have areas of equal size.
In a parallelogram with a point on the diagonal , the parallel to through intersects the side in and the side in . Similarly the parallel to the side through intersects the side in and the side in . Then the theorem of the gnomon states that the parallelograms and have equal areas.
Gnomon is the name for the L-shaped figure consisting of the two overlapping parallelograms and . The parallelograms of equal area and are called complements (of the parallelograms on diagonal and ).
The proof of the theorem is straightforward if one considers the areas of the main parallelogram and the two inner parallelograms around its diagonal:
The theorem of the gnomon can be used to construct a new parallelogram or rectangle of equal area to a given parallelogram or rectangle by the means of straightedge and compass constructions. This also allows the representation of a division of two numbers in geometrical terms, an important feature to reformulate geometrical problems in algebraic terms. More precisely, if two numbers are given as lengths of line segments one can construct a third line segment, the length of which matches the quotient of those two numbers (see diagram). Another application is to transfer the ratio of partition of one line segment to another line segment (of different length), thus dividing that other line segment in the same ratio as a given line segment and its partition (see diagram).
A similar statement can be made in three dimensions for parallelepipeds. In this case you have a point on the space diagonal of a parallelepiped, and instead of two parallel lines you have three planes through , each parallel to the faces of the parallelepiped. The three planes partition the parallelepiped into eight smaller parallelepipeds; two of those surround the diagonal and meet at . Now each of those two parallepipeds around the diagonal has three of the remaining six parallelepipeds attached to it, and those three play the role of the complements and are of equal volume (see diagram).
The theorem of gnomon is special case of a more general statement about nested parallelograms with a common diagonal. For a given parallelogram consider an arbitrary inner parallelogram having as a diagonal as well. Furthermore there are two uniquely determined parallelograms and the sides of which are parallel to the sides of the outer parallelogram and which share the vertex with the inner parallelogram. Now the difference of the areas of those two parallelograms is equal to area of the inner parallelogram, that is:
This statement yields the theorem of the gnomon if one looks at a degenerate inner parallelogram whose vertices are all on the diagonal . This means in particular for the parallelograms and , that their common point is on the diagonal and that the difference of their areas is zero, which is exactly what the theorem of the gnomon states.
The theorem of the gnomon was described as early as in Euclid's Elements (around 300 BC), and there it plays an important role in the derivation of other theorems. It is given as proposition 43 in Book I of the Elements, where it is phrased as a statement about parallelograms without using the term "gnomon". The latter is introduced by Euclid as the second definition of the second book of Elements. Further theorems for which the gnomon and its properties play an important role are proposition 6 in Book II, proposition 29 in Book VI and propositions 1 to 4 in Book XIII.
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https://scholar.nycu.edu.tw/zh/publications/covering-graphs-with-matchings-of-fixed-size
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math
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Let m be a positive integer and let G be a graph. We consider the question: can the edge set E (G) of G be expressed as the union of a set M of matchings of G each of which has size exactly m? If this happens, we say that G is [m]-coverable and we call M an [m]-covering of G. It is interesting to consider minimum[m] -coverings, i.e. [m]-coverings containing as few matchings as possible. Such [m]-coverings will be called excessive[m] -factorizations. The number of matchings in an excessive [m]-factorization is a graph parameter which will be called the excessive[m] -index and denoted by χ[m]′. In this paper we begin the study of this new parameter as well as of a number of other related graph parameters.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154320.56/warc/CC-MAIN-20210802110046-20210802140046-00202.warc.gz
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CC-MAIN-2021-31
| 715 | 1 |
https://www.topperlearning.com/icse-class-8-maths/probability
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math
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ICSE Class 8 Maths Probability
What can be the possible outcomes when a die is thrown? What is the possibility that the total pages chosen at random is 12? Our ICSE Class 8 Maths Chapter 24 resource notes will help you find the answers by using the concept of Probability.
The exam questions which are likely to come from this chapter are simple application-based problems. You need to work on your logical thinking ability by practising problems from this chapter. Now, you can relearn the Probability lesson and improve your logical thinking ability with TopperLearning’s study materials. Also, these easy-to-access study materials are designed as per the latest ICSE Class 8 Mathematics syllabus.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335504.37/warc/CC-MAIN-20220930212504-20221001002504-00213.warc.gz
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CC-MAIN-2022-40
| 701 | 3 |
https://ez.analog.com/wide-band-rf-transceivers/design-support-ad9371/f/discussions/535795/ad9375-full-scale-power/389599
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math
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I've read the previous discussions on this matter and find the common answer seems to be:
0.707 mVpp which corresponds to +7 dBm based on a 50ohm system.
Also, commonly cited is a note about Sigma-Delta Converters exhibiting a soft overload characteristic, which is only important near maximum inputs.
We are using the AD9375 EVM connected to a custom FPGA EVM. We have a RSSI calculation block built into our RX Signal Chain. This block does a sum of I^2 + Q^2 of the received samples and we then use that to calculate RSSI of our input signal.
For testing and calibration we use a CW tone, 1MHz offset from the tuned frequency. Applying the +7 dBm Full Scale Power, the calculation seems to be about 16.4 dB off expected.
To troubleshoot, I performed the following test. Using a calibrated cable connected between the Sig Gen and the 9375 EVM RX1 port at 680 MHz, Rx tuned to 679 MHz, RX1 Gain index set to 255 (0 dB of attenuation), Logic Analyzer connected to capture the raw 14 bit JESD I/Q samples from the 9375, I see a very nice sinewave with peak amplitude of 2414. Since the samples are 14 bits, this is 2414/8191 in amplitude. 20 * log10(2414/8191) is -10.6 dB. This says my signal is -10.6 dB below full scale. My input is -20.0 dBm, so this says Full Scale Power is actually -9.4 dBm.
I understand the recommended max input to the 9375 is -14 dBm, but I was able to get up -11 dBm with no noticeable distortion in the observed sinewave samples, got a peak sample value of 6840, which using the same math as above yields -1.56 dB or a SP of -9.4 again.
Can you please advise where I went wrong in my assessment of Full Scale Power?
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587963.12/warc/CC-MAIN-20211026231833-20211027021833-00093.warc.gz
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CC-MAIN-2021-43
| 1,643 | 8 |
https://cfrce.com/geometric-mechanics
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math
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Geometric Mechanics & Dynamical Systems
“Formal perfection, in mathematics, is never negligible; it is even a necessary ingredient for progress. However, it seems that the classical formalization of analytical mechanics has overlooked an important part of Lagrange's ideas. Without doubt this happened because the mathematics of the first part of the 19th century did not have the necessary scope; also because the successes of the theory (first in celestial mechanics and later in statistical mechanics) hid the necessity of questioning categories so classical that they seemed natural. One had to wait until the 20th century to learn that the words time, space, and matter do not have any direct physical meaning, but are only formal symbols of revisable physical theories, and nowadays are outdated.
Analytical mechanics is not an outdated theory, but it appears that the categories which one classically attributes to it such as configuration space, phase space, Lagrangian formalism, Hamiltonian formalism, are, simply because they do not have the required covariance; in other words, because these categories are in contradiction with Galilean relativity. A fortiori, they are inadequate for the formulation of relativistic mechanics in the sense of Einstein.”
- J M Souriau, “Structure of Dynamical Systems”
Geometric Mechanics is Classical Mechanics formulated in the language of modern Differential Geometry. Of course, while Lagrangian Mechanics, to a certain extent, retains the standard Differential Geometric form, Hamiltonian Mechanics alters it significantly enough to give it a special name, -Symplectic Geometry. Lagrangian Mechanics itself initially takes the form of Riemannian Geometry as was first clearly demonstrated by Hertz in his “Principles of Mechanics.” The departure from Riemannian to Symplectic takes place via the Legendre transform (or fibre derivative, in symplectic language) that maps the Lagrangian to the Hamiltonian. When the transform is regular (or rather, hyperregular), the map in a sense, takes the “velocities” to the “momenta.” Otherwise, there arise singular constraints and need to be treated quite differently.
John L. Synge was one of the first to cast Lagrangian Mechanics into a geometric framework. In his beautiful Handbuch der Physik encyclopedia article, he gave a treatment of Lagrangian Mechanics as Riemannian Geometry. But the modern, qualitative-quantitative form of Mechanics really took off with Henri Poincare’s introduction of the qualitative methods of Topological Analysis into Mechanics. His methods were characterised by the global geometric point of view. He treated a dynamical system as a vector field on the phase space of the system. A solution then corresponded to a smooth curve tangent at each of its points to the vector based at that point. This global point of view was capable of giving the complete information of the dynamical system. The manifold or bundle that arose could then be studied and the necessary structures like the metric, connections, almost-tangent structures, almost-complex structures as have now been developed, could be imposed. After Poincare, George Birkoff contributed immensely to the development of Dynamical systems, with the publication of his American Mathematical Society monograph, “Dynamical Systems,” one of the most illuminating books on the subject.
But there was another immense source of ideas and methods infiltrating into Mechanics. It was that of Elie Cartan. Elie Cartan’s work revolutionised Mechanics like nothing before. His powerful Exterior Calculus and classification of Lie Algebras and Lie Groups changed the face of Mechanics forever.
These twin streams of ideas and methods, from Poincare and Cartan were taken up by a new generation of mathematicians and the very fertile field of Geometric Mechanics was born. Presently, Geometric Mechanics has matured to take the shape of one of the most extensively developed and developing fields of Mathematics and Mathematical Physics.
Source Books & Links
- V I Arnold - Mathematical Methods of Classical Mechanics: The most straightforward and enjoyable introduction to Geometric Mechanics, and indeed, to modern Differential Geometric and Symplectic methods in Physics.
- Abraham and Marsden - Foundations of Mechanics: The most extensive, rigorous, complete and beautiful treatment of Geometric Mechanics, Dynamical Systems and Topological Dynamics in the field.
- G Marmo, Salaten, Simoni, Vitale - Dynamical Systems, A Differential Geometric Approach to Symmetry and Reduction: The most insightful and beautiful treatment of the subject with an orientation towards physical intuition.
Henri Poincare: The last “Universalist,” as E. T. Bell calls him in his “Men of Mathematics,” and perhaps the greatest mathematician of the 20th Century sharing that position only with David Hilbert. Poincare is the real founder of modern Geometric Mechanics with his introduction of qualitative methods into the analysis of dynamical systems. In his researches on Celestial Mechanics, he was led to introduce the enormously insightful concept of the phase portrait. Almost in parallel, he initiated Analysis Situs, that developed and matured into modern Topology. As he writes, “As for me all all the various journeys, one by one I found myself engaged, were leading me to Analysis Situs.”
He explained what he meant by Analysis Situs as follows.
“L’ Analysis Situs est la science qui nous fait connaitre les proprettes qualitatives des figures géométriques non seulement dans l’ espace ordinaire, mais dans l’ espace a plus trois dimensions. L’ Analysis Situs a trois dimensions est pour nous une connaissance presque intuitive, L’ Analysis Situs a plus de trios dimensions au contraire des difficultés énormes; il faut pour tenter de les surmounter être bien persuade de l’ extreme importance de cette science.”
(“Analysis Situs is a science which lets us learn the qualitative properties of geometric figures not only in the ordinary space, but also in the space of more than three dimensions. Analysis Situs in three dimensions is almost intuitive knowledge for us. Analysis Situs in more than three dimensions presents, on the contrary, enormous difficulties, and to attempt to surmount them, one should be persuaded of the extreme importance of this science. If this importance is not understood by everyone, it is because everyone has not sufficiently reflected upon it.”)
The modern theory of Dynamical Systems, singularities and bifurcations, Chaos, and a host of topological and differential geometric constructions are an offshoot of Poincare’s ideas.
George D Birkhoff: Birkhoff proved Poincare’s Geometric Theorem almost immediately as it was posed by Poincare. The theorem may be stated in a simple form as follows: Let us suppose that a continuous one-to-one transformation T takes the ring R, formed by concentric circles Ca and Cb of radii a and b respectively (a > b > 0), into itself in such a way as to advance the points of Ca in a positive sense, and the points of Cb in the negative sense, and at the same time to preserve areas. Then there are at least two invariant points.
Birkhoff’s American Mathematical Society monograph, “Dynamical Systems,” is a classic and one of the first books that is still worth reading for its elegant treatment of the subject.
Constantin Caratheodory: Was David Hilbert’s successor at Gottingen University and a versatile mathematician and one of the most insightful developers of the field of Partial Differential Equations, the Calculus of Variations and Complex Function Theory. His 2-Volume monograph, “Calculus of Variations and Partial Differential Equations of First Order,” is the finest book on the Calculus of Variations and Partial Differential Equations and develops especially the Hamilton-Jacobi theory in all its detail. His book on Function theory is a classic. His approach to the second law of thermodynamics, captured by the famous “Caratheodory’s Theorem,” (as presented for example, in S. Chandrasekhar’s Introduction to the Study of Stellar Structure) is elegant and is taken as the starting point in several treatments of the subject.
Jacques Hadamard: One of the greatest mathematicians of the 20th Century and perhaps the most influential next only to Poincare, Hilbert and Weyl, and in the same class as Elie Cartan, Hadamard inspired and guided an entire generation of mathematicians including Nicholas Bourbaki, Andre Weil, Jean Dieudonne, John Leray, Laurent Schwartz…Hadamard had an pervasive influence on modern mathematics and in Geometric Mechanics his name is associated with the Cartan-Hadamard theorem a statement in Riemannian geometry concerning the structure of complete Riemannian manifolds of non-positive sectional curvature.
Elie Cartan: One of the greatest mathematicians of all time, and unquestionably, the greatest geometer of the 20th Century, Elie Joseph Cartan’s influence on mathematics and mathematical thought has been all-pervading, from Differential Geometry, Topology, Lie Groups and Lie Algebras, Theory of Spinors (that he had introduced and developed earlier to Dirac), General Relativity (the famous Einstein-Cartan theory), the classification problem of Riemannian manifolds. His most important contribution being the exterior derivative that changed Calculus forever after Newton and Leibniz. The modern coordinate-free approach that pervades modern physics is due to him. He was also the first to cast Newtonian mechanics into geometric form. After Poincare, it was Elie Cartan who inspired an entire generation of mathematicians including that of Nicholas Bourbaki. In a sense, therefore, it is Elie Cartan who laid the structural foundations of Geometric Mechanics and Dynamical Systems. His obituary by Chern and Chevalier, “Elie Cartan and his Mathematical Work,” and biography by Akvis and Rosenfeld, Elie Cartan, is a most inspiring and instructive read. Cartan’s own works were not that easy to read.
In Robert Bryant's words, “You read the introduction to a paper of Cartan and you understand nothing. Then you read the rest of the paper and still you understand nothing. Then you go back and read the introduction again and there begins to be the faint glimmer of something very interesting.” Nevertheless, his books, “Leçons sur les invariants intégraux” and “Leçons sur la géométrie des espaces de Riemann” are masterpieces of mathematical writing.
Amalie Emmy Noether: One of the greatest mathematicians of the 20th Century and whose work forms the cornerstone of the foundations of Classical Mechanics, Field Theory and Gauge Theory. Indeed, it is impossible to imagine proceeding in any of these fields without encountering “Noether’s theorem.” Albert Einstein wrote of her, “In the judgment of the most competent living mathematicians, Fraulein Noether was the most significant creative mathematical genius since the higher education of women began”. Noether’s first and second theorems are the starting point of field theory and of Singular Constraint Systems. Nina Byer’s two articles, “The Life and Times of Emmy Noether,” and “Emmy Noether’s Discovery of the Deep Connection between Symmetry and Conservation Laws,” are most instructive to read.
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CC-MAIN-2019-13
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https://goldams.com/a-three-question-quiz/
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math
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In “Clever fools: Why a high IQ doesn’t mean you’re smart” (New Scientist, 02 November 2009), Michael Bond said:
When Shane Frederick at the Yale School of Management in New Haven, Connecticut, put [these] counter-intuitive questions to about 3400 students at various colleges and universities in the US – Harvard and Princeton among them – only 17 per cent got all three right (see “Test your thinking”). A third of the students failed to give any correct answers (Journal of Economic Perspectives, vol 19, p 25). © Copyright Reed Business Information Ltd.Here are the questions (click on the link for the answers):
1) A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost? 2) If it takes five machines 5 minutes to make five widgets, how long would it take 100 machines to make 100 widgets? 3) In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of it? © Copyright Reed Business Information Ltd.Yes, I got all three right. And it didn’t take very long. Note that they are all math questions. Another question (more “logical” than “mathematical”) asked in the article is:
Jack is looking at Anne, and Anne is looking at George; Jack is married, George is not. Is a married person looking at an unmarried person?
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573533.87/warc/CC-MAIN-20220818215509-20220819005509-00659.warc.gz
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CC-MAIN-2022-33
| 1,428 | 4 |
https://scholarship.claremont.edu/hmc_fac_pub/590/
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math
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A Fast Parallel Algorithm for Routing in Permutation Networks
An algorithm is given for routing in permutation networks-that is, for computing the switch settings that implement a given permutation. The algorithm takes serial time O(n(log N)2) (for one processor with random access to a memory of O(n) words) or parallel time O((log n)3) (for n synchronous processors with conflict-free random access to a common memory of O(n) words). These time bounds may be reduced by a further logarithmic factor when all of the switch sizes are integral powers of two.
© 1981 Institute of Electrical and Electronics Engineers
Lev, G.F.; Pippenger, N.; Valiant, L.G., "A fast parallel algorithm for routing in permutation networks," Computers, IEEE Transactions on , vol.C-30, no.2, pp.93,100, Feb. 1981 doi: 10.1109/TC.1981.6312171
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CC-MAIN-2021-17
| 821 | 4 |
https://www.hackmath.net/en/math-problem/2655
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math
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Paul save 155Kč in 46 2 Kc and 5Kc coins. How much saved 2Kc and 5Kc coins?
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In ticket maschine were together one hundred coins. They were only 20 and 50 cent coins. The sum total was 29 euros and 60 cents. How many were in ticket maschine coins and which type?
Jane buy gift together for 464 Sk. For tie paid 4.5 times less than in the shirt, but 56 Sk more than for socks. How much she paid for each item in gift?
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When Lenka bought pants from 1/3 of her savings shirt from 1/5 and 1/8 spent at the hairdresser, she is left 328 Kč. How much money was saved? How much hairdresser cost?
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At the beginning of the year, Tomas had saved 230kc, after half a year even 590 CZK. How many crowns did he save each month when saving the same amount?
We want to prepare 5 kg of sweets for 150 CZK. We will mix cheaper candy: 1 kg for 120 CZK and more expensive candy: 1 kg per 240 CZK. How much of this two types of candy is necessary to prepare this mixture?
On the football tournament ticket cost 45 Kc for standing and 120kč for sitting. Sitting spectators was 1/3 more than standing. The organizers collected a total 12 300 Kc. How many seated and standing seats (spectators)?
Along the road were planted 250 trees of two types. Cherry for 60 CZK apiece and apple 50 CZK apiece. The entire plantation cost 12,800 CZK. How many was cherries and apples?
Create a mixture of 50 kg of candy on price 700Kč. Candies has prices: 820Kč, 660Kč and 580Kč. Use cross rule.
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Of the two sort of tea at a price of 180 CZK/kg and 240 CZK/kg we make a mixture 12 kg that should be prepared at a price of 200 CZK / kg. How many kilos of each sort of tea will we need to be mixed?
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Tea blends are maked from two kinds of tea. In standard tea mixture are two teas in the ratio 1:3 and 40 g costs 42 CZK. In the premium tea mixture are weighing two teas in the ratio 1:1 and 50 grams costs 60 CZK. How much cost 10 grams of more expensive
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CC-MAIN-2020-50
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https://www.brighthubengineering.com/hydraulics-civil-engineering/49592-accelerations-in-fluid-flow/
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math
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After the basic description of the position and velocity for fluid flow analysis, let us move up one more step to another higher derivative of position, acceleration. Mathematically the acceleration of fluid particles in any flow field is the first derivative of the velocity vector of the flow field. And generally the velocity vector of any flow field description is a function of space as well as time.
Acceleration of Fluid Particles
Physically acceleration of any object is a measure of the change in its velocity. If the velocity vector of any fluid flow is a function of space and time, then it can change with space and as well as with time. Thus the acceleration, or change in velocity, experienced by the fluid particles can be due to the change of velocity with space and can be due to the change of velocity with time.
The acceleration of fluid particles due to change in velocity in space is called convective acceleration and acceleration due to change in velocity in time is called local or temporal acceleration. Acceleration of fluid particles can thus have two components: tangential and normal acceleration.
Tangential acceleration is due to the change in velocity along the direction of motion. This tangential change in velocity or the tangential acceleration of fluid particles is the sum of tangential convective (change with space) and tangential local (change with time) accelerations.
Normal acceleration of any particle is the component of the change in velocity normal to the direction of motion or the tangential velocity. Normal acceleration comes into picture when fluid particles move in curved paths. While moving in curved paths the velocity of the fluid particle changes in direction; it can also change in magnitude, too.
For motion of fluid particles along curved paths the change in velocity has two components, one along the direction of motion and other normal to that. Obviously the normal component produces the normal acceleration. Like tangential acceleration normal acceleration is also the sum of convective and local acceleration components.
Examples of Acceleration in Fluid Flow
Examples of Acceleration in Fluid Flow
Generally acceleration of fluid flow has two components, convective (with space) and local (with time). But for steady flow, where flow field is constant in time, fluid flow experiences only convective acceleration.
No Acceleration: For the steady flow through straight and parallel boundaries with constant cross section the velocity of flow doesn’t change, so, there is no type of acceleration.
Tangential Convective Acceleration/ Deceleration: For straight and converging boundaries the flow speed increases with decreasing area of cross section. The speed of flow increases but the direction remains same, thus, the flow experiences tangential convective acceleration only. The fluid flow through straight and diverging boundaries experiences tangential convective deceleration.
Normal Convective Acceleration: Flow through the concentric curved boundaries has parallel streamlines and velocity of flow is constant along the flow direction. The flow through such paths experiences only normal convective acceleration.
Tangential Acceleration/Deceleration and Normal Acceleration: Fluid flow through converging curved boundaries will accelerate along the flow with decreasing cross sectional area and also experience acceleration normal to the flow direction because of the curved path. And for diverging curved boundaries, fluid experiences tangential deceleration as well as normal acceleration.
This post is part of the series: Analysis of Fluid Flow
For the efficient design of the hydraulic systems in civil engineering it is very important to first analyze the flow of fluid through the system. This article series tells what the concepts for analysis of fluid flow are and how these concepts are used in the context of the fluid flow analysis?
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s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347414057.54/warc/CC-MAIN-20200601040052-20200601070052-00250.warc.gz
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CC-MAIN-2020-24
| 3,922 | 16 |
https://www.sonikaanandacademy.com/blog/reflection-and-refraction-of-light
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math
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google.com, pub-2985501598867446, DIRECT, f08c47fec0942fa0
Reflection and Refraction of Light
Define focus . If the radius of curvature of mirror is 20 cm find its focal length
Que - Define power of lens ? what is its unit? Find the power of lens having focal length 2 m and focal length 50 cm
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Que -What is refraction give laws of refraction?
Que - A concave mirror produces three times magnified real image of an object placed in front of 10 cm where is image located
Sat Dec 3, 2022
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224650264.9/warc/CC-MAIN-20230604193207-20230604223207-00135.warc.gz
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CC-MAIN-2023-23
| 934 | 15 |
https://www.econstor.eu/handle/10419/179170?locale=de
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math
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In this paper, we present an application of the dynamic tracking games framework to a monetary union. We use a small stylized nonlinear three-country macroeconomic model of a monetary union to analyze the interactions between fiscal (governments) and monetary (common central bank) policy makers, assuming different objective functions of these decision makers. Using the OPTGAME algorithm, we calculate solutions for several games: a noncooperative solution where each government and the central bank play against each other (a feedback Nash equilibrium solution), a fully-cooperative solution with all players following a joint course of action (a Pareto optimal solution) and three solutions where various coalitions (subsets of the players) play against coalitions of the other players in a noncooperative way. It turns out that the fully-cooperative solution yields the best results, the noncooperative solution fares worst and the coalition games lie in between, with a broad coalition of the fiscally more responsible countries and the central bank against the less thrifty countries coming closest to the Pareto optimum.
dynamic game feedback Nash equilibrium Pareto solution monetary union macroeconomics public debt coalitions
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s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141195745.90/warc/CC-MAIN-20201128184858-20201128214858-00636.warc.gz
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CC-MAIN-2020-50
| 1,236 | 2 |
https://research.chalmers.se/publication/514834
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math
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Writing the History of Mathematics: Interpretations of the Mathematics of the Past and Its Relation to theMathematics of Today
Kapitel i bok, 2019
In the present chapter, interpretations of the mathematics of the past are problematized, based on examples such as archeological artifacts, as well as written sources from the ancient Egyptian, Babylonian, and Greek civilizations. The distinction between history and heritage is considered in relation to Euler’s function concept, Cauchy’s sum theorem, and the Unguru debate. Also, the distinction between the historical past and the practical past, as well as the distinction between the historical and the nonhistorical relations to the past, are made concrete based on Torricelli’s result on an infinitely long solid from the seventeenth century. Two complementary but different ways of analyzing the mathematics of the past are the synchronic and diachronic perspectives, which may be useful, for instance, regarding the history of school mathematics. Furthermore, recapitulation, or the belief that students’ conceptual development in mathematics is paralleled to the historical epistemology of mathematics, is problematized emphasizing the important role of culture.
History of mathematics,
Synchronic and diachronic perspectives,
History and heritage,
Epistemology of mathematics,
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s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738878.11/warc/CC-MAIN-20200812053726-20200812083726-00247.warc.gz
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CC-MAIN-2020-34
| 1,343 | 7 |
https://www.law.cornell.edu/cfr/text/42/412.322
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math
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42 CFR § 412.322 - Indirect medical education adjustment factor.
(a) Basic data. CMS determines the following for each hospital:
(3) The measurement of teaching activity is the ratio of the hospital's full-time equivalent residents to average daily census. This ratio cannot exceed 1.5.
(b) Payment adjustment factor. The indirect teaching adjustment factor equals [e (raised to the power of .2822 × the ratio of residents to average daily census)−1].
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s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988753.97/warc/CC-MAIN-20210506114045-20210506144045-00590.warc.gz
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CC-MAIN-2021-21
| 455 | 4 |
https://www.hindawi.com/journals/ahep/2020/7032834/
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math
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Research Article | Open Access
R. G. G. Amorim, S. C. Ulhoa, J. S. da Cruz Filho, A. F. Santos, F. C. Khanna, "Spin-1/2 Particles in Phase Space: Casimir Effect and Stefan-Boltzmann Law at Finite Temperature", Advances in High Energy Physics, vol. 2020, Article ID 7032834, 8 pages, 2020. https://doi.org/10.1155/2020/7032834
Spin-1/2 Particles in Phase Space: Casimir Effect and Stefan-Boltzmann Law at Finite Temperature
The Dirac field, spin 1/2 particles, is investigated in phase space. The Dirac propagator is defined. The Thermo Field Dynamics (TFD) formalism is used to introduce finite temperature. The energy-momentum tensor is calculated at finite temperature. The Stefan-Boltzmann law is established, and the Casimir effect is calculated for the Dirac field in phase space at zero and finite temperature. A comparative analysis with these results in standard quantum mechanics space is realized.
The Wigner function formalism [1, 2] and noncommutative geometry play a fundamental role in the study of phase space quantum mechanics. The Wigner formalism enables a quantum operator, , defined in the Hilbert space, , to have an equivalent function of the type , in phase space , using the Moyal-product or star-product (å). Such a formalism leads to the classical limit of a quantum theory. In fact, quantum mechanics is a noncommutative theory whose representation in phase space is an object of debate. The opposite question, i.e., for a given classical function, what is its quantum counterpart? It is solved by using the Weyl transformation which is formulated independent of the phase space. In fact, it can be established within the configuration space of the generalized coordinates. The phase space has a well-defined physical meaning. The Hamiltonian function is naturally identified with the energy of the system. Establishing a field theory in phase space sheds light on some obscure points in quantum mechanics. For instance, the quantum symmetries are better understood in the symplectic structure of phase space which is similar to the role of Lorentz transformation in the covariant formulation of special relativity. This theoretical framework has to include a finite temperature in order to be suitable for experiments.
The star product has been employed for different objectives. In particular, it has been used for development of a nonrelativistic quantum mechanics formalism in terms of a phase space using the Galilean symmetry representation . Thus, the Schrödinger equation is obtained. In this case, the wave function is a quasiprobability amplitude defined in phase space and the Wigner function is obtained in an alternative way, i.e., by using . The Dirac equation coupled with the electromagnetic field in phase space and applications has been obtained.
Our goal is to explore the quasiprobability amplitude to study the effect of temperature using Thermo Field Dynamics (TFD) formalism [7–13] in a system for spin-1/2 particles. The principles of this theory are the duplication of the Fock space using the Bogoliubov transformations. The TFD formalism is used to study the Casimir effect, at zero and finite temperature. The scalar field in phase space has been studied , and some exclusive effects have been found at finite temperature. In addition, the Stefan-Boltzmann law for spin- particles in phase space is described in details.
In Section 2, the symplectic Dirac field is introduced. In Section 3, the Thermo Field Dynamics formalism is presented. In Section 4, the Stefan-Boltzmann law is established and the Casimir effect for the Dirac field is calculated in phase space at zero and finite temperature. In the last section, some concluding remarks are presented.
2. Spin-1/2 Field in Phase Space
A brief outline for spin-1/2 particles in phase space formalism is described. For this purpose, the following star operators in phase space are defined: which satisfy the Heisenberg commutation relation , with . The Poincaré algebra has the form
The operators in Equations ((1)–(3)) are defined on a Hilbert space, , associated with the phase space . The operators and stand for translations, rotations, and boosts, respectively. Functions defined on the Hilbert space are defined as
The Casimir invariants are and , where are Pauli-Lubansky matrices and is the Levi-Civita symbol.
The Dirac equation in phase space is obtained using the invariant operator . It is defined as where are the Dirac matrices. The Lagrangian density for the Dirac equation is where and is the mass of the particle.
The Wigner function provides the physical interpretation and is given as where the star product is defined by
Using the Noether theorem in phase space , the energy-momentum tensor for the Dirac field is
Then, the Green function, , is defined as which may be written as where . The propagator of the Dirac field is
Taking , the expression is
This leads to the Green function for the Dirac equation in phase space
is defined as where is the modified Bessel function. It should be noted that due to the dependence on the Dirac matrices, the Green’s function has matrix properties itself.
3. Thermo Field Dynamics Formalism
The Thermo Field Dynamics (TFD) is a thermal quantum field theory at finite temperature [7–13]. It has two basics elements: (i) doubling the degrees of freedom in a Hilbert space and (ii) the Bogoliubov transformation. The doubling of Hilbert space is given by the tilde () conjugate rules where the thermal space is , with being the standard Hilbert space and the tilde (dual) space. There is a mapping between the two spaces; i.e., the map between the tilde and nontilde operators is defined by the following tilde conjugation rules: with for bosons and for fermions.
The Bogoliubov transformation corresponds to a rotation of the tilde and nontilde variables. Using the doublet notation, for fermions leads to where are creation operators, are destruction operators, and is the Bogoliubov transformation given by
Taking ( with being the Boltzmann constant and the temperature), the thermal operators are written explicitly as
These thermal operators satisfy the algebraic rules and other anticommutation relations are null. In addition, the quantities and are related to the Fermi distribution, i.e., such that . The parameter is associated with temperature, but, in general, it may be associated with other physical quantities. In general, a field theory on the topology with , is considered. are the space-time dimensions, and is the number of compactified dimensions. This establishes a formalism such that any set of dimensions of the manifold can be compactified, where the circumference of the th is specified by . The parameter is assumed as the compactification parameter defined by . The effect of temperature is described by the choice and .
Any field in the TFD formalism may be written in terms of the parameter. As an example, the scalar field is considered. Then, the -dependent scalar field becomes where the Bogoliubov transformation is used.
The -dependent propagator for the scalar field is where is the time-ordering operator. Using leads to the Green function where with being the Bogoliubov transformation and where is the scalar field propagator and is the scalar field mass. Here, is the complex conjugate of .
It is important to note that the physical quantities are given by the nontilde variables. Then, the physical Green function is written as where is the generalized Bogoliubov transformation , where is the number of compactified dimensions, for fermions (bosons), denotes the set of all permutations with elements, and is the 4-momentum. In the next section, three different topologies are used : (i) the topology , where . In this case, the time axis is compactified in , with circumference ; (ii) the topology with , where the compactification along the coordinate is considered; and (iii) the topology with is used. In this case, the double compactification consists in time and the coordinate . Then, thermal effects are considered for the Casimir effect and Stefan-Boltzmann law.
4. Stefan-Boltzmann Law and Casimir Effect for the Dirac Field in Phase Space
The Stefan-Boltzmann law is calculated by analyzing the energy-momentum tensor given as where
It should be noted that the field is the Dirac field in phase space as a function of the variables (), i.e., . The vacuum expectation value of the energy-momentum tensor is
The Dirac propagator in phase space is defined in Equation (16) as
Then, the energy-momentum tensor has the form
The vacuum average of the energy-momentum tensor in terms of -dependent fields becomes
In order to obtain measurable physical quantities at finite temperature, a renormalization procedure is carried out. The physical energy-momentum tensor is defined as where
Now, the Stefan-Boltzmann law and the Casimir effect in phase space are calculated at finite temperature.
4.1. Stefan-Boltzmann Law
The study of the Stefan-Boltzmann law in phase space corresponds to a choice of the parameter . It is important to note that the parameter is the compactification parameter that is defined as . The temperature effect is described by the choice
The generalized Bogoliubov transformation, Equation (31), for these parameters is
The Green’s function for the Dirac field in phase space is where is a time-like vector. Then, the physical energy-momentum tensor is
In order to calculate the Stefan-Boltzmann law, taking leads to
This is the Stefan-Boltzmann law for the Dirac field in phase space. It is worth pointing out that the result is recovered by taking the limit of the momentum variable. This result in phase space is necessary to compare with experiments. In this sense, we can integrate over the momenta which explicitly yield and take the limit; then, the only remaining part is the factor ofthat leads to the dependency , once the limit of Bessel function is taken. On the other hand, it is possible to project in the momentum space by integrating over coordinates. This process leads to a divergence which is of the same nature of the coordinate projection in the absence of temperature. Hence, a quantity in the momentum space analogous to the temperature is necessary, that is, the thermal energy. The introduction of TFD formalism introduces the role of temperature, but it can equally do the same for the thermal energy. Using phase space and TFD allows us to deal with systems where microscopic energy is dominant.
4.2. Casimir Effect for the Dirac Field in Phase Space
Here, the choice is , then
The Green function is this case is where is a space-like vector. Then, the energy-momentum tensor is
By taking , the Casimir energy for the Dirac field in phase space at zero temperature is
And for , the Casimir pressure in phase space is
It reproduces the usual result when and integrated over the momenta which means the projection on coordinate space. Then, only the factors of is left; the limit of this part yields the dependency . Here, the dependency on matrices should be viewed as part of the phase space formalism which is by its core matricial. This part does not survive once the projection on coordinates is performed, but it is part of the behavior in phase space. In order to be compared with experimental data, the projection on momentum space requires the introduction the thermal energy.
4.3. Casimir Effect for the Dirac Field in Phase Space at Finite Temperature
The effect of temperature is introduced by taking . Then, the generalized Bogoliubov transformation becomes
The first two terms of these expressions correspond, respectively, to the Stefan-Boltzmann term and the Casimir effect at . The third term is analyzed and it leads to the Green function
Then, the Casimir energy at finite temperature is and the Casimir pressure at finite temperature is
It should be noted that in the limit , both the Casimir energy and pressure are real quantities at zero and finite temperature. In the limit , i.e., , the Casimir energy and pressure become
It is important to note that in this limit, both the Casimir energy and pressure depend only on the distance between the plates. The dependence on gamma matrices is not a problem since the formalism of the phase space is matrix. It leads to the conclusion that neither the energy nor the pressure are scalars but components of a tensor.
The Dirac field in phase space is considered. Using the Dirac equation, the propagator for spin-1/2 particles is calculated. This form of the propagator is similar to that in the usual quantum mechanics. The TFD results are obtained by using the temperature effects in the Dirac propagator. TFD, a real-time finite temperature formalism, is a thermal quantum field theory. Using this formalism, a physical (renormalized) energy-momentum tensor is defined. Then, the Stefan-Boltzmann law in phase space and the Casimir effect are calculated at finite temperature. The results lead to the usual results for the Dirac field when they are projected in the quantum field theory space. The TFD formalism allows studying the finite temperature effects in phase space. On the other hand, such a formalism also may be used to explore the role of a thermal energy which is possibly related to the fermionic feature of the field.
This is a theoretical work, and all previous results are listed in the references.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
This work by A. F. S. is supported by CNPq projects 308611/2017-9 and 430194/2018-8.
- E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Physics Review, vol. 40, no. 5, pp. 749–759, 1932.
- M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, “Distribution functions in physics: fundamentals,” Physics Reports, vol. 106, no. 3, pp. 121–167, 1984.
- H. Weyl, “Quantenmechanik und gruppentheorie,” Zeitschrift für Physik, vol. 46, no. 1-2, pp. 1–46, 1927.
- M. D. Oliveira, M. C. B. Fernandes, F. C. Khanna, A. E. Santana, and J. D. M. Vianna, “Symplectic quantum mechanics,” Annals of Physics, vol. 312, no. 2, pp. 492–510, 2004.
- R. G. G. Amorim, M. C. B. Fernandes, F. C. Khanna, A. E. Santana, and J. D. M. Vianna, “Non-commutative geometry and symplectic field theory,” Physics Letters A, vol. 361, no. 6, pp. 464–471, 2007.
- R. G. G. Amorim, S. C. Ulhoa, and E. O. Silva, “On the symplectic Dirac equation,” Brazilian Journal of Physics, vol. 45, no. 6, pp. 664–672, 2015.
- F. C. Khanna, A. P. C. Malbouisson, J. M. C. Malboiusson, and A. E. Santana, Themal Quantum Field Theory: Algebraic Aspects and Applications, World Scientific, Singapore, 2009.
- Y. Takahashi and H. Umezawa, “Higher order calculation in thermo field theory,” Collective Phenomena, vol. 2, p. 55, 1975.
- Y. Takahashi and H. Umezawa, “Thermo field dynamics,” International Journal of Modern Physics B, vol. 10, pp. 1755–1805, 1996.
- H. Umezawa, H. Matsumoto, and M. Tachiki, Thermofield Dynamics and Condensed States, North-Holland Pub. Co., North Holland, Amsterdan, 1982.
- H. Umezawa, Advanced Field Theory: Micro, Macro and Thermal Physics, AIP, New York, 1993.
- A. E. Santana, A. M. Neto, J. D. M. Vianna, and F. C. Khanna, “Symmetry groups, density-matrix equations and covariant Wigner functions,” Physica A, vol. 280, no. 3-4, pp. 405–436, 2000.
- F. C. Khanna, A. P. C. Malbouisson, J. M. C. Malbouisson, and A. E. Santana, “Thermoalgebras and path integral,” Annals of Physics, vol. 324, no. 9, pp. 1931–1952, 2009.
- R. G. G. Amorim, J. S. da Cruz Filho, A. F. Santos, and S. C. Ulhoa, “Stefan-Boltzmann Law and Casimir Effect for the Scalar Field in Phase Space at Finite Temperature,” Advances in High Energy Physics, vol. 2018, Article ID 1928280, 9 pages, 2018.
- F. C. Khanna, A. P. C. Malbouisson, J. M. C. Malbouisson, and A. E. Santana, “Quantum fields in toroidal topology,” Annals of Physics, vol. 326, no. 10, pp. 2634–2657, 2011.
- F. C. Khanna, A. P. C. Malbouisson, J. M. C. Malbouisson, and A. E. Santana, “Quantum field theory on toroidal topology: algebraic structure and applications,” Physics Reports, vol. 539, no. 3, pp. 135–224, 2014.
Copyright © 2020 R. G. G. Amorim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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http://www.osti.gov/eprints/topicpages/documents/record/262/1994134.html
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math
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Summary: On the non-optimality of LAS
within the class IMRL
Samuli Aalto (Helsinki University of Technology)
Urtzi Ayesta (LAAS-CNRS)
Scheduling in a M/G/1 Queue
Poisson arrivals with rate . Service requirements are i.i.d. with
distribution F(x)=P[X x].
Attained service is known (total service requirement unknown)
Optimality criterion: Mean number of jobs in the system
Monotonous Hazard Rate
Hazard rate of a distribution function: h(x)dx=P[x< X x+dx | X > x]
IHR: Non-preemptive discipline (FCFS etc.)
Exponential: M/M/1 Mean number of jobs is policy independent
DHR: Least Attained Service (LAS) is optimal. The job(s) who has
attained the least amount of service is served.
( ) ( )
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https://www.jiskha.com/display.cgi?id=1332183896
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math
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MATH FOR TEACHERS
posted by brittney .
the roof is a right rectangular prism and the floor is a rectangle. (its the outside of a warehouse). for the roof- the base has 51 x 51. The rectangular for the floor is 120 (l) x 20 (h) x 90 (w). need to find the volume and surface area. (counting the floor) Give an organized list for how you figured out the SA (floor= 120x90=10,800, front left=etc.) teacher said I would have to find the missing piece for the roof using the pathagorean theorem but what is the missing peice? Height maybe?
Can you tell me something? Why should "math for teachers" be any different from math for everyone? Shouldn't teachers be as well taught as everyone else?
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http://ilcasarosf.com/6th-grade-math-distributive-property-worksheets/worksheet-distributive-property-worksheet-6th-grade-grass-fedjp/
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math
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By Carolyn C. Diaz on August 10 2018 09:35:48
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http://forums.tokipona.org/search.php?st=0&sk=a&sd=a&sr=posts&author_id=117&start=50
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math
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Yes I matriculated!
I don't understand tawa.
pi = means of transportation
e = to where?
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https://myassignmenthelp.com/answers/epidemiology-for-public-health-tm-5515-question-1-what-is-the-research-question-3.html
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math
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Question 1: What is the research question? [3 marks]
Question 2: Describe the study population. How were participants recruited? Are there any potential sources of bias related to the sample? If so, how would this have impacted on the observed results? [8 marks]
a) What is the exposure and how is it measured? [3 marks]
b) What is the outcome and how is it measured? [3 marks]
c) Discuss the potential for (differential and non-differential) measurement bias in this study, related to both the exposure and outcome variables. Did the authors address these potential sources of error? Describe the likely practical consequences on the results.
What are the main findings of the study? In your answer, include an explanation of the odds ratio (OR), incidence rate, incidence rate ratio (IRR) and 95% confidence interval, as appropriate. Are the results likely to be affected by chance variation? Why or why not?What variables did the authors consider as potential confounders? Explain the term “confounding” using one of these confounders to illustrate your answer. How do the authors deal with confounding in this study? Are there any other potential confounders not taken into account? Are the results likely to be affected by confounding? If so, describe how.external validity. Consider whether the findings can be applied to the actual population from which the study population was derived, and the target population; and whether the results can be applied to other relevant populations.
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http://www.msri.org/workshops/703/schedules/20584
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math
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Minimal submanifolds and lower curvature bounds I
Location: MSRI: Simons Auditorium
Ricci curvature lower bounds
In these lectures we will discuss the role that minimal submanifolds play in the study of lower curvature bounds. The first lecture will be an introduction to the theory including existence theory and the geometry of the second variation. The second lecture will be a survey of applications especially to lower scalar and isotropic curvature bounds
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http://slideplayer.com/slide/3422477/
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math
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2 Signal Strength Measure signal strength in dBW = 10*log(Power in Watts)dBm = 10*log(Power in mW)can legally transmit at 10dBm (1W).Most PCMCIA cards transmit at 20dBm.Mica2 (cross bow wireless node) can transmit from –20dBm to 5dBm. (10microW to 3mW)Mobile phone base station: 20W, but 60 users, so 0.3W / user, but antenna has gain=18dBi, giving effective power of 42.Mobile phone handset – 21dBm
3 Noise Interference Thermal noise From other users From other equipment E.g., microwave ovens 20dBm 50% duty-cycle with 16ms period.Noise in the electronics – e.g., digital circuit noise on analogue parts.Non-linearities in circuits.Often modeled as white Gaussian noise, but this is not always a valid assumption.Thermal noiseDue to thermal agitation of electrons. Present in all electronics and transmission media.kT(W/hz)k Boltzmann’s constant = 1.3810-23T – temperture in Kelvin (C+273)kTB(W)B bandwidthE.g.,Temp = 293,=> -203dB, -173dBm /HzTemp 293 and 22MHz => -130dB, -100dBm
4 Signal to Noise Ratio (SNR) SNR = signal power / noise powerSNR (dB) = 10*log10(signal power / noise power)Signal strength is the transmitted power multiplied by a gain – impairmentsImpairmentsThe transmitter is far away.The signal passes through rain or fog and the frequency is high.The signal must pass through an object.The signal reflects of an object, but not all of the energy is reflected.The signal interferes with itself – multi-path fadingAn object not directly in the way impairs the transmission.
5 Receiver SensitivityThe received signal must have a strength that is larger than the receiver sensitivity20dB larger would be good. (More on this later)E.g.,802.11b – Cisco Aironet 250 (the most sensitive)1Mbps: -94dBm; 2Mbps: -91dBm; 5.5Mbps: -89dBm; 11Mbps: -85dBmMobile phone base station: -119dBmMobile phone hand set: -118dBmMica2 at 868/916MHz: -98dBm
6 Simple link budgetDetermine if received signal is larger than the receiver sensitivityMust account for effective transmission powerTransmission powerAntenna gainLosses in cable and connectors.Path lossesAttenuationGround reflectionFading (self-interference)ReceiverReceiver sensitivityLosses in cable and connectors
7 Antenna gain Vertical direction Horizontal direction isotropic antenna – transmits energy uniformly in all directions.Antenna gain is the peak transmission power over any direction divided by the power that would be achieved if an isotropic antenna is used. The units is dBi.Sometime, the transmission power is compared to a ½ wavelength dipole. In this case, the unit is dBD.The ½ wavelength dipole has a gain of 2.14dB.Vertical directionHorizontal direction
8 Antenna gainAntenna gain is increased by focusing the antennaThe antenna does not create energy, so a higher gain in one direction must mean a lower gain in another.Note: antenna gain is based on the maximum gain, not the average over a region. This maximum may only be achieved only if the antenna is carefully aimed.This antenna is narrower and results in 3dB higher gain than the dipole, hence, 3dBD or 5.14dBiThis antenna is narrower and results in 9dB higher gain than the dipole, hence, 9dBD or 11.14dBi
9 Antenna gainInstead of the energy going in all horizontal directions, a reflector can be placed so it only goes in one direction => another 3dB of gain, 3dBD or 5.14dBiFurther focusing on a sector results in more gain.A uniform 3 sector antenna system would give 4.77 dB more.A 10 degree “range” 15dB more.The actual gain is a bit higher since the peak is higher than the average over the “range.”Mobile phone base stations claim a gain of 18dBi with three sector antenna system.4.77dB from 3 sectors – dBiAn 11dBi antenna has a very narrow range.
10 Simple link budget – 802.11b receiver sensitivity Thermal noise: -174 dBm/HzChannel noise (22MHz): 73 dBNoise factor: 5 dBNoise power (sum of the above): -96 dBmReceiver requirements:3 dB interference margin0 dB is the minimum SINRMin receiver signal strength: -93 dBm
11 Simple link budget – 802.11 example From base station+20dBm transmission power+6dBi transmit antenna gain+2.2dBi receiver antenna gain-91dBm minimum receiver power=> dB path losses=> 99 dB path losses if 20dB of link margin is added (to ensure the link works well.)From PCMCIA to base station+0dBm transmission power=> 99.4 dB path losses=> 79.2 dB path losses if 20dB of link margin is added (to ensure the link works well.)From PCMCIA to PCMCIA+2.2dBi transmit antenna gain=> 95.4 dB path losses=> 75.4 dB path losses if 20dB of link margin is added (to ensure the link works well.)
12 Simple link budget – mobile phone – downlink example Transmission power (base station): 20W (can be as high as 100W)Transmission power for voice (not control): 18WNumber of users: 60Transmission power/user: 0.3W, 300mW, 24.8dBmBase station antenna gain (3-sectors): 18dBiCable loss at base station: 2dBEffective isotropic radiated power: 40dBm (sum of the above)Receiver:Thermal noise: -174 dBm/HzMobile station receiver noise figure (noise generated by the receiver, Johnson Noise, ADC quantization, clock jitter): 7dBReceiver noise density: -167 dB/Hz (-174+7)Receiver noise: dBm (assuming 3.84MHz bandwidth for CDMA)Processing gain: 25dB (CDMA is spread, when unspread(demodulated) and filtered, some of the wide band noise is removed)Required signal strength: 7.9dBReceiver sensitivity: – =Body loss (loss due to your big head): 3dBMaximum path loss: 40 – (-118.3) –3 = 155.3
13 Simple link budget – mobile phone – uplink example Transmission power (mobile): 0.1W (21 dBm)Antenna gain: 0 dBiBody loss: 3 dBEffective isotropic radiated power: 18 dBm (sum of the above) (maximum allowabel by FCC is 33 dBm at 1900MHz and 20dBm at 1700/2100 MHzReceiver/base stationThermal noise: -174 dBm/HzMobile station receiver noise figure (noise generated by the receiver, Johnson Noise, ADC quantization, clock jitter): 5dBReceiver noise density: -169 dB/Hz (-174+5)Receiver noise: dBm (assuming 3.84MHz bandwidth for CDMA)Processing gain: 25dB (CDMA is spread, when unspread(demodulated) and filtered, some of the wide band noise is removed)Margin for interference: 3dB (more interference on the uplink than on the downlink)Required signal strength: 6.1dBReceiver sensitivity:Maximum path loss: 153.3
14 Required SNRFor a given bit-error probability, different modulation schemes need a higher SNREb is the energy per bitNo is the noise/HzBit-error is given as afunction of Eb / NoRequired SNR = Eb / No * Bit-rate / bandwidthA modulation scheme prescribes a Bit-rate / bandwidth relationshipE.g., for 10^-6 BE probability over DBPSK requires 11 dB + 3 dB = 14 dB SNR
16 Shannon CapacityGiven SNR it is possible to find the theoretical maximum bit-rate:Effective bits/sec = B log2(1 + SNR), where B is bandwidthE.g.,B = 22MHz,Signal strength = -90dBmN = -100dBm=> SNR = 10dB => 1022106 log2(1 + 10) = 76MbpsOf course, b can only do 1Mbps when the signal strength is at –90dBm.
17 PropagationRequired receiver signal strength – Transmitted signal strength is often around99 dB base station -> laptop79.2 dB b laptop -> base station75.4 dB laptop -> laptop155.3 Mobile phone downlink153.3 Mobile phone uplink.Where does all this energy go…Free space propagation – not valid but a good startGround reflection2-ray – only valid in open areas. Not valid if buildings are nearby.Wall reflections/transmissionDiffractionLarge-scale path loss modelsLog-distanceLog-normal shadowingOkumuraHataLongley-RiceIndoor propagationSmall-scale path lossRayleigh fadingRician Fading
18 Free Space Propagation The surface area of a sphere of radius d is 4 d2, so that the power flow per unit area w(power flux in watts/meter2) at distance d from a transmitter antenna with input accepted power pT and antenna gain GT isThe received signal strength depends on the “size” or aperture of the receiving antenna. If the antenna has an effective area A, then the received signal strength isPR = PT GT (A/ (4 d2))Define the receiver antenna gain GR = 4 A/2. = c/f2.4GHz=> = 3e8m/s/2.4e9/s = 12.5 cm933 MHz => =32 cm.Receiver signal strength: PR = PT GT GR (/4d)2PR (dBm) = PT (dBm) + GT (dBi) + GR (dBi) + 10 log10 ((/4d)2)2.4 GHz => 10 log10 ((/4d)2) = -40 dB933 MHz => 10 log10 ((/4d)2) = -32 dB
19 Free Space Propagation - examples Mobile phone downlink = 12.5 cmPR (dBm) = (PTGGL) (dBm) dB + 10 log10 (1/d2)Or PR-PT - 40 dB = 10 log10(1/d2)Or 155 – 40 = 10 log10 (1/d2) =Or (155-40)/20 = log10 (1/d)Or d = 10^ ((155-40)/20) = 562Km or Wilmington DE to Boston MAMobile phone uplinkd = 10^ ((153-40)/20) = 446Km802.11PR-PT = -90dBmd = 10^((90-40)/20) = 316 m11Mbps needs –85dBmd = 10^((85-40)/20) = 177 mMica2 Mote-98 dBm sensitivity0 dBm transmission powerd = 10^((98-30)/20) = 2511 m
20 Ground reflectionFree-space propagation can not be valid since I’m pretty sure that my cell phone does reach Boston.You will soon see that the Motes cannot transmit 800 m.There are many impairments that reduce the propagation.Ground reflection (the two-ray model) – the line of sight and ground reflection cancel out.
21 Ground reflection (approximate) Approximation! When the wireless signal hits the ground, it is completely reflected but with a phase shift of pi (neither of these is exactly true).The total signal is the sum of line of sight and the reflected signal.The LOS signal is = Eo/dLOS cos(2 / t)The reflected signal is -1 Eo /dGR cos(2 / (t – (dGR-dLOS)))Phasors:LOS = Eo/dLOS 0Reflected = Eo/dGR (dGR-dLOS) 2 / For large d dLOS = dGRTotal energyE = (Eo/dLOS) ( (cos ((dGR-dLOS) 2 / ) – 1)2 + sin2((dGR-dLOS) 2 / ) ) ½E = (Eo/dLOS) 2 sin((dGR-dLOS) / )
22 Ground reflection (approximate) dGR-dLOSdGR = ((ht+hr)^2 + d^2)^1/2dLOS = ((ht-hr)^2 + d^2)^1/2dGR-dLOS 2hthr/d -> 0 as d-> inf2 sin((dGR-dLOS) / ) -> 0,For large d, 2 sin((dGR-dLOS) / ) C/dSo total energy is 1/d^2And total power is energy squared, or K/d^4
23 Ground reflection (approximate) For d > 5ht hr, Pr = (hthr)^2 / d^4 Gr GT PTPr – PT – 10log((hthr)^2) - log(Gr GT ) = 40 log(1/d)Examples:Mobile phoneSuppose the base station is at 10m and user at 1.5 md = 10^((155 – 12)/40) = 3.7Km802.11Suppose the base station is at 1.5m and user at 1.5 md = 10^((90 – 3.5)/40) = 145mBut this is only accurate when d is large 145m might not be large enough
24 Ground reflection (more accurate) When the signal reflects off of the ground, it is partially absorbed and the phase shift is not exactly pi.PolarizationTransmission line model of reflections
25 PolarizationThe polarization could be such that the above picture is rotated by pi/2 along the axis.It could also be shifted.If a rotated and shifted
26 PolarizationThe peak of the electric field rotates around the axis.
27 PolarizationIf a antenna and the electric field have orthogonal polarization, then the antenna will not receive the signal
28 Polarization Vertically/ horizontally polarized When a linearly polarized electric field reflects off of a vertical or horizontal wall, then the electric field maintains its polarization.In practice, there are non-horizontal and non-vertical reflectors, and antenna are not exactly polarized. In practice, a vertically polarized signal can be received with a horizontally polarized antenna, but with a 20 dB loss.Theoretically, and sometimes in practice, it is possible to transmit two signals, one vertically polarized and one horizontally.Vertically/ horizontally polarized
29 Snell's Law for Oblique Incidence yqqTqqTxGraphical interpretation of Snell’s law
30 Transmission Line Representation for Transverse Electric (TE) Polarization yqzxqTEz+ -Hx
31 Transmission Line Representation for Transverse Magnetic (TM) Polarization yqzxqTEx+ -Hz
32 Reflection from a Dielectric Half-Space TE PolarizationTM Polarization90º-1GEqGHqBno phase shift
33 Magnitude of Reflection Coefficients at a Dielectric Half-Space TE PolarizationTM Polarization1530456075900.10.20.30.188.8.131.52.80.91Reflection coefficient |GE |Incident Angle qIer=81er=25er=16er=9er=4er=2.56Reflection coefficient |GH |
35 Path losses Propagation Ground reflection Other reflections We could assume that walls are perfect reflectors (||=1). But that would be poor approximation for some angles and materials. Also, this would assume that the signal is not able to propagate into buildings, which mobile phone users know is not the case.
36 Reflection and Transmission at Walls Transmission line formulationHomogeneous wallsAttenuation in wallsInhomogeneous walls
37 Transmission Line Formulation for a Wall ZdTEZaTEwZdTEZaTE
38 Transmission Line Method airwallairZ(w)ZL= ZaZaZwStanding Wave- wTransmittedIncidentReflected
39 Reflection at Masonry Walls (Dry Brick: er 5, e”=0) 20cm1020304050607080900.20.40.60.81900MHzTE1.8GHzTMAngle of Incidence qI (degree) G 2BZaTEZdTEZaTEBrewster angle
40 Reflection Accounting for Wall Loss The relative dielectric constant has an imaginary componentZaZw, kwZ(w)- wz
41 Comparison with Measured |G| 4 GHz for Reew = 4, Imew = 0 Comparison with Measured |G| 4 GHz for Reew = 4, Imew = 0.1 and l = 30 cm Landron, et al., IEEE Trans. AP, March 1996)1530456075900.10.20.30.184.108.40.206.80.91Measured dataAngle of Incidence qTE PolarizationG w = w = 30cm1530456075900.10.20.30.220.127.116.11.80.91Measured dataAngle of Incidence qTM PolarizationG w = w = 30cm
42 Transmission Loss Through Wall, cont. Now the might be imaginary => phaseSee mathcad file
43 Dielectric constantsWhen conductivity exists, use complex dielectric constant given bye = eo(er - je") where e" = s/weo and eo 10-9/36pMaterial* er s (mho/m) e" at 1 GHzLime stone wallDry marbleBrick wallCementConcrete wallClear glassMetalized glassLake waterSea WaterDry soilEarth* Common materials are not well defined mixtures and often contain water.
44 Diffraction sources Idea: The wave front is made of little sources that propagate in all directions.If the line of sight signal is blocked, then the wave front sources results propagation around the corner.The received power is from the sum of these sourcessourcesDefine excess path = h2 (d1+d2)/(2 d1d2)Phase difference= 2/Normalize Fresnel-Kirchoff diffraction parameter
45 Knife edge diffraction Path loss from transmitter to receiver is-10-5510-30-25-20-15Received Signal(dB)v
46 Multiple diffractions If there are two diffractions, there are some models. For more than 2 edges, the models are not very good.
47 Large-scale Path Loss Models Log-distancePL(d) = K (d/do)nPL(d) (dB) = PL(do) + 10 n log10(d)Redo examples
48 Large-scale Path Loss Models Log-normal shadowingPL(d) (dB) = PL(do) + 10 n log10(d) + XX is a Gaussian distributed random number32% chance of being outside of standard deviation.16% chance of signal strength being 10^(11/10) = 12 times larger/smaller than 10 n log10(d)2.5% chance of the signal being 158 times larger/smaller.The fit shown is not very good.This model is very popular.
49 Outdoor propagation models OkumuraEmpirical modelSeveral adjustments to free-space propagationPath Loss L(d) = Lfree space + Amu(f,d) – G(ht) – G(hr) – GAreaA is the median attenuation relative to free-spaceG(ht) = 20log(ht /200) is the base station height gain factorG(hr) is the receiver height gain factorG(hr) = 10log(hr /3) for hr <3G(hr) = 20log(hr /3) for hr >3Garea is the environmental correction factorHata
50 Hata Model Valid from 150MHz to 1500MHz A standard formula For urban areas the formula is:L50(urban,d)(dB) = logfc loghte – a(hre) (44.9 – 6.55loghte)logd wherefc is the ferquency in MHzhte is effective transmitter antenna height in meters (30-200m)hre is effective receiver antenna height in meters (1-10m)d is T-R separation in kma(hre) is the correction factor for effective mobile antenna height which is a function of coverage areaa(hre) = (1.1logfc – 0.7)hre – (1.56logfc – 0.8) dB for a small to medium sized city
51 Indoor propagation models Types of propagationLine of sightThrough obstructionsApproachesLog-normalSite specific – attenuation factor modelPL(d)[dBm] = PL(d0) + 10nlog(d/d0) + Xsn and s depend on the type of the buildingSmaller value for s indicates the accuracy of the path loss model.
52 Path Loss Exponent and Standard Deviation Measured for Different Buildings Frequency (MHz)ns (dB)Retail Stores9142.28.7Grocery Store1.85.2Office, hard partition15003.07.0Office, soft partition9002.49.619002.614.1Factory LOSTextile/Chemical13002.040002.1Paper/Cereals6.0Metalworking1.65.8Suburban HomeIndoor StreetFactory OBS18.104.22.168
53 Site specific – attenuation factor model PL(d) (dB) = PL(do) + 10 n log(d/do) + FAF + PAFFAF floor attenuation factor - Losses between floorsNote that the increase in attenuation decreases as the number of floors increases.PAF partition attenuation factor - Losses due to passing through different types of materials.BuildingFAF (dB)s (dB)Office Building 1Through 1 Floor12.97.0Through 2 Floors18.72.8Through 3 Floors24.41.7Through 4 Floors27.01.5Office Building 216.22.927.55.431.67.2
55 Small-scale path loss See matlab file They are summed as phasors. The received signal is the sum of the contributions of each reflection.They are summed as phasors.The received signal is the phasor sum of the contributions of each reflection.A small change in the position of the receiver or transmitter can cause a large change in the received signal strength.See matlab file
56 Rayleigh and Rician Fading The inphase and quadrature parts can be modeled as independent Gaussian random variables.The energy is the (X^2 + Y^2)^ ½ where X and Y are Gaussian => the energy is Rayleigh distributed.The power is (X^2 + Y^2) which is exponentially distributed.Rician – if there is a strong line-of-sight component as well as reflections. Then the signal strength has a Ricain distribution.
57 SummaryThe signal strength depends on the environment in a complicate way.If objects are possible obstructing, then the signal strength may be log-normal distributed => large deviation from free-spaceIf the signal is narrow band, then the the signal could be completely canceled out due to reflections and multiple paths.Reflection, transmission, and diffraction can all be important
58 Path Losslocation 1, free space loss is likely to give an accurate estimate of path loss.location 2, a strong line-of-sight is present, but ground reflections can significantly influence path loss. The plane earth loss model appears appropriate.location 3, plane earth loss needs to be corrected for significant diffraction losses, caused by trees cutting into the direct line of sight.location 4, a simple diffraction model is likely to give an accurate estimate of path loss.location 5, loss prediction fairly difficult and unreliable since multiple diffraction is involved.
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http://www.sciepub.com/IJP/content/1/4
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math
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International Journal of Physics. 2013, 1(4), 84-93DOI:
Abstract: I consider a specially designed simple mechanical problem where a “particle acceleration” due to an external force creates sound waves. Theoretical description of this phenomenon should provide the total energy conservation. To introduce small “radiative losses” into the phenomenological “mechanical” equation, I advance first an “interaction Lagrangian” similar to that of the Classical Electrodynamics (kind of a self-action ansatz). New, “better-coupled” “mechanical” and “wave” equations manifest unexpectedly wrong dynamics due to changes of their coefficients (masses, coupling constant); thus this ansatz fails. I show how we make a mathematical error with advancing a self-interaction Lagrangian. I show, however, that renormalization of the fundamental constants in the wrong equations works: the original “inertial” properties of solutions are restored. The exactly renormalized equations contain only physical fundamental constants, describe well the experimental data, and reveal a deeper physics – that of permanently coupled constituents. The perturbation theory is then just a routine calculation only giving small corrections. I demonstrate that renormalization is just illegitimately discarding harmful corrections fortunately compensating this error, that the exactly renormalized equations may sometimes accidentally coincide with the correct equations, and that the right theoretical formulation of permanently coupled constituents can be fulfilled directly, if realized.
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https://www.hamilton.edu/news/story/gibbons-speaks-at-society-for-industrial-and-applied-mathematics-conference-at-georgia-tech
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math
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Assistant Professor Courtney Gibbons presented joint work at the SIAM Applied Algebraic Geometry meeting at Georgia Tech in Atlanta in August . She spoke about finding the number of solutions to the maximum likelihood equations for discrete cycle models.
Understanding the principal A-determinant for the matrix describing the toric variety arising from the model can allow researchers to find solutions to the maximum likelihood equations in a well-behaved parametrization and track those solutions to the parametrization necessary for solving a real-life problem using a technique called homotopy continuation. Slides from the talk are available on Gibbons’ website.
Gibbons also has begun writing the Errorbusters column in the math bimonthly magazine "Girls' Angle Bulletin." Her inaugural column appear in the June/July 2017 issue and tackles "errors of apathy," or the mistakes you make when you don't care about the "why" and just care about getting an answer.
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http://ipta2014.iopconfs.org/254885
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math
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Inverse problems for non-linear wave equations and the Einstein equations
We consider inverse problem for a non-linear wave equation with a time-depending metric tensor on manifolds. In addition, we study the question, do the observation of the solutions of coupled Einstein equations and matter field equations in an open subset U of the space-time M corresponding to sources supported in U determine the properties of the metric in a larger domain W⊂M containing U.
To study these problems we define the concept of light observation sets and show that these sets determine the conformal class of the metric.
The results have been done in collaboration with Yaroslav Kurylev and Gunther Uhlmann.
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http://www.thehindu.com/thehindu/br/2003/08/26/stories/2003082600120300.htm
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math
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The legendary genius
RAMANUJAN Essays and Surveys: Bruce C. Brendt, Robert A. Rankin Editors; Published by Hindustan Book Agency (India), 17, UB, Jawahar Nagar, New Delhi-110016. Price not mentioned.
THIS, AN Indian edition of the book published earlier by the American Mathematical Society, presents a fascinating and thought-provoking account of Ramanujan's life, from his birth at Kumbakonam on December 22, 1887 till his demise on April 26, 1920 at the young age of 32. The story is well told with the scientific ferment and personalities of his time.
Since the Indian postage stamp appeared in 1962 commemorating Ramanujan's 75th birthday, several articles appeared on his life and work. But, for the first time, we have a thought-provoking and timely agenda in this book, which will be of interest to a variety of readers. Each of the eight parts, into which the book is divided, sets the stage for understanding "a mathematician so great that his name transcends jealousies, the one superlatively great mathematician whom India has produced in the last 1000 years." (Prof. Neville, University of Reading)
It offers insight into the influence on Ramanujan's development before he left for England. For example, the assistance that S. Narayana Iyer gave is narrated: working on problems with Ramanujan at night after his work at the Port Trust Office, publishing Ramanujan's discoveries in the theory of prime numbers, composing letters to Hardy and offering home to Ramanujan's parents after his death. In 1903, there came into his hands Carr's Synopsis of Mathematics, a book containing the enunciation of some 6000 theorems, mostly in geometry, for the most part without proofs. Geometry did not appeal to Ramanujan but in algebra and calculus he found himself in a magic world. In proving one formula, he discovered many others; be began the practice of compiling a notebook, the first one became famous afterwards.
It was in April 1914 that Ramanujan arrived in Cambridge, where his name became well known. Early in 1919, he returned to Madras, a tired and sick man of 31, nursed by his wife. There were many public receptions in his honour. The conversations with his wife, Janaki Ammal recorded in part III are very moving.
Parts VI to VIII are completely mathematical, delving into Ramanujan's manuscripts and notebooks. Some representative topics are listed: modular functions with various surprising symmetries, nested radicals, elementary identities involving radicals, formulas for finding equal sums of powers and polynomial identities.
The calculation of "pi" (the ratio of any circle's circumference to its diameter) has something of a benchmark in computation. Ramanujan's approach is now incorporated in computer algorithms yielding millions of digits of "pi", when he knew nothing of computer programming. Sophisticated algebraic manipulation software has allowed further exploration of the road Ramanujan travelled alone and unaided 90 years ago.
There are many wonderful formulas contained in his "Notebooks" that revolve around integrals, infinite series and continued fractions. Bruce Berndt is now completing the Herculean task of editing these.
It seems no person in the history of mathematics possessed the skills that Ramanujan had in determining continued fractions for various functions or finding closed form representation for continued fraction. It is high time that our students study Ramanujan's theorems in university courses, instead of merely extolling him as an enigmatic Indian genius.
Send this article to Friends by
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https://slidetodoc.com/distances-a-natural-or-ideal-measure-of-distance/
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math
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- Slides: 53
A natural or ideal measure of distance between two sequences should have an evolutionary meaning. One such measure may be the number of nucleotide substitutions that have accumulated in the two sequences since they have diverged from each other.
To derive a measure of distance, we need to make several simplifying assumptions regarding the probability of substitution of a nucleotide by another.
Jukes & Cantor one-parameter model
Assumption: • Substitutions occur with equal probabilities among the four nucleotide types.
Kimura’s two-parameter model
Assumptions: • The rate of transitional substitution at each nucleotide site is per unit time. • The rate of each type of transversional substitution is per unit time.
NUMBER OF NUCLEOTIDE SUBSTITUTIONS BETWEEN TWO DNA SEQUENCES
After two nucleotide sequences diverge from each other, each of them will start accumulating nucleotide substitutions. If two sequences of length N differ from each other at n sites, then the proportion of differences, n/N, is referred to as the degree of divergence or Hamming distance. Degrees of divergence are usually expressed as percentages (n/N 100%).
The observed number of differences is likely to be smaller than the actual number of substitutions due to multiple hits at the same site.
13 mutations = 3 differences
Number of substitutions between two noncoding sequences
The one-parameter model In this model, it is sufficient to consider only I(t), which is the probability that the nucleotide at a given site at time t is the same in both sequences.
where p is the observed proportion of different nucleotides between the two sequences.
L = number of sites compared in the ungapped alignment between the two sequences.
The two-parameter model
The differences between two sequences are classified into transitions and transversions. P = proportion of transitional differences Q = proportion of transversional differences ATCGG ACCCG Q = 0. 2 P = 0. 2
Numerical example (2 P-model)
-Substitution schemes with more than two parameters. - Parameter-free substitution schemes.
Number of substitutions between two protein-coding genes
Difficulties with denominator: 1. The classification of a site changes with time: For example, the third position of CGG (Arg) is synonymous. However, if the first position changes to T, then the third position of the resulting codon, TGG (Trp), becomes nonsynonymous.
T Trp Nonsynonymous
Difficulties with denominator: 2. Many sites are neither completely synonymous nor completely nonsynonymous. For example, a transition in the third position of GAT (Asp) will be synonymous, while a transversion to either GAG or GAA will alter the amino acid.
Difficulties with nominator: 1. The classification of the change depends on the order in which the substitutions had occurred.
Difficulties with nominator: 2. Transitions occur with different frequencies than transversions. 3. The type of substitution depends on the mutation. Transitions result more frequently in synonymous substitutions than transversions.
Miyata & Yasunaga (1980) and Nei & Gojobori (1986) method
Step 1: Classify Nucleotides into non-degenerate, twofold and fourfold degenerate sites L 0 L 2 L 4
Number of Amino-Acid Replacements between Two Proteins • The observed proportion of different amino acids between the two sequences (p) is p = n /L • n = number of amino acid differences between the two sequences • L = length of the aligned sequences.
Number of Amino-Acid Replacements between Two Proteins The Poisson model is used to convert p into the number of amino replacements between two sequences (d ): d = - ln(1 – p) The variance of d is estimated as V(d) = p/L (1 – p)
How do you detect adaptive evolution at the genetic level?
Theoretical Expectations Deleterious mutations Neutral mutations Advantageous mutations Overdominant mutations 48
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http://www.studentpartnersite.com/downloads.aspx?categoryid=289
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math
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Instant download to solution. Once the payment is made, the solution file link will be auto-mailed to your specified E-mail id. Check your inbox as well as spam folder. You can download the solution file by clicking that link.
(22-1) Vandell’s free cash flow (FCF0) is $2 million per year and is expected to grow at a constant rate of 5% a year; its beta is 1.4. What is the value of Vandell’s operations? If Vandell has $10.82 million in debt, what is the current value of Vandell’s stock? (Hint: Use the corporate valuation model from Chapter 7.)
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https://www.drinkmixguide.com/Drinking-Games/Circle-of-Death-3
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math
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Drinking Game Instructions
Arrange all cards in concentric circles face down. The object is to guess the proper suit of the card which will be turned over. Begin on the outer circle.
1. The first player will call 'red' or 'black', and;
a) if correct, the other player must drink the number on the card.
b) if incorrect, the flipper drinks that many drinks.
2. This continues until the circle is finished, but every time you reach the end of a circle, the number of drinks are doubled for the interior circles.
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http://take.brooklyn-chess.com/rules
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math
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Take is easy to play. In each puzzle, use the white piece to take all the black pawns. Unlike chess, the black pawns do not move, it is your turn again right after each move. There is one catch: every move you make must capture a pawn, so you cannot move to empty squares. To move a piece simply tap on the pawn you wish to take or drag the white piece to that square.
How do the pieces move?
If you are unfamiliar with chess, that is no problem. You only need to know how four pieces move, not all the rules of chess. In chess you can take the pieces of the opponent by moving one of your pieces onto a square where an opponent's piece is standing. The opponent's piece is then taken off the board.
Here is how each of the four pieces you need to know move:
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https://www.physicsforums.com/threads/translational-and-rotational-equilibrium.760800/
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math
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Hi Everyone, I'm having some trouble with a problem concerning translational and rotational equilibrium. The question involves a balance with various masses suspended from it (see attached image). The question states that the counterweight is moved from 1cm away from the fulcrum to 2cm away from the fulcrum and asks whether or not the rod is still under rotational and translational equilibrium. I understand that it is no longer in rotational equilibrium because there is now a net torque acting on the rod, however the translational equilibrium portion is unclear to me. The answer argues that the masses suspended from the rod no longer exert the same force on the rod because they are now accelerating, thus translational equilibrium is no longer present. I am unclear as to why they are accelerating. I realize that the apparatus will rotate which gives it angular acceleration, but is this enough to conclude that it has linear acceleration as well (alpha =a/r)? If this is the case, how could we ever have have translational equilibrium while not having rotational equilibrium? I'd appreciate any help, thanks.
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https://www.dallasfed.org/en/research/basics/annualizing.aspx
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math
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How to annualize percent changes in quarterly and monthly data
The Economic Problem
Annualizing Data Facilitates Comparison of Growth Rates of Various Time Periods
Suppose Texas employment grew 0.92 percent in the first five months of a particular year. Then in June and July, employment advanced 0.15 percent and 0.22 percent, respectively. Would employment growth in June and July be above or below the pace set in the first five months of the year?
While this simple problem could probably be tackled in a few different ways, the most common one is a process called data annualization. In this method, growth rates are adjusted to reflect the amount a variable would have changed over a year’s time, had it continued to grow at the given rate. The result is a percent change that is easily comparable to other annualized data.
In this case, the 0.92 percent translates into an annualized 2.22 percent. The 0.15 becomes 1.81 percent (annualized), and the 0.22 figure becomes 2.67 percent (annualized). Thus, employment growth in June was below the rate established in the first five months, while the July figure was above it, in annualized terms. This kind of data adjustment is very common in economic analysis. It allows for quick comparison of percent changes, no matter the time period.
The Technical Solution
The formula for annualizing monthly data is straightforward:
where Xm and Xm – 1 are the values of the economic variable in months m and m –1, respectively (for example, m = February, then m – 1 = January), and gm is the annualized percent change.
For year-to-date calculations on monthly data, the formula is:
where XDec is the value of the economic variable in the December of a given year, m is the number of the month in question, Xm is the value of the economic variable in the mth month of the given year, and hm is the annualized year-to-m percent change.
change (not annualized)
On the July row, 0.22 is found by calculating the percent change between 9,553,800 (June) and 9,574,800 (July). The annualized figure of 2.67 is found by applying Equation 1: Divide 9,574,800 by 9,553,800, raise this quotient by 12, subtract 1, and multiply the whole thing by 100 (Calculation 1). This rate represents the amount employment would have increased for the year had it expanded at that monthly rate all 12 months. The calculation for the other months is the same.
In the last row, the 0.92 figure is found by calculating the simple percent change between 9,452,500 (December) and 9,539,500 (May). The annualized figure of 2.22 percent is found by applying Equation 2: Divide 9,539,500 by 9,452,500, raise this quotient by 2.4 (12/5), subtract 1, and multiply the whole thing by 100 (Calculation 2). This rate represents the amount employment would have increased for the year had it continued to expand at the pace set between January and May.
The annualizing methodology offers a simple way to compare the growth rates of economic variables presented across different periods. Analysts can regularly assess the monthly or quarterly performance of key economic indicators relative to their changes in recent years.
Annualized rates of growth in monthly or quarterly data are generally only calculated for data that are not seasonal, or that have had the seasonality removed.
Glossary at a Glance
- Adjusting a growth rate to reflect the amount a variable would have changed over a year's time had it continued to grow at the given rate.
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CC-MAIN-2022-27
| 3,461 | 18 |
https://pothi.com/pothi/book/ebook-massimo-moruzzi-15-questions-about-online-advertising
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math
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#NOT a real book (Just a screed)
The real question of course is: Does online advertising work?
Unfortunately, it's impossible to give a simple answer to this apparently straightforward question.
For starters, this is not a single question, but at least three different ones.
The right question to ask would be: for whom does online advertising work?
Do banner ads, what we once called interactive advertising and now call display ads because nobody clicks on them, and much less "interacts" with them, work for publishers? Do they work for advertisers? Or do they just work for the middlemen based in Silicon Valley?
Quantitative Techniques Volume-I by Narender Sharma
Managing Business in Turbulent Times: A Case Study Approach by Prof. Kunal Gaurav
Marketing Management by Jayen K. Thaker
Summary of Why We Buy by Jaya Jha
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s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202804.80/warc/CC-MAIN-20190323121241-20190323143241-00094.warc.gz
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CC-MAIN-2019-13
| 824 | 10 |
https://qspace.library.queensu.ca/handle/1974/14146
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math
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Proton Formation in 2+1 Resonance Enhanced Multiphoton Excitation of HCl and HBr via „=0… Rydberg and Ion-Pair States
MetadataShow full item record
Molecular beam cooled HCl was state selected by two-photon excitation of the V (1) summation operator(0(+)) [v=9,11-13,15], E (1) summation operator(0(+)) [v=0], and g (3) summation operator(-)(0(+)) [v=0] states through either the Q(0) or Q(1) lines of the respective (1,3) summation operator(0(+))<--<--X (1) summation operator(0(+)) transition. Similarly, HBr was excited to the V (1) summation operator(0(+)) [v=m+3, m+5-m+8], E (1) summation operator(0(+)) [v=0], and H (1) summation operator(0(+)) [v=0] states through the Q(0) or Q(1) lines. Following absorption of a third photon, protons were formed by three different mechanisms and detected using velocity map imaging. (1) H(*)(n=2) was formed in coincidence with (2)P(i) halogen atoms and subsequently ionized. For HCl, photodissociation into H(*)(n=2)+Cl((2)P(12)) was dominant over the formation of Cl((2)P(32)) and was attributed to parallel excitation of the repulsive [(2) (2)Pi4llambda] superexcited (Omega=0) states. For HBr, the Br((2)P(32))Br((2)P(12)) ratio decreases with increasing excitation energy. This indicates that both the [(3) (2)Pi(12)5llambda] and the [B (2) summation operator5llambda] superexcited (Omega=0) states contribute to the formation of H(*)(n=2). (2) For selected intermediate states HCl was found to dissociate into the H(+)+Cl(-) ion pair with over 20% relative yield. A mechanism is proposed by which a bound [A (2) summation operatornlsigma] (1) summation operator(0(+)) superexcited state acts as a gateway state to dissociation into the ion pair. (3) For all intermediate states, protons were formed by dissociation of HX(+)[v(+)] following a parallel, DeltaOmega=0, excitation. The quantum yield for the dissociation process was obtained using previously reported photoionization efficiency data and was found to peak at v(+)=6-7 for HCl and v(+)=12 for HBr. This is consistent with excitation of the repulsive A(2) summation operator(12) and (2) (2)Pi states of HCl(+), and the (3) (2)Pi state of HBr(+). Rotational alignment of the Omega=0(+) intermediate states is evident from the angular distribution of the excited H(*)(n=2) photofragments. This effect has been observed previously and was used here to verify the reliability of the measured spatial anisotropy parameters.
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| 2,433 | 3 |
https://deepai.org/publication/partial-differential-equations-on-hypergraphs-and-networks-of-surfaces-derivation-and-hybrid-discretizations
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math
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This manuscript establishes a general approach to formulate partial differential equations (PDEs) on networks of (hyper)surfaces, referred to as hypergraphs. Such PDEs consist of differential expressions with respect to all hyperedges (surfaces) and compatibility conditions on the hypernodes (joints, intersections of surfaces). These compatibility conditions ensure conservation properties (in case of continuity equations) or incorporate other properties—motivated by physical or mathematical modeling. We illuminate how to discretize such equations numerically using hybrid discontinuous Galerkin (HDG) methods, which appear to be a natural choice, since they consist of local solvers (encoding the differential expressions on hyperedges) and a global compatibility condition (related to our hypernode conditions). We complement the physically motivated compatibility conditions by a derivation through a singular limit analysis of thinning structures yielding the same results.
Albeit many physical, sociological, engineering, and economic processes have been described by partial differential equations posed on domains which cannot be described as subsets of linear space or smooth manifolds, there is still a lack of mathematical tools and general purpose software specifically addressing the challenges arising from the discretization of these models.
Fractured porous media (see [BerreDK2019] for a comprehensive review) have gained substantial attention and have become an active field of research due to their critical role with respect to flow patterns in several applications in the subsurface, in material science, and in biology. Most commonly, a fracture is described as a very thin, not necessarily planar object in which, for example Darcy’s equation holds. This motivates the singular limit approximation in which a fracture is assumed to be a two dimensional surface within the three dimensional space. When several of these fractures meet, they form a fracture network of two-dimensional surfaces. Thus, fracture networks illustrate a physical application of the type of problem we investigate in this publication. Moreover, a model in which the joints of two (or more) fractures are assigned additional physical properties can be found in [ReichenbergerJBH2006]. Beyond this, fracture networks have been simulated using hybrid high order (HHO) methods [HedinPE2019].
Graph based models for porous media (without fractures) consist of simulating preferential flow paths within the porous matrix. One of the first publications implementing this idea is [Fatt1956] who observed that a network of tubes might approximate the flow of porous media better than the classical model of tube bundles, which has also been used in the most common upscaling techniques—see [SchulzRZRK2019, RayRSK2018] and the references therein for a discussion of those tube models in upscaling procedures. The tube network approach [Fatt1956] has been successfully applied to couple porous media flow to free (Navier–) Stokes flow [WeishauptJH2019].
PDEs on hypergraphs are especially suitable to be used in the description of elastic networks [Eremeyev2019]: Here, we discriminate between one dimensional elastic beam (rod) networks, trusses, etc. and two dimensional elastic plate (shell) networks [LagneseL1993], respectively. Beam networks have been used to model truss bridges and towers (most prominently the Eiffel tower) and other mechanical structures, originating the field of elastic beam theory (for instance [BauchauC2009] for an introduction which also covers elastic plate models). Elastic plate models describe the stability of houses and have several engineering applications such as the description of the stability of (bend) plates (used in automobile industries and several others). They have even been used to understand interseismic surface deformation at subduction zones [KandaS2010].
Elastic beam networks have been used to evaluate elastic constants in amorphous materials. That is, the elastic properties of stiff, beam like polymers have been investigated. Such polymers are key to understanding the cytoskeleton which is an important part of biological cells [Heussinger2007, Lieleg2007], but they are also important for the healing of wounds (fibrin), for skin stability (collagen), and for the properties of paper. Moreover, such models can be used for modelling rubber [PhysRevE.76.031906], foams, and fiber networks [PhysRevLett.96.017802].
Conservation laws in the form of PDEs on hypergraphs have been used in the simulation and optimization of gas networks [RuefflerMH2018] and other networks of pipelines. They have been extended to networks of traffic (streets and data), (tele-)communication, and blood flow. For an overview of the main ideas that are related to these applications, the reader may consult [Garavello2010, BressanCGHP2014]. Additionally, rigorous mathematical analysis of such problems is developing to a field of current research [SkreMR2021].
We conclude the overview over some applications by stating that regular surfaces and volumes can also be interpreted as hypergraphs. Thus, PDEs on surfaces [DziukE2013] and standard “volume” problems (in which the hyperedges have the same dimension as the surrounding space and at most two hyperedges meet in a common hypernode) are also covered by our approach.
Hypergraph models usually are approximations of problems in higher dimensional networks of thin structures, for example a network of thin pipes or thin plates in 3D. As a model example we give a rigorous derivation of a diffusion equation on a hypergraph. More precisely, we consider a network of thin plates in three dimensions, where the thickness of the plates is small compared to their length. We denote the ratio between the thickness and the length by the small parameter
. Due to the different scales the computational effort for numerical simulations is very high. To overcome this problem the idea is to replace the thin-structure by a hypergraph. For this we give a rigorous mathematical justification using asymptotic analysis. We pass to the limitin the weak formulation of the problem, and derive a limit problem stated on the hypergraph. The solution of this limit-problem is an approximation of the model in the higher-dimensional thin domain. Singular limits for thin plates and shells (leading to lower-dimensional manifolds in the limit ) in elesticity can be found in [ciarlet1997mathematical, ciarlet2000theory]. Dimension reduction for a folded elastic plate is treated in [le1989folded]. Singular limits leading to hypergraphs for fluid equations can be found in [maruvsic2003rigorous], where a Kirchhoff law in a junction of thin pipes is derived, and [maruvsic2019mathematical] where junctions of thin pipes and plates are treated using the method of two-scale convergence.
The remainder of this manuscript is structured as follows: First, we discuss conservation equations on hypergraphs. Second, we rigorously formulate an elliptic model equation and investigate some of its properties in Section 3. Third, we discuss its discretization by means of the HDG method in Section 4. Fourth, we discuss how PDEs on hypergpahs can be obtained by a model reduction approach, in particular, by considering singular limits. The publication is wrapped up, by a section on possible conclusions.
2. Conservation equations on geometric hypergraphs
A hypergraph consists of a finite set of hyperedges and a finite set of hypernodes. We refer to it as a geometric hypergraph if the hyperedges are smooth, open manifolds of dimension with piecewise smooth, Lipschitz boundary and the hypernodes can be identified with smooth subsets of the boundaries of these hyperedges. More specifically, the boundary of each hyperedge is subdivided into nonoverlapping subsets such that . We associate to
an index vectorand isometries
The hypernodes are thus identified with the closures of the subsets of the boundaries of one or more hyperedges. Their dimension is .
has the structure of a hypergraph in the classical sense as each edge connects a set of nodes . The dual hypergraph describes the situation where each hypernode connects hyperedges with indices .
We call a hypernode a boundary hypernode if , i.e., it is part of the boundary of only a single hyperedge. Accordingly, we define the set of boundary hypernodes and the set of interior hypernodes .
As special cases: a geometric graph is a geometric hypergraph where the edges are smooth curves and the nodes are their end points. If every hypernode is either at the boundary or connects exactly two hyperedges, the hypergraph represents a piecewise smooth manifold.
The structure might become more evident if we consider an embedded geometric hypergraph in some ambient space , as in Figure 1 on the left. In this case, the isometries are identical mappings and the hypernodes are identified with the boundary pieces . On the right of this figure, the same hypergraph is displayed without embedding. In this case, the hyperedges are objects in , possibly with a non-flat metric. Hypernodes are intervals in , inheriting their metric through the isometries .
Due to the isometries , every point of a hypernode is uniquely identified with a point on the boundary of each of the hyperedges it connects. Thus, convergence of a point sequence in the union of these hyperedges to a point on the hypernode is well-defined, for instance by considering the (finitely many) subsequences on each hyperedge. Also, a distance between two points on different hyperedges sharing a hypernode is defined locally by these isometries and triangle inequality.
The domain of the hypergraph, its closure, and its boundary are
In this definition, the hyperedges are considered open with respect to their topology and do not contain their boundaries. The hypernodes are closed. We introduce the skeletal domain
We make the assumption that is connected. Note that this implies that any two hyperedges are either connected by a common node or not connected, since is open, see (2.2). Without such an assumption, the problems of partial differential equations below separate into subproblems, which then can be analyzed and solved independently.
In Figure 1, comprises all blue hypernodes, which also include the end points of the red hypernode. The union of the red and blue hypernodes is . The domain consists of the interior of the red hypernode and the the three hyperedges.
Many concepts of standard domains in transfer to , even if it is not a manifold. In particular, the notion of a small open ball with radius around , see Figure 2, in is maintained by construction and thus the notion of open subsets. A subset is called compactly embedded in if its closure is contained in and thus has a positive distance to .
A function is continuous on , if it is continuous inside each hyperedge and its limits on a hypernode are consistent between all hyperedges connected by this hypernode. Analogously, a function is in if it is in for all and it is in if it is in for all .
Remark 2.1 (Comparison to standard nomenclatures).
In this article, we mix concepts from graph theory, partial differential equations, and finite elements. Thus, a clash of names was unavoidable. What is referred to as a hypernode here, is a face —an edge in two dimensions— in finite element literature, while the hyperedges here correspond to mesh cells or elements. In order to reduce ensuing confusion, we consistently use the term “hyperedge”. Another difference to finite element literature is established by the fact that we consider the hypergraph fixed and are not concerned with refinement limits. Finally, we would like to point out that there has been a concept of geometric hypergraphs in the literature; it is nevertheless very limited, such that we coin this term in a new way here, meaning a hypergraph whose elements are geometric shapes themselves.
2.2. Continuity equations on hypergraphs
Next, we conduct a heuristic derivation, employing control volumesin the shape of infinitesimal, open hyperballs. Let be a conserved quantity and be its flux. Then, the conservation property of is usually stated in integral form such that for any such control volume there holds
When is a subset of a Lipschitz manifold , the meaning of this statement is clear if is a smooth tangential vector field in and is the outer normal vector to in the tangential plane of . The term denotes the volume element of the manifold, and is the induced surface element.
If the hyperball intersects a hypernode in which several edges meet, meaning can be given to equation (2.4) by the following observation: if are the hyperedges which meet in inside , then for the intersection has a piecewise smooth boundary . We observe that is in the interior of (see Figure 2 for an illustration) and the boundary of is nowhere tangential to . Thus, with the assumption that no mass is created or destroyed in the hypernode , the conservation property (2.4) can be restated as
Again, the flux and the outer normal vector to are well defined along in the tangential plane of .
As a generalization of (2.5), we allow for sinks and sources living in the hyperedges and living within hypernode : This can be implemented by setting
where positive and describe sources, while negative and describes sinks.
Before we convert (2.4) into a problem of partial differential equations, we make the simplifying assumption that the hyperedges and hypernodes are planar and that is the standard Lebesgue measure. This way, we avoid delving into the complexities of surface partial differential equations. This simplification is purely for the ease of presentation and we refer the readers to [DziukE2013] and [BENARTZI2007989] for more general surfaces in the elliptic and hyperbolic settings, respectively.
Thus, in the interior of each hyperedge , we can apply Gauss’ divergence theorem in standard form to obtain
If on the other hand overlaps a hypernode which connects hyperedges , we can still apply the divergence theorem in each hyperedge to obtain
This notion also extends to control volumes intersecting with several hypernodes in a natural way. Then, rearranging the sum over boundary integrals yields
for any control volume . Here, is the standard divergence of the differentiable vector field and is the summation operator such that on a hypernode with hyperedges there holds
A vector field is usually called solenoidal, if the left side of equation (2.9) vanishes for any control volume . The right hand side of this equation generalizes this notion from standard domains to hypergraphs. Therefore, we call a piecewise smooth vector field solenoidal, if
Note that the second condition is an extension of Kirchhoff’s junction rule from points to higher dimensional hypernodes.
To put it in a nutshell, assuming there are no leaks and sources in hypernodes and hyperedges, the conservation condition (2.5) induces the PDE–interface problem to find and such that
Analogously, the continuity condition (2.6) induces the PDE interface problem to find and such that
In (2.12) and (2.13), and might be linked by some phenomenological description, i.e., (depending on the specific application). Both equations are complemented by appropriate initial and boundary conditions. Beyond this, additional continuity constraints might be formulated, such as , , ….
3. Elliptic model equation
The standard diffusion equation in mixed form defined on a hypergraph is a conservation equation of type (2.12) for the flux of a scalar function . This is for instance known as Fourier’s law of thermal conduction, where is the temperature and is the dimensionless heat conductivity of the material. It is also Fick’s law of diffusion where is a concentration and is the diffusion coefficient.
Like in the previous section, we simplify the presentation by assuming that all hyperedges are flat and thus can be identified with a domain in . In the more general case, the differential operators must be replaced by their differential geometric counterparts as in [DziukE2013].
We focus on the stationary case and set the time derivative in (2.12) to zero. Thus, the discussion of the previous section leads to the following problem: find satisfying
for all , right hand sides and , and a diffusion coefficient . A justification by taking the limit of thin domains can be found in Section 5 below.
We observe that in (3.1) the diffusion equation (3.1a) is complemented by three boundary and interface conditions. First, it is closed by a “Dirichlet” boundary condition (3.1b): We choose a non-empty set of “Dirichlet” hypernodes, on which we impose for a prescribed boundary value . In (3.1c), we employ a continuity constraint. This constraint prohibits jumps in the primary unknown across interior nodes, and therefore, loosely speaking, imitates the standard constraint that of the domain.
On interior nodes , we set out with Kirchhoff’s junction law, but with the option of a concentrated source in (3.1d). This equation also incorporates the Neumann condition , since on a boundary hypernode the sum in the definition (2.10) of the operator reduces to a single hyperedge. Note that (3.1d) for on interior nodes serves as compatibility condition for mimicking .
Definition 3.1 (Function spaces on hypergraphs).
For each let be the standard Sobolev space on and be the standard trace operator.
Then, we define
where and are the traces of from the hyperedges and on , respectively. Due to the equality of traces in the definition of , we can define the trace operator to the skeleton
Additionally, the spaces and are defined as
and we denote the dual spaces of by and of by .
Norms ( and ) on the respective spaces ( and ) are induced by summed versions of the local scalar-products:
These definitions have a few immediate consequences:
is a well-defined and surjective, linear, and continuous operator.
We have the Gelfand triple relations
Note that is analogous to space in of Raviart and Thomas [RaviartT1977a].
The space with inner product is a Hilbert space.
Obviously, is a subspace of the Hilbert space , and the function
is continuous and is its kernel. Thus, is closed. ∎
A weak solution to the primal formulation of (3.1) with , , and is a function with on all , and
In particular, if and , we can rewrite (3.11) as
3.1. Existence and uniqueness of solutions
Assume for that there is a lifting with on all . If with a. e., , , and all are Lipschitz domains, there is an unique weak solution according to Definition 3.3, which continuously depends on the data.
Due to the existence of , we can reduce the problem to the one with homogeneous Dirichlet values if we replace by and modifying the right hand side accordingly. Since the right hand side is bounded and is a Hilbert space, it suffices to show ellipticity of the weak form to conclude the proof by the Lax–Milgram lemma. We note that for there holds
Thus, the following Poincaré–Friedrichs inequality implies ellipticity and concludes the proof. ∎
Lemma 3.5 (Poincaré–Friedrichs inequality for ).
For all it holds that
Similar to the standard case of subdomains in , this inequality follows easily by contradiction: To this end, we assume that there is a sequence with
Thus, is bounded in for all . Hence, by the weak compactness of the unit ball in and the Rellich-Kondrachov theorem, there exists a subsequence (also denoted ) such that
We have that (due to its completeness), and that the seminorm . Thus, is constant in all and overall continuous. Therefore it is overall constant and has to be zero, due to the zero boundary condition on Dirichlet nodes and the connectedness of . Hence, the strong convergence of in implies , which contradicts . Therefore, the Poincaré–Friedrichs inequality is valid. ∎
4. HDG method for elliptic model equation
When we derived PDE problems on hypergraphs, we were led to a formulation local on each hyperedge with coupling conditions on hypernodes. This is a structure which is nicely reflected in hybridized methods. Indeed, there the separation goes one step further. By putting degrees of freedom on the hypernode, values on hyperedges are not coupling anymore to other hyperedges across these hypernodes, but only to the values on the hypernodes constituting their boundary. Thus, differing from standard or discontinuous finite element methods, the number of hyperedges attached to a hypernode does not affect the solution process on a single hyperedge. Therefore, we consider hybridized methods ideally suited to PDEs on hypergraphs.
Hybridized discontinuous Galerkin (HDG) methods break the continuity condition (3.1c) by introducing Lagrange multipliers on each hypernode which enforce the continuity of fluxes (3.1d) weakly. It turns out though, that the Lagrange multiplier is an approximation to the solution of (3.1) on the skeleton itself.
With such methods, the actual PDE (3.1a) is represented locally on each hyperedge by Steklov-Poincaré operators on the hyperedges, which transform function values to flux values on the boundary of the hyperedges, a process called “local solver” in HDG terminology. The global problem is posed in terms of the degrees of freedom on the hypernodes only, yielding a square, linear system of equations.
In this respect, HDG methods have a similar structure as the family of HHO methods. These are based on hybridizing the primal formulation and lead to a rather simple error analysis on polytopic meshes where only projections are used (as opposed to the rather complicated projections used for HDG). This is achieved by a novel stabilization design [DiPietro2015]. For recent developments in hybrid high-order and HDG methods, the reader may consult [Burman2018, Qiu2016].
The separation of the local solution of bulk problems from the global coupling of interface variables is also achieved by the virtual element method [VEM0, VEM1]. Thus, it fits into our view of coupled differential equations on connected hyperedges. Different to the methods discussed so far, it does not rely on polynomial shape functions inside mesh cells but rather on forms of fundamental solutions of any shape [VEM2]. Accordingly, when applied to hypergraphs, the actual type of local solvers and of the specific boundary trace operators will differ from our approach, but remain within the same principal concept.
4.1. The hybridized dual mixed formulation
In physical applications, there often is a need to receive reasonable approximations for both the primal unknown and the dual unknown . In other words, considering diffusion, we would like to know both the distribution of some species’ concentration and the species “movement” (flux). This becomes particularly important if we interpret as pressure and as fluid flow through a porous medium (Darcy’s equation). In this situation, the flow field will govern the movement of chemical species dissolved within the fluid. It is often the main quantity of interest and conservativity is crucial. Therefore, we turn to the mixed formulation.
The mixed HDG methods use the weak, dual, mixed, hybrid formulation of (3.1), i.e., find with on all such that
Well-posedness of this formulation can be deduced from Theorem 3.4 if . Indeed, on the one hand, this implies that the (uniquely existing) solution of Definition 3.3 solves (4.1) with , , and . On the other hand, for any solution of (4.1), we have (by the space’s definition), and in the weak sense. Therefore, any solution to (4.1) satisfies Definition 3.3.
Equations (4.1a) & (4.1b) are local equations on the hyperedge, like in the standard case of a domain. They only couple to the Lagrange multipliers on the boundary of the hyperedge. Thus, we can eliminate them locally in the fashion of the Schur complement method. To this effect, we introduce the local solution operator for the right hand side . It is in fact a Steklov-Poincaré operator on mapping the Dirichlet data to the normal trace of the flux in (4.1c).
Then, the solution of (4.1) can be characterized as
The Steklov-Poincaré operators in this equation are the same ones as in the case of a manifold. They do not depend on the connectivity of a hypernode to other hyperedges. Thus, their implementation does not differ from that of a standard finite element method. The only difference lies in the structure of the sum on the left, and is thus almost purely of algebraic nature.
For inhomogeneous right hand side , we can define the operators
In order to obtain a better understanding of the Steklov-Poincaré operators, we follow the route laid out in [CockburnGL2009] for the discrete version and define the solution operators
The well-posedness and linearity of all local solution operators follow directly from the fact (see for instance [BoffiBrezziFortin13]) that the mixed formulation on a single hyperedge is well-posed for any given and its solution depends continuously on . Entering these solution operators into (4.1c) yields
since . By some simple transformations of (4.1), we can write (4.2) with inhomogeneous right hand sides in terms of bilinear and linear forms. This argument allows to reduce the problem to finding with on all , such that
Obviously, bilinear form and linear form are continuous due to the continuity of operators and . Surprisingly, we have recovered a symmetric bilinear form. The following lemma is a key to the discrete well-posedness and adds the fact that this form is even -elliptic.
If and , bilinear form from (4.6b) is elliptic.
Like in the proof of the Poincaré-Friedrichs inequality, we prove ellipticity of by a contradiction argument. To this end, let a sequence in such that
Thus, there exists a subsequence in , and by the compact embedding of in there holds again for a subsequence in . Since is continuous and converges weakly in we obtain weakly in for each hyperdege and therefore also in . Thus, (4.7) implies that . We denote by the solution to (4.1a) and (4.1b) associated to , especially we have . Hence, for every we have
Moreover, we have that the divergence operator
is surjective, and therefore
This, however, implies that is constant on . Furthermore, since is constant on , we can deduce by (4.8) and Gauss’ divergence theorem that is constant and
The contradiction argument is concluded by the fact that some hyperedges are adjacent to the Dirichlet nodes and thus on their boundary. For the other hyperedges, follows from connectedness of . Thus, on in contradiction to . Altogether we showed that for all it holds that
Together with (4.6b) we obtain for a positive constant
i.e., the ellipticity of on .
4.2. HDG methods in dual mixed form
Let be some finite dimensional, scalar function space. Then, we define the space of discrete functions on the skeleton by
The mixed HDG methods involve a local solver on each hyperedge , producing hyperedge-wise approximations and and of the functions and in equation (4.1), respectively. Here, is some finite dimensional, scalar function space, and is some finite dimensional, vector valued function space. We will also use the concatenations of the spaces and , respectively, as a function space on , namely
The HDG scheme for (4.1) on a hypergraph consists of the local solver and a global coupling equation. The local solver is defined hyperedge-wise by a weak formulation of (4.1) in the discrete spaces and defining suitable numerical traces and fluxes. Namely, given find and , such that
hold for all , and all , and for all . Here, is the penalty coefficient. While the local solvers are implemented hyperedge by hyperedge, it is helpful for the analysis to combine them by concatenation. Thus, the local solvers define a mapping
where for each hyperedge holds and . Analogously, we set and , where now the local solutions are defined by the system
Once has been computed, the HDG approximation to (4.1) on will be computed as
The global coupling condition is derived through a discontinuous Galerkin version of mass balance and reads: Find , such that for all
Hybridized DG methods in dual mixed form differ by the choice of local polynomial spaces and the stabilization parameter . Defining as the space of multivariate polynomials of degree at most , Table 1 lists some well-known combinations on simplices.
Well-posedness of the local solvers for all of them is proven in [CockburnGL2009]
and the works cited there. Analogous combinations based on tensor product polynomials exist for hypercubes.
Existence and uniqueness of the discrete solution , , and to the HDG method can be shown repeating the arguments mentioned in Section 4.1 in the finite-dimensional setting. A natural assumption is the well-posedness of the local problems (4.14), see Remark 4.3.
Given the local solvers, the HDG method for elliptic diffusion problems is consistent with respect to the solution to (4.1). Using consistency, we can immediately apply the analysis in [CockburnGW2009], as it proceeds locally for each hyperedge. Thus, we obtain optimal convergence rates for LDG-H (and also RT-H by slight adaptions) on simplicial hypergraphs. They also transfer to quadrilateral hypergraphs, since these allow for a Raviart–Thomas projection satisfying equation (2.7) in [CockburnGW2009].
4.3. Numerical convergence tests for LDG-H
errors (err) and estimated orders of convergence (eoc) of linear approximation to the diffusion equation for hypergraphs with hyperedge dimension.
Next, we consider a convergence example on a hypergraph. It is constructed to approximate
where the Dirichlet nodes are those that are located on the boundary of with .
The filling indicates that the cube has been times uniformly refined (in the standard three dimensional sense), and the calculation is conducted on the dimensional “surfaces” of this filling. These surfaces themselves might be further refined times, and these refined surfaces are identified to be our standard hyperedges, see Figure 3 for an illustration.
The dimensional faces of this approach are interpreted as nodes and the nodes located on the boundary of the unit cube are considered Dirichlet nodes. All other nodes are supposed to be interior nodes. The solution is constructed to be , diffusion coefficient , and right-hand side . Of course, polynomial degrees are supposed to exactly reproduce the given solution, which is true in our numerical experiments. Thus, we only plot the errors for in Table 2.
Interestingly, the errors converge although with filling , also the computational domain increases for and . However, the rate of convergence deteriorates by if , and if . The optimal order is obtained for .
Beyond this, the refinement indicated with uses filling level and then uniformly refines the respective faces. This does not lead to an increase of the computational domain (even if ) and, therefore, gives the optimal convergence rate .
The aforementioned results have been obtained using our code HyperHDG [HyperHDGgithub].
5. Hypergraph PDE as singular limit
The aim of this section is to derive the hypergraph model (3.1) as a singular limit of a 3D-model problem as illustrated in Figure 4. We exemplary use the figure to illuminate the basic ideas: We assume to have a diffusion problem on a domain consisting of three thin plates (in gray) and a (red) joint. This is the problem, which we would like to solve. However, we do not want to solve it in three spatial dimensions, but would like to reduce it to a two-dimensional problem—for example since we have limited compute sources, the domain is very large, or the domain is very complicated to mesh. Thus, we let the thickness of the three plates (and therefore also the thickness of the joint) go to zero by considering , and construct a two dimensional limit problem. The solution of this two dimensional problem lives on the mid-planes of the three planes and their joint. It in some sense is supposed to approximate the solution of the original (three-dimensional) problem for which is a small, positive number.
The principal idea of the limit process is to map equations on the thin structures depending on to fixed reference domains independent of , where we can use standard compactness methods from functional analysis. However, the transformed problem includes -dependent coefficients. Thus, the crucial point for the derivation of the limit model is to establish a priori estimates that are uniform with respect to .
5.1. Description of the 3D model problem
We consider the simplified case of one hypernode with length connecting hyperedges for which are rectangles with side lengths and . Thus, Figure 4 shows the case with . The opposite node of with respect to is denoted by (and is a boundary node). Without loss of generality, we assume that lies in the -axis and we have
We denote by a unit normal vector to and define extruded hyperedges for and
Hence, is a hexahedron with side lengths and , and with thickness . We construct now a domain which contains the union of all these extruded hyperedges and a nonoverlapping decomposition of this domain. To this end, let be chosen such that the sets
do not overlap. We denote the side of that contains by , and define
The side lengths of are and . Additionally, we define the convex hull of the node and the sides :
By construction, we have
Then, we define the thin domain as
On we define a diffusion problem and then to pass to the limit in order to derive a problem on the hypergraph . To ensure uniqueness for our model we assume a zero-Dirichlet boundary condition on one face . We consider the following problem for the unknown
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http://www.123rf.com/search.php?word=pain&alttext=1&orderby=
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math
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https://henheiprophtext.web.app/1370.html
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math
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In particular, capm only works when we make assumptions about preferences which dont make much sense. Arbitrage arises if an investor can construct a zero investment portfolio with a sure profit. The capitalassetpricing model and arbitrage pricing theory. Ppt arbitrage pricing theory powerpoint presentation. Arbitrage from wikipedia, the free encyclopedia for the film, see arbitrage film. What are the practical applications of arbitrage pricing. The arbitrage pricing theory and subsequent models advanced thinking from a singlefactor beta world to a view of return and risk through multiple factors. Practical applications of arbitrage pricing theory are as follows.
The arbitrage pricing theory apt was proposed as a more complex and therefore more complete alternative to the capital asset pricing model capm which was thought to be too simple and limited. Arbitrage pricing theory apt is a multifactor asset pricing model based on the idea that an assets returns can be predicted using the linear relationship between the assets expected return and a number of macroeconomic variables that capture systematic risk. A simple explanation about the arbitrage pricing theory. The weak form states that current asset prices reflect all of the information implicit in past prices and trades. The market permits no arbitrage opportunities if and only if for any portfolio p, vp cp 0 implies ep 0. An apt arbitrage pricing theory model has 3 factors namely, market, inflation and exchange rate risk. Arbitrage pricing theory model application on tobacco and.
Arbitrage pricing theory apt is an alternative to the capital asset pricing model capm for explaining returns of assets or portfolios. Factor models, basis portfolios, apt, intertemporal asset. It is a much more general theory of the pricing of risky securities than the capm. Chapter 10 arbitrage pricing theory and pdf chapter 11. The model identifies the market portfolio as the only risk factor the apt makes no assumption about. Intuitively, our formulation can be viewed as a transposed version of standard continuoustime nance theory, where the index of the stochastic process refers. Arbitrage pricing theory apt is an alternate version of the capital asset pricing model capm. Such a necessity condition is surprisingly absent in the apt literature. Focusing on asset returns governed by a factor structure, the apt is a oneperiod. Based on intuitively sensible ideas, it is an alluring new concept.
Since no investment is required, an investor can create large positions to secure large levels of profit. Arbitrage pricing theory how is arbitrage pricing theory abbreviated. It states that the market price which reflects the associated risk factors of an asset represents the value that prevents an investor from exploiting it. Arbitrage pricing theory, apt, stockholm stock exchange. The arbitrage pricing theory apt model may be considered as an extension of the capm allowing for multiple factors.
While the capm is a singlefactor model, apt allows for multifactor models to describe risk and return relationship of a stock. Apt abbreviation stands for arbitrage pricing theory. Speci cally, we propose a di erent formulation of the classical apt in terms of cumulative portfolios of assets in the economy. Arbitrage pricing theory apt spells out the nature of these restrictions and it is to that theory that we now turn. The capital asset pricing model capm and the arbitrage pricing theory apt help project the expected rate of return relative to risk, but they. According to the arbitrage pricing theory, the return on a portfolio is influenced by a number of independent macroeconomic variables. The arbitrage pricing theory apt was developed primarily by ross 1976a, 1976b.
K k f ik k i k k k k e rtrack ik rf ik k rf r e r 11 1 6 1. Theory, are discussed as special cases of modern asset pricing theory using stochastic discount factor. Arbitrage pricing theory stephen kinsella the arbitrage pricing theory, or apt, was developed to shore up some of the deficiences of capm we discussed in at the end of the last lecture. Pdf the arbitrage pricing theory approach to strategic. Arbitrage pricing theory assumptions explained hrf. Arbitrage pricing theory apt columbia business school. Arbitrage pricing theory apt like the capm, apt is an equilibrium model as to how security prices are determined this theory is based on the idea that in competitive markets, arbitrage will ensure that riskless assets provide the same expected return created in 1976 by stephen ross, this theory predicts a relationship between the returns of a. It is a oneperiod model in which every investor believes that the stochastic properties of returns of capital assets are consistent with a factor structure.
Unlike the capm, which assume markets are perfectly efficient. In finance, arbitrage pricing theory apt is a general theory of asset pricing that holds that the expected return of a financial asset can be modeled as a linear function of various factors or theoretical market indices, where sensitivity to changes in each factor is represented by a factorspecific beta coefficient. Primer on merger arbitrage a merger arbitrage opportunity is one in which a probable event occurring in the future, i. In the lzth economy there are n risky assets whose returns are generated by a kfactor model k is a fixed number. This is known as the arbitrage pricing theory apt in equilibrium, this relationship must hold for all securities and portfolios of securities ri. The corresponding expected risk premium of each factor is 4. It is considered to be an alternative to the capital asset pricing model as a method to explain the returns of portfolios or assets. The capital asset pricing model capm and the arbitrage pricing theory apt have emerged as two models that have tried to scientifically measure the potential for assets to generate a return or a loss.
Apt considers risk premium basis specified set of factors in addition to the correlation of the price of the asset with expected excess return on the market portfolio. Stephen ross developed the arbitrage pricing theory apt in 1976. Loosely speaking, arbitrage is the possibility to have arbitrarily large returns. The purpose of this study was to applicant the arbitrage pricing theory model in the tobacco and cigarette industry listed on the idx. Both of them are based on the efficient market hypothesis, and are part of the modern portfolio theory. When implemented correctly, it is the practice of being able to take a positive and. Espen eckbo 2011 basic assumptions the capm assumes homogeneous expectations and meanexpectations and meanvariance variance preferences. Apt involves a process which holds that the asset in question and the returns which are related to it can be predetermined pretty easily when the relationship that the assents returns have with all the different macroeconomic factors affecting the risk of the asset. Solutions chapter 010 arbitrage pricing theory and.
Arbitrage pricing theory apt is an asset pricing model which builds upon the capital asset pricing model capm but defines expected return on a security as a linear sum of several systematic risk premia instead of a single market risk premium. It involves the possibility of getting something for nothing. Furthermore, we exhibit the practical relevance and assumptions of these models. The formula includes a variable for each factor, and then a factor beta for each factor, representing the securitys sensitivity to movements in that factor. It is a one period model in which every investor believes that the stochastic properties of capital assets returns are consistent with a factor structure. The capitalassetpricing model and arbitrage pricing. Arbitrage pricing theory, often referred to as apt, was developed in the 1970s by stephen ross. The capital asset pricing model and the arbitrage pricing. This theory, like capm, provides investors with an estimated required rate of return on risky securities. The arbitrage pricing theory has been estimated by burmeister and mcelroy to test its sensitivity through other factors like default risk, time premium, deflation, change in expected sales and market returns are not due to the first four variables. The arbitrage pricing theory apt was developed primarily by ross. Factor representing portfolios in large asset markets cemfi.
The counterexample is valuable because it makes clear what sort of additional assumptions must be imposed to validate the theory. If we combine expressions 1 and 6, we finally obtain that in terms of excess. The arbitrage pricing theory approach to strategic portfolio planning. Arbitrage arises if an investor can construct a zero beta investment portfolio with a return greater than the riskfree rate if two portfolios are mispriced, the investor could buy the lowpriced portfolio and.
Arbitrage pricing theory university at albany, suny. It needs to be emphasized that the no arbitrage condition is not only sufficient but also necessary for the validity of the asset pricing formula. Overview and comparisons the arbitrage pricing theory apt was developed by stephen ross us, b. Arbitrage pricing theory definition arbitrage pricing. An overview of asset pricing models university of bath bath. Arbitrage pricing theory the notion of arbitrage is simple. Because it includes more factors, consider the arbitrage pricing theory more nuanced if not more accurate, than the capital asset pricing model.
The arbitrage pricing theory apt ross 1976,1977 constitutes one of the most. What is the abbreviation for arbitrage pricing theory. Arbitrage pricing theory apt is a multifactor asset pricing theory using various macroeconomic factors. Capital asset pricing andarbitrage pricing theory prof. Arbitrage pricing theory and multifactor models of risk and return frm p1 book 1. Apt, see arbitrage pricing theory apt apv, see adjusted present value apv model arbitrage pricing theory apt, 112 arbitrage proof example, 30, 33, 34 asset earning power, 104 audit, 349, 388, 393, 493 average rates of return, 1 b bankruptcy costs, 226, 241, 242, 246 beta value. Pdf the arbitrage pricing theory relates the expected rates of. A short introduction to arbitrage pricing theory apt is the impressive creation of steve ross. The theory was first postulated by stephen ross in 1976 and is the.
Arbitrage pricing theory gur huberman and zhenyu wang federal reserve bank of new york staff reports, no. Arbitrage pricing theory asserts that an assets riskiness, hence its average longterm return, is directly related to. Apt is an interesting alternative to the capm and mpt. Arbitrage pricing theory apt and multifactor models. Arbitrage pricing theory and multifactor models of risk and return 104 important to pork products, is a poor choice for a multifactor sml because the price of hogs is of minor importance to most investors and is therefore highly unlikely to be a priced risk factor. A more rigorous derivation 9 each of the coefficients. It was developed by economist stephen ross in the 1970s. Arbitrage pricing theory apt is a multifactor asset pricing model based on the idea that an assets returns can be predicted using the linear relationship between the assets expected return. Pdf the arbitrage pricing theory apt of ross 1976, 1977, and. The revised estimate of the expected rate of return on the stock would be the old estimate plus the sum of the products of the unexpected change in each factor times the respective sensitivity coefficient.
Arbitrage pricing the arbitrage pricing theory considers a sequence of economies with increasing sets of risky assets. The arbitrage pricing theory apt is due to ross 1976a, b. Are practitioners and academics, therefore, moving away from capm. Financial economics arbitrage pricing theory theorem 2 arbitrage pricing theory in the exact factor model, the law of one price holds if only if the mean excess return is a linear combination of the beta coef. Arbitrage pricing theory definition of arbitrage pricing. Pdf the arbitrage pricing theory and multifactor models of asset. G12 abstract focusing on capital asset returns governed by a factor structure, the arbitrage pricing theory apt is a oneperiod model, in which preclusion of arbitrage over static portfolios. The literature on asset pricing models has taken on a new lease of life since the emergence of the arbitrage pricing theory apt, formulated by ross 1976, as an alternative theory to the renowned capital asset pricing model capm, proposed by sharp 1964, lintner 1965 and mossin 1966. Arbitrage refers to nonrisky profits that are generated, not because of a net investment, but on account of exploiting the difference that exists in the price of identical financial instruments due to market imperfections. Arbitrage pricing theory synonyms, arbitrage pricing theory pronunciation, arbitrage pricing theory translation, english dictionary definition of arbitrage pricing theory. The apt model in this study uses macroeconomic variables consisting of exports, inflation, exchange rates, gdp and economic growth. Arbitrage pricing theory for idiosyncratic variance factors. Since its introduction by ross, it has been discussed, evaluated, and tested.
Capital asset pricing model and arbitrage pricing theory. Pdf describe the arbitrage pricing theory apt model. One of the two leading capital market theories of 1960s and 1970s, it is based on the law of one price. Arbitrage pricing theory how is arbitrage pricing theory. Classical asset pricing models, such as capm and apt arbitrage pricing 1. Ki november 16, 2004 principles of finance lecture 7 20 apt. The arbitrage pricing theory is something that can be used for asset pricing.348 257 415 645 1518 1532 129 1323 119 848 30 1132 127 1279 379 326 171 705 1177 1148 526 1038 972 699 845 623 1227 1466 435 936 1149 109 554
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http://wikamn.se/guestbook/?page=4472
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math
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http://www.chegg.com/homework-help/physics-for-scientists-and-engineers-volume-1-6th-edition-chapter-9-solutions-9781429201322
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math
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Solutions for Chapter 9
First point is an the rim
2nd point is between the rim and axis of rotation of half distance
(a) since so.
Point moves more distance than in a given time.
(b) But both the points moves the some angle because both are stationary w. r. t rim.
(c) since, so,
Hence, because R > r
(d) Two points have same angular velocity (w) because both are stationary w. r. t. to rim
(e) Two points have tangential acceleration because
(f) Two points have zero angular acceleration because and w is constant
(g) since, or,
As, so, point on rim has more centripetal acceleration.
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https://integrafinserve.in/2013/10/22/atm-banks-should-show-real-yield-on-fixed-deposits/
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math
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The main problem lies in the fact that what banks are projecting is the simple interest and not the compound annual growth rate.
By Narendra Nathan, ET Bureau | 22 Oct, 2013, 11.45AM IST | Economic Times
MUMBAI: Recently, the Reserve Bank of India has taken steps to increase the level of transparency in bank loans. For example, RBI has restricted banks from charging higher interest rates and at the same time projecting them as “zero interest loans”. However, banks continue to follow less transparent practice with other products and most important among them is the interest paid on fixed deposits (FDs). For example, the FD pamphlets from most banks usually carry two columns – one for the interest rate and other for the “annualised yield”. The explanation to the annualised yield column will also state that the “annualised yield is calculated on the basis of quarterly compounding for the entire tenure“.
Why is giving annualised yield bad, you may ask. The problem is not in giving the annualised yield, but in giving the wrong yield (i.e, much higher figures) to grab the attention of FD investors. For example, a bank offering an interest of 8.75% per annum for its 10-year deposits usually projects that the annualised yield for the same is as 13.76%. Though the actual yield will be slightly higher due to quarterly compounding, the compound annual growth rate (CAGR) for a 10-year FD will only be 9.04% and not 13.76% as projected by the bank.
Now, let us take a closer look at how these banks arrive at this 13.76% figure for the 10-year FDs. To make the computation easier, let us assume that the amount invested in the 10-year FD is Rs 1 lakh. Since the FD is compounded quarterly, 2.19% (i.e, 1/4 of 8.75%) of Rs 1 lakh is added at the end of first quarter. So the value at the end of first quarter goes up to 102,190. Similarly, 2.19% of 102,190 is added at the end of second quarter and this process is continued till the end of 10 years. So the initial investment value of Rs 1 lakh grows to Rs 237, 635 at the end of 10 years. Since this is an absolute return of 137.64%, banks divide this value by 10 years to arrive at the 13.76% yield.
Since the above mentioned computation is correct, what is the problem, you may ask. The main problem lies in the fact that what they are projecting is the simple interest and not the compound annual growth rate. For example, the CAGR of an investment that has generated an absolute return of 300% in 10 years is just 14.87% and not 30% per annum. CAGR is the best way to compare return rates between two financial products and that explains why Sebi has made it mandatory for mutual funds to use CAGR while giving their historical returns.
Source : http://goo.gl/obpdcR
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| 2,745 | 7 |
http://broadwayentertainmentgroup.com/lib/category/topology/page/4
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math
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Contributions via 3 authors deal with facets of noncommutative geometry which are relating to cyclic homology. The authors supply fairly entire money owed of cyclic concept from various issues of view. The connections among (bivariant) K-theory and cyclic conception through generalized Chern-characters are mentioned intimately. Cyclic conception is the average environment for various normal summary index theorems. A survey of such index theorems is given and the options and concepts keen on those theorems are explained.
By H. S. M. Coxeter
Among the attractive and nontrivial theorems in geometry present in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. a pleasant evidence is given of Morley's striking theorem on perspective trisectors. The transformational standpoint is emphasised: reflections, rotations, translations, similarities, inversions, and affine and projective modifications. many desirable homes of circles, triangles, quadrilaterals, and conics are built.
By I.M. James
Scholars of topology rightly whinge that a lot of the elemental fabric within the topic can't simply be present in the literature, at the least now not in a handy shape. during this booklet i've got attempted to take a clean examine a few of this simple fabric and to prepare it in a coherent model. The textual content is as self-contained as i'll kind of make it and may be fairly available to a person who has an undemanding wisdom of point-set topology and crew concept. This ebook relies on a process sixteen graduate lectures given at Oxford and in different places at times. In a process that size one can't talk about too many issues with no being unduly superficial. even though, this used to be by no means meant as a treatise at the topic yet relatively as a brief introductory direction to be able to, i'm hoping, turn out worthy to experts and non-specialists alike. The creation incorporates a description of the contents. No algebraic or differen tial topology is concerned, even if i've got borne in brain the desires of scholars of these branches of the topic. routines for the reader are scattered in the course of the textual content, whereas feedback for additional examining are inside the lists of references on the finish of every bankruptcy. generally those lists contain the most resources i've got drawn on, yet this isn't the kind of e-book the place it's viable to provide a reference for every thing.
By R. Brown, T. L. Thickstun
This quantity includes the court cases of a convention held on the collage university of North Wales (Bangor) in July of 1979. It assembles study papers which replicate assorted currents in low-dimensional topology. The topology of 3-manifolds, hyperbolic geometry and knot concept end up significant subject matters. The inclusion of surveys of labor in those components may still make the booklet very worthwhile to scholars in addition to researchers.
By Stephen Lipscomb
Historically, for metric areas the hunt for common areas in size concept spanned nearly a century of mathematical examine. The background breaks evidently into classes - the classical (separable metric) and the fashionable (not-necessarily separable metric).
The classical concept is now good documented in different books. This monograph is the 1st publication to unify the trendy thought from 1960-2007. just like the classical conception, the trendy thought essentially consists of the unit interval.
Unique gains include:
* using pictures to demonstrate the fractal view of those spaces;
* Lucid assurance of various issues together with point-set topology and mapping thought, fractal geometry, and algebraic topology;
* a last bankruptcy comprises surveys and gives historic context for similar study that comes with different imbedding theorems, graph idea, and closed imbeddings;
* every one bankruptcy includes a remark part that gives ancient context with references that function a bridge to the literature.
This monograph should be worthy to topologists, to mathematicians operating in fractal geometry, and to historians of arithmetic. Being the 1st monograph to target the relationship among generalized fractals and common areas in size thought, it is going to be a usual textual content for graduate seminars or self-study - the reader will locate many correct open difficulties as a way to create extra study into those topics.
Topology, for a few years, has been the most interesting and influential fields of study in sleek arithmetic. even if its origins can be traced again a number of hundred years, it was once Poincaré who "gave topology wings" in a vintage sequence of articles released round the flip of the century. whereas the sooner historical past, also known as the prehistory, is usually thought of, this quantity is especially fascinated about the more moderen background of topology, from Poincaré onwards.
As may be noticeable from the checklist of contents the articles disguise quite a lot of themes. a few are extra technical than others, however the reader with no good deal of technical wisdom may still locate lots of the articles obtainable. a few are written through expert historians of arithmetic, others via historically-minded mathematicians, who are likely to have a distinct standpoint.
This textbook treats the classical elements of mapping measure idea, with a close account of its background traced again to the 1st 1/2 the 18th century. After a ancient first bankruptcy, the remainder 4 chapters boost the math. An attempt is made to take advantage of in simple terms straight forward tools, leading to a self-contained presentation. on the other hand, the publication arrives at a few actually striking theorems: the category of homotopy sessions for spheres and the Poincare-Hopf Index Theorem, in addition to the proofs of the unique formulations by means of Cauchy, Poincare, and others. even supposing the mapping measure idea you can find during this booklet is a classical topic, the therapy is clean for its easy and direct sort. the easy exposition is accented via the looks of numerous unusual subject matters: tubular neighborhoods with no metrics, adjustments among type 1 and sophistication 2 mappings, Jordan Separation with neither compactness nor cohomology, particular buildings of homotopy sessions of spheres, and the direct computation of the Hopf invariant of the 1st Hopf fibration. The e-book is appropriate for a one-semester graduate direction. There are a hundred and eighty routines and difficulties of other scope and hassle.
Broadway Entertainment E-books 2017 | All Rights Reserved
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s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647660.83/warc/CC-MAIN-20180321141313-20180321161313-00116.warc.gz
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CC-MAIN-2018-13
| 6,644 | 20 |
https://digithour.com/how-to-find-atomic-mass/
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math
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If you have a question about an atomic mass, you are not alone. You probably have come across this question several times. Atomic mass refers to the number of protons and neutrons within an atom. But how do you calculate this? There are several methods, and it all depends on what information you have. Below are some of the common methods. Follow these steps to calculate the mass of an element. They will help you identify the element’s isotopes and calculate its mass.
Atomic mass is the sum of protons and neutrons in an atom
A mass of an atom can be calculated in several ways. One method is to calculate its atomic mass using a standard value. Then, subtract the mass of the neutrons and protons. The final result is the atomic mass of the atom. There are three common methods for calculating an atom’s mass. They are: from a natural sample to a standard value.
The first atomic mass was calculated by William Herschel in 1856, and it is the same for all elements. The electron has an extremely small mass, about 1800 times smaller than the proton. Therefore, the mass number of an atom is the sum of the masses of its protons and neutrons, rounded to the nearest integer value. However, the mass number of an atom is often calculated by multiplying the atomic weights of each constituent atom.
In addition to being the number of protons and neutrons in an element, the atomic mass of an atom can be measured with the help of a periodic table. In this way, we can easily calculate the mass of different substances. Atomic mass is also important for determining the relative weight of the various elements. The atomic mass of an atom is the sum of the mass of the protons and neutrons in the nucleus.
The atomic mass of an element is also known as the atomic number. The number of protons is always the same for atoms of the same element. However, the number of neutrons varies for different elements. For example, an oxygen atom has eight protons, whereas sodium has eleven. However, the atomic mass of a substance is expressed in terms of its mass of protons and neutrons.
The atomic mass of an atom can be determined by multiplying the total mass of its protons and neutrons by the mu, a constant metric that can be derived from the relative isotopic mass. For example, a carbon atom is defined to have an atomic mass of 12 Da. Consequently, the relative atomic mass of all the carbon atoms in a molecule is twelve.
Atomic mass is a counted number
The atomic mass of a substance is a counted number, and is measured in atomic mass units, or amu. For instance, carbon has an atomic mass of 12 amu, and its neutrons and protons make up six amu of its mass. The number of these particles in an atom is also known as atomic weight, or atomic mass. However, this definition only works for one atom.
The mass of an atom is derived from the amount of protons and neutrons that compose it. The electrons make up very small amounts of mass, so they are not included in the calculation. Atomic mass is also used to refer to the average mass of all the different isotopes of an element. This metric is often expressed in decimal numbers. In addition, it can be calculated relative to other elements to determine their weight in terms of other substances.
Protons and neutrons have equal masses. Electrons are slightly heavier than protons. Generally, the atomic mass of an atom will be based on the number of protons and neutrons in the nucleus. However, if you subtract the electrons from the total mass of an atom, the atom will have more mass than the nucleus. In this way, it is possible to determine how much a particular element weighs in the mass of all its constituents.
The atomic mass of an atom can be calculated by adding the protons, electrons, and neutrons. In addition, the weighted measures of isotopes can also be used to estimate the atomic mass. The atomic mass of hydrogen is H = 1.00797 times the mass of the atom of water, which is u.m.a. (unit mass).
When looking up a specific atom, it can be confusing to determine which nucleons make up that atom. In addition to the mass, the neutrons must also be counted, and this is the best way to figure out the nucleon count. You can also look up the atomic number by subtracting the protons. If you know how many protons a certain atom has, then you can calculate its atomic mass.
Atomic mass is found in a nuclear symbol
The atomic mass number, abbreviated A, is the total number of protons and neutrons in an atom. In the periodic table, A is the mass number of carbon, and B is the mass of lead. Listed below are the mass numbers of the first six elements. Atoms can be defined as any combination of two elements. In other words, one element has two protons, and the other has four.
The atomic number of an atom is a major characteristic. It represents the number of protons in an atom, and is important in determining the chemical properties of an atom. The number of protons is indicated by the letter P. The number of electrons in an atom is represented by the letter N. The total mass of an atom is given by the sum of the mass numbers of the protons and neutrons, which are also found in an atomic symbol.
The atomic mass number of an atom is the same for all the atoms of a given element, but is not necessarily the same for all atoms of the same element. Atoms with similar numbers of protons and neutrons are called isotopes. For example, carbon atoms contain one or two extranuclear electrons, but have a different mass number. Carbon-12 and carbon-13 are symbolically the same, but have different mass numbers.
The atomic mass number is also known as the atomic weight. For example, the atomic mass number of silicon is 14 and it has fifteen neutrons. This means that a given isotope of silicon has a mass number of 29. In a nuclear symbol, the mass number is written in terms of atomic mass units. In the nuclear symbol, the number indicates the actual mass of the atom.
A nuclear symbol can contain a nucleus with a different mass. If the atom contains a neutron, it must also contain 33 protons. Therefore, the atomic mass number is equal to two-thirds of the total mass of the atom. It is important to understand the differences between the different nuclei, since the atomic mass of a certain atom is the dominant factor in the nuclear symbol.
Atomic mass is a quantity that represents all isotopes of an element
An atom’s mass is its average, or “atomic mass.” This is also known as atomic weight, because it is the average of all the isotopes present in the sample. Atomic mass of a single atom is less than the mass of all the protons, neutrons, and atomic nuclei in the sample. This difference is due to binding energy mass loss.
Because the difference between the atomic masses of two common isotopes is usually small, it can affect calculations, either in bulk or on an individual level. However, in some cases, atomic mass differences are substantial, affecting the result of bulk calculations or individual calculations. It is important to note that while atomic mass numbers can be useful in the calculation of mass for elements, their properties vary significantly among isotopes.
The number of protons and neutrons present in an atom is called its atomic mass. The two protons make up approximately equal mass, while the electrons contribute very little. The atomic weight of an element is known as the atomic weight. The weight of an atom in one element is equivalent to one-twelfth its mass in its ground state.
In nature, there are many isotopes of an element. In the laboratory, one of these is the most common of them all – carbon-12. Despite their similarities, they differ in their chemical behavior. Carbon-13 has more neutrons than carbon-12. In contrast, the latter has less mass, which is why it has a higher atomic mass.
The atomic mass of an element is known as its atomic number. The mass number of an atom is related to the number of protons. Carbon contains six protons and eight neutrons. Carbon-14 has eight neutrons. The two are oppositely polar, but they both have the same atomic number. Therefore, it has the same atomic mass as carbon.
In the case of hydrogen, an atom is made up of one proton and one electron. It is therefore electrically neutral. The positive charge in the nucleus must balance the negative charge of the electron. The electrons contribute little mass to the atom. But their presence pointed to the existence of other particles in the atom. And if there are other particles present in the atom, the positive charge must make up most of the mass of the atom.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948765.13/warc/CC-MAIN-20230328042424-20230328072424-00275.warc.gz
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CC-MAIN-2023-14
| 8,605 | 26 |
https://math-mprf.org/journal/articles/id1436/
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math
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An SDE Approximation for Stochastic Differential Delay Equations with State-Dependent Colored Noise
2016, v.22, Issue 3, 595-628
We consider a general multidimensional stochastic differential delay equation (SDDE) with state-dependent colored noises. We approximate it by a stochastic differential equation (SDE) system and calculate its limit as the time delays and the correlation times of the noises go to zero. The main result is proven using a theorem about convergence of stochastic integrals by Kurtz and Protter. It formalizes and extends a result that has been obtained in the analysis of a noisy electrical circuit with delayed state-dependent noise, and may be used as a working SDE approximation of an SDDE modeling a real system where noises are correlated in time and whose response to noise sources depends on the system's state at a previous time.
Keywords: stochastic differential equations, stochastic differential delay equations, colored noise, noise-induced drift
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100626.1/warc/CC-MAIN-20231206230347-20231207020347-00245.warc.gz
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CC-MAIN-2023-50
| 984 | 4 |
https://plati.market/itm/stats-option-1/1594317
|
math
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Theory of Statistics
1. Construct a discrete and interval series of distribution and represent them graphically. The interval number divided into four groups with equal intervals closed.
2. Calculate the number of indicators of the distribution center (average number, fashion, median) and variation indices of interval ryadu.Sdelat analysis of the results.
Industrial profitability level,% 13, 18, 26, 10, 18, 15, 20, 24, 18, 15, 24, 20, 22, 18.
1. Calculate the baseline (compared to 200 a year) and chain absolute and relative performance analysis of the dynamics of summary indicator values \u200b\u200b(first line).
2. Determine the average number of speakers.
3. identify the main trends of the dynamics of a number of methods of three-level moving average and the analytical equation for a straight alignment.
4. Calculate possible level summary measure for 2008 while maintaining the current trends, using average figures and analytical smoothing method.
5. Construct a line diagram of the dynamics of the original (actual) and calculated (theoretical) levels.
6. To study the changes in the structure of the indicator 200a, compared with 200 a year + 4. Show the relative values \u200b\u200bof the structure obtained in the form of pie charts.
7. Analyze all the results and draw conclusions.
Data on the production of gross regional product, bn. Rub.
+ 1 200a 200a 200a 200a + 2 + 3 + 4 200a
The gross regional product, only 29.31 30.12 32.35 33.98 35.74
Industry 12.46 15.26
agriculture and forestry 1.36 1.39
Construction 1.48 1.48
transport and communications 3.49 3.03
trade and public catering 1.8 1.31
Other industries 10.34 13.27
According to the data below on the implementation of the three types of goods to determine:
1. Individual indices amount of goods sold and prices.
2. Summary (total) index turnover.
3. The price index Paasche system.
4. The composite index of the physical volume of realization.
5. To check the correctness of calculations using the relationship formula indexes.
6. Perform a factor analysis changes turnover, defining its absolute change due to changes in the number of sales and due to price changes.
7. To analyze the results and draw conclusions.
The dynamics of sales of goods in the markets of the city.
Goods January January February February
A 223 20 250 25
B 342 30 400 35
257 45 350 40
Task 1. The following data is for the year:
• population, thousand people .:
at 1 January - 530.0; April 1 - 530.5; July 1 - 530.6; October 1 - 530.7; January 1, 200a of - 530.9
• The number of dead persons. - 9374
• The number of departures for permanent residence in other towns, people. - 680
• coefficient of vitality - 1.08
• The proportion of women in the total population,% - 59
• The proportion of women aged 15-49 in the total number of women,% - 40
Define: coefficients of fertility, mortality, este¬st¬vennogo, mechanical and general population growth;
- The number of births;
the number of arrivals for permanent residence from other localities;
- Specific fertility rates.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510730.6/warc/CC-MAIN-20230930213821-20231001003821-00882.warc.gz
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CC-MAIN-2023-40
| 3,042 | 45 |
http://www.solutioninn.com/suppose-that-you-are-given-the-following-information-about-two
|
math
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Question: Suppose that you are given the following information about two
Suppose that you are given the following information about two callable bonds that can be called immediately:
You are told that both of these bonds have the same maturity and that the coupon rate of one bond is 7% and of the other is 13%. Suppose that the yield curve for both issuers is flat at 8%. Based on this information, which bond is the lower coupon bond and which is the higher coupon bond? Explain why.
Relevant QuestionsThe theoretical value of a noncallable bond is $103; the theoretical value of a callable bond is $101. Determine the theoretical value of the call option. Suppose that a support bond is being analyzed using the Monte Carlo simulation methodology. The theoretical value using 1,500 interest-rate paths is 88. The range for the path present values is a low of 50 and a high of 115. ...Answer the below questions. (a) What assumption is made about the OAS in calculating the effective duration and effective convexity of a RMBS? (b) Is it warranted? The following excerpt is taken from an article titled “Fidelity Eyes $250 Million Move into Premium PACs and I-Os” that appeared in the January 27, 1992, issue of BondWeek, pp. 1 and 21: “Three Fidelity investment ...The following quotes are from Mihir Bhattacharya, “Convertible Securities and Their Valuation,” Chapter 51 in Frank J. Fabozzi (ed.), The Handbook of Fixed Income Securities: Sixth Edition (New York: McGraw-Hill, ...
Post your question
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s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818691476.47/warc/CC-MAIN-20170925111643-20170925131643-00488.warc.gz
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CC-MAIN-2017-39
| 1,513 | 5 |
https://www.allmapdata.com/glossary/unit-postcode/
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math
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Unit PostcodeJanuary 29th, 2016
A full postcode e.g. TW8 8JA. In this example, the postcode area is TW, the postcode district is TW8, and the postcode sector is TW8 8. Each level nests into the level above it. There are roughly 1.75m unit postcodes in the UK, each covering an average of 18 addresses.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988763.83/warc/CC-MAIN-20210506205251-20210506235251-00538.warc.gz
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CC-MAIN-2021-21
| 301 | 2 |
https://projecteuclid.org/journals/annals-of-probability/volume-5/issue-4/Pointwise-Convergence-Theorems-for-Self-Adjoint-and-Unitary-Contractions/10.1214/aop/1176995773.full
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math
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Some conditions are introduced which imply pointwise convergence theorems for increasing sequences of orthogonal projections on $L^2(\mu), \mu$ finite, as well as a pointwise ergodic theorem for self-adjoint and unitary contractions. These results generalize to the case of nonpositive operators some theorems of E. M. Stein.
"Pointwise Convergence Theorems for Self-Adjoint and Unitary Contractions." Ann. Probab. 5 (4) 622 - 626, August, 1977. https://doi.org/10.1214/aop/1176995773
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573744.90/warc/CC-MAIN-20220819161440-20220819191440-00737.warc.gz
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CC-MAIN-2022-33
| 484 | 2 |
http://mathhelpforum.com/pre-calculus/72796-solved-cosine-rule-help.html
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math
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I have racked my brain trying to think of what I've done wrong, but I just can't.
Jim and Tony leave the same point at the same time with Jim walking away at the speed of 1.4m/s and tony at a speed of 1.7m/s, the two directions of travel making a angle of 50 degrees with eachother. If they continue on the same straight line paths how far apart are they after 8 seconds?
Can someone please help me? I want to know what I've done wrong! and thank you for taking the time to read this post =]
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917126538.54/warc/CC-MAIN-20170423031206-00377-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 491 | 3 |
https://eric.ed.gov/?id=EJ554552
|
math
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ERIC Number: EJ554552
Record Type: Journal
Publication Date: 1997
Reference Count: N/A
Using Mathematica and Maple To Obtain Chemical Equations.
Missen, Ronald W.; Smith, William R.
Journal of Chemical Education, v74 n11 p1369-71 Nov 1997
Shows how the computer software programs Mathematica and Maple can be used to obtain chemical equations to represent the stoichiometry of a reacting system. Specific examples are included. Contains 10 references. (DKM)
Publication Type: Guides - Classroom - Teacher; Journal Articles
Education Level: N/A
Authoring Institution: N/A
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s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221211146.17/warc/CC-MAIN-20180816171947-20180816191947-00287.warc.gz
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CC-MAIN-2018-34
| 570 | 11 |
https://vivo.library.tamu.edu/vivo/display/n187458SE
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math
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Measurements of charm fragmentation into D s * + and D s+ in e + e - annihilations at s=10.5 GeV
Additional Document Info
A study of charm fragmentation into D s * + and D s+ in e + e - annihilations at s=10.5 GeV is presented. This study using 4.720.05 fb -1 of CLEO II data reports measurements of the cross sections (D s * + ) and (D s+ ) in momentum regions above x=0.44, where x is the D s momentum divided by the maximum kinematically allowed D s momentum. The D s vector to vector plus pseudoscalar production ratio is measured to be P V (x(D s+ )>0.44)=0.440.04. 2000 The American Physical Society.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224645595.10/warc/CC-MAIN-20230530095645-20230530125645-00708.warc.gz
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CC-MAIN-2023-23
| 606 | 3 |
http://eprints.pascal-network.org/archive/00008978/
|
math
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Generalised Pinsker Inequalities
Mark Reid and Bob Williamson
In: Conference on Learning Theory 2009, 18-21 June 2009, Montreal.
We generalise the classical Pinsker inequality
which relates variational divergence to Kullback-
Liebler divergence in two ways: we consider
arbitrary f-divergences in place of KL divergence,
and we assume knowledge of a sequence
of values of generalised variational divergences.
We then develop a best possible inequality for
this doubly generalised situation. Specialising
our result to the classical case provides a new
and tight explicit bound relating KL to variational
divergence (solving a problem posed by
Vajda some 40 years ago). The solution relies
on exploiting a connection between divergences
and the Bayes risk of a learning problem
via an integral representation.
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s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246636255.43/warc/CC-MAIN-20150417045716-00075-ip-10-235-10-82.ec2.internal.warc.gz
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CC-MAIN-2015-18
| 808 | 18 |
http://fashionlosdaeroh.cf/xysa/homework-help-predicate-logic-277.php
|
math
|
What are some specific things you don't understand? Are you comfortable with everything in propositional or sentential logic? May 5, 3. May 5, 4. Hell, all these are hard. The next ones are: May 5, 5. May 5, 6. According to your definitions, those problems look like: Pretty sure I got the first one. May 5, 7. Anyhow, thanks for the help. Might've gotten the last one, but I'm heading off to class now. Serves me right for procrastinating. May 5, 8. May 5, 9. I did manage to get 4 right before I left for class.
I'm working on some homework questions and I am struggling very hard with the logic proofs. I might have an incorrect answer for 1 of the predicate questions but I think my question makes some sort of sense. I think I have more of an issue with the logic proofs, any help or hints would be great. I'd appreciate any help, I think i would need more help for the logic proof questions than the predicate questions because I am very lost on how to move from a statement to a different statement.
Logic Proof Questions Decide whether the inferences are valid in each case. This is where I got lost, I don't know how to get from that statement to r.
If so, 1 must be: Thanks Mauro I really appreciate it. I will study this and try to understand so I can get these answers correct next time.
Take a step beyond Aristotle to homework help predicate logic evaluate sentences whose truth cannot be proved by his system. Those nasty hobbitsess stoless it from homework help predicate logic us, precioussss. Help me with Predicate Logic? Dissertation english language noah webster Philosophy Logic Homework Help professional phd thesis writers do angel investors uc college essay help look.
A predicate is a property or characteristic of a mode of existence which a given subject may or may not possess. For example, an individual (the subject) can be skillful or not (predicate) and all men (subject) may or may not be brothers (predicate). ready to assist college students who need homework help with all aspects of logic. Our.
May 05, · I am taking a logic class and we are getting into Predicate Logic and i have no idea how to do it can someone help me? To receive homework help you must be able to substantially describe what effort you have made to solve the problem(s) before you asked for help. Follow this format when asking homework questions: (Homework) Predicate logic question. submitted 3 years ago by Freyarghh.
buy a dissertation online abstracts Homework Help Predicate Logic thesis create custom page phd thesis english education. capstone research paper Homework Help Predicate Logic assignment helper in malaysia music essay introductions.
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CC-MAIN-2019-22
| 2,664 | 8 |
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