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http://www.jiskha.com/display.cgi?id=1363832550 | math | Posted by Adam on .
Is log_3 (5) equal to log_5 (3)? Explain your answer. Do not evaluate the logarithms.
is my question. What is a surefire way to show this is false.
let x = log (base3) 5
then 3^x = 5 , clearly x > 1 ,
because 3^1 = 3 and 3^2 = 25 ,so x must be between 1 and 2
let y = log(base5)^3
then 5^y = 3 , clearly y < 1,
because 5^0 = 1 and 5^1 = 5
so y has to be between 0 and 1
so x ≠ y
and the two log expressions cannot be equal
fantastic, makes so much sense now, thx
and btw 3^2 = 25 is typo | s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218188717.24/warc/CC-MAIN-20170322212948-00589-ip-10-233-31-227.ec2.internal.warc.gz | CC-MAIN-2017-13 | 509 | 14 |
https://www.hackmath.net/en/math-problem/18943 | math | Two siblings, Eva and Peter, saved a total of 228 CZK. Eva saved three times more than Peter. How much did each of them save?
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Ema has 3 times more picture cards in her collection than Dana. They have a total of 240 images. They are bought in packs of 10 for CZK 14. How much did Dana's pictures cost? | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100135.11/warc/CC-MAIN-20231129173017-20231129203017-00018.warc.gz | CC-MAIN-2023-50 | 3,684 | 39 |
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# / posted on Mar 15, 2009 | s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368704713110/warc/CC-MAIN-20130516114513-00038-ip-10-60-113-184.ec2.internal.warc.gz | CC-MAIN-2013-20 | 337 | 2 |
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http://cdk.github.io/cdk/latest/docs/api/org/openscience/cdk/graph/invariant/package-summary.html | math | ClassDescriptionAn implementation based on the canon algorithm [Weininger, David et. al.. Journal of Chemical Information and Computer Sciences. 1989. 29].Deprecated.this labeller uses slow data structures and has been replaced -
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SmiFlavorsettings.An algorithm for topological symmetry.This class is intended to provide the user an efficient way of implementing matrix of double number and using normal operations (linear operations, addition, subtraction, multiplication, inversion, concatenation) on them.Collection of methods for the calculation of topological indices of a molecular graph as described in [Chang-Yu Hu and Lu Xu. J. Chem. Inf. Comput. Sci.. 1996. 36].Tool for calculating atom numbers using the InChI algorithm.Compute the extended connectivity values (Morgan Numbers) [Morgan, H.L.. J.Chem.Doc.. 1965. 5]. | s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710974.36/warc/CC-MAIN-20221204140455-20221204170455-00088.warc.gz | CC-MAIN-2022-49 | 935 | 3 |
http://stogienet.com/index.cfm?a=details&blog=133 | math | Posted by Jack | in Illusione | on 12 Sep 2013 | at 2:04 PM | 2671 views
Among my five favorite brands, Illusione cigars retain a certain enigmatic quality. Dion Giolito makes some marvelous cigars to be certain, but there is a wonderful mysterious quality to the brand. The naming convention is often simplistic - a few numbers or letters - and the tobaccos he uses are often unusual. To this day, the Epernay still ranks as one of the best cigars I have ever had, the CG4 is on my short list for my top 25 this year, and the Holy Lance is one of the best lancero cigars money can buy. So, droppping by The Market, I spied the as-yet-untried Crusado line just sitting there looking gorgeous and mouth watering. I picked up a couple of the more ostentatious looking vitolas - both wrapped in gold foil. The subject this review is the Marelas Supremas. Draped in another unusual wrapper leaf, a gorgeous Nicaraguan Criollo Rosado, the Marelas snagged me with the presentation alone. Let's get to the review....
Construction: The Marelas is a beautiful cigar both before and after you unwrap it. The half gold foil presentation is just gorgeous. Once removed - which is very simple as the band peels off easily and the foil slides off in one piece - the Marelas shows a nice red-brown wrapper with a few very minor veins and some subtle color mottling. The real eye-catcher is the Cuban Partagas 109 style cap. Rather than a standard parejo dome shaped cap, this one is like a morph a quarter of the way to a classic belicoso. It's a very unique rolling that makes the whole thing even cooler.
Pre-light Aroma and Draw: Once out of the foil, this version of the Crusado gives off a nice cedar spice, barnyard, and leather aroma. Even using a depth restrictive cutter - where I could only snip about an eighth of an inch from the cap, the draw is perfect. A cold pull gives a nice sweet tobacco and earthy flavor.
Light and Burn: Lighting was really not an issue - it rarely is. The burn started off a little troublesome for about a half and inch and then it performed perfectly until the end with a heavy dark gray ash and no coning.
Tasting: The start is creamy smooth with a dry cocoa and earthy profile.
The first third starts with a hefty amount of cinnamon, oak, red pepper, leather and earth. The flavors are very uniquely blended and unusual. It smooths out after a tiny bit of harshness and adds a cocoa flavor to the mix. It seems to get richer, smoother, and toastier as the first section burns through.
The second third pumps up the leather a bit more while adding a heavy espresso note. It is retaining that nice dense earth touched by some cinnamon. There are some mild herbal notes and the cocoa from the first third drops off a bit as well. The smoke is very dense and aromatic.
The final third shifts the pepper from red to black with the continuation of the earthy, leathery, creamy core. I get some nutty flavors with touches of black coffee and unsweetened cocoa. The flavors mingle in the last three inches into one well balanced amalgam. A very interesting and tasty surprise.
Value: The Marelas Supremas will run you around $10, which is easily worth it for such a great cigar with a killer vintage presentation.
Final Thoughts: Every single Illusione I try is terrific. I have yet to try one I don't like - and that is saying something. The Crusado Marelas Supremas is easily tied for second place among my favorite Dion Giolito crafted cigars. So far it shows signs worthy of my top cigars of the year list. Highly recommended.
Wrapper: Nicaraguan Criollo Rosado
Size: 6.5 x 52
Simply beautiful presentation
Love the gothic style band in conjunction with the foil
There is the 109 style cap. It's an amazing thing I would love to see on more cigars
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https://studysoup.com/note/76808/ucr-bpsc-148-fall-2015 | math | QUANTITATIVE GENETICS BPSC 148
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Chapter 14 Basic Concepts of Selection Evolutionary forces Evolutionary forces are factors that can change the genetic properties of a population There are four evolutionary forces selection mutation migration and genetic drift Selection is considered to be the most important one Selection is de ned as a phenomenon that parents who contribute to the next generation are not a random sample but selected based on some criteria Genetic properties of a population include gene frequencies and genotype frequencies However these are not observable what we can observe are the population mean and variance that re ect gene and genotype frequencies of the population Change in gene and genotype frequencies Here we use deleterious recessive gene as an example Assuming that Al is completely dominant overAz allele so that A1141 and11A are indistinguishable in terms of selection Genotype 141A1 141A2 A2 A2 Total Initial freq p2 2pq q2 1 Coef cient of 0 0 3 Selection Fitness 1 1 ls Garnetic p2 qu 13q2 13q2 contribution The tness denoted by w is de ned as w 1 s where s is the selection coef cient The garnetic contribution of each genotype is the initial frequency multiplied by the tness After selection the genotype frequencies will change ie the genotype frequencies in the selected parents will be different from the frequencies of the initial unselected population Genotype 141A1 141A2 A2 A2 Total New freq in p2 2 pg 1 3M2 1 selected parents l sq2 1 59 l sq2 De ne the initial frequency of A1 and A2 by p0 and q0 respectively then the new allelic frequencies forll and A2 are 2 2 p1PlH1 p0 p0q0 p0 1 qu 2 1 qu l sqg lW2 1 Mar 617 sq2 q1Q1H1 1 20 0t 20 20 sq0 2 1 qu 1 qu The change of gene frequency in one generation of selection is 2393090 1 M q1 qo M 0 S 0 So ql S qo meaning that frequency of A2 has been decreased due to selection against this allele If the selected parents are randomly mated the genotype frequencies in the offspring will be Genotype Frequency A1141 1 11 2 A1142 2q11q1 Aw q Therefore after one generation of selection both the gene and genotype frequencies have changed As a result the population mean and genetic variance have also changed 162 Changes of a metric character Truncation selection An individual is selected if its phenotypic value is greater than a threshold T otherwise it is culled Insert Fig 171 here The tness of an individual is de ned as 1 if y 2 T 0 if y lt T Selection dz erentials De ne 7 and J75 as the means of the parental population before and after selection respectively The selection differential is de ned by S J73 y Response to selection Response to selection is de ned as the difference between the mean of offspring and the mean of the parental generations Denote the response to selection by S the relationship between R and S is given by R hZS This equation also called the selection equation is important in plant and animal breeding as well as in evolution Selection intensity Selection differentials cannot be compared for different traits A large value of selection differential does not mean a strong selection The strength of a selection is measured by selection intensity Selection intensity denoted by i is also called standardized selection differential It is defined as the selection differential divided by the phenotypic standard deviation ie where UP is the standard deviation of phenotypic value ie 6P 1 6 46 JV We now express the selection response as a function of the selection intensity RhZSh2ioP hioA Proportion selected p The proportion selected p is the ratio of the number of selected individuals to the total number of individuals measured Theoretically if y is normally distributed ie y N NL6p is defined by T TLUP t p 1Lofydy 1 Lo fy H6pdy H6P1liwfxdx 1 0 where x y u OP is the standardized normal variable and t T u OP is the standardized truncation point in the N 01 scale Relationship between i and p If the selected character is normally distributed there is a simple relationship between i and p 1 1 2 Z tmexp7t t 1 2 pl q3tl Lomexp x dx Z in See the appendix of this chapter for the numerical values of the relationship among i tand p 164 When males and females have different selection differentials their average should be used S S selection d1fferent1al for males lead1ng to im 039 m P S S f selection differential for females leading to if f 039 P S Sm Sf leading to 139 im z39f Therefore R hZS h2Sm h2Sf hzimcp h2ifcp An example Given 6p 5 u 25 and p 020 find the truncation point selection intensity selection differential and response to selection 1 From the appendix table we get I 084 and z39 140 whenp 020 Note that tis the truncation point in the standardized scale What is the truncation point in the real scale T Because I THwe have Tt6Pu0842X525292l 6 F 2 Selection differential S 1390 l40gtlt5070 3 Assume that both the males and the females have the same selection intensity and h2 050 then the predicted selection response is R h2 S 05gtlt70 35 The population mean ofthe offspring will be u R 25 35 285 165 Truncation selection an AD YNuio 9 n1 5 gm gum Em a DUI p y u T Phenotypic value in the original scale y m m g xN g ml 01 Emma E 1 t gm p lt1gt Em a 76 4 72 u 2 a a XY 39 MVG Phenotypic value in the standardized normal scale x Chapter 3 Population Mean Phenotypic value the value observed when a character is measured on an individual For example the body weight of a particular pig is 300 lb The value of 300 1b is the phenotypic value of this pig for body weight Genotypic value average of the phenotypic values of all individuals who have the same genotype For example there are 1000 individuals in a population who have the same genotype A1142 For a particular trait the phenotypic values of the 1000 individuals are 125 089 210 Because all the 1000 individuals have the same genotype 1000 the average values of their phenotypic values 025 089 210 is the genotypic value of genotype A1142 Environmental deviation the difference between the phenotypic value and the genotypic value The rst genetic model P G E phenotypicwlue genotypicvalue environmentaldeviation Because environmental deviations can be positive and negative the average of E s for all individuals will be zero and thus the average phenotypic values is the genotypic value For the purpose of deduction we must assign arbitrary values to the genotypes under discussion This is done in the following way Considering a single locus with two alleles A1 and A2 we call the genotypic value of one homozygote a that of the other homozygote 7a and that of the heterozygote d We shall adopt the convention that11 is the allele that increases the value We thus have a scale of genotypic values as in Fig 31 Genotype A2142 141142 A1f1 Genotypic a 0 d a value Fig 31 Arbitrarily assigned genotypic values The genotypic value of the heterozygote al indicates the dominance effect If there is no dominance effect the genotypic value of A 1A2 should be half way between A1141 and 142142 ie al 0 With dominance d at 0 and the degree of dominance is usually expressed by the ratio d a Note the value 0 re ects the midpoint in the arbitrary scale The actual midpoint value can be different from 0 as shown in the following example The example also shows how to calculate the arbitrarily scaled genotypic values from the actual values Example dwar ng gene in the mouse Genotype A1A1 pgA1Az pg pgAzAz Actual weight g 14 12 6 14 6 10 The From this table we can calculate the actual midpoint value which is arbitrarily scaled genotypic values are then obtained by subtracting the actual midpoint value from the actual values of the genotypes After the subtractions we have al4 104 a6 10 4 d12 102 The degree of dominance is 6161 24 05 Note that midpoint is just a convenient way to express the position of the population There are several other ways to express the population position Remember to adjust the data by the midpoint before conducting any data analysis Population mean Let p and q be the frequencies of allele A1 and A2 respectively The population mean expectation is calculated using the following table Genotype Frequency y Value y y X f y 141A1 p2 a ap2 A1141 2m d dam AM q2 a aq2 The population mean in the arbitrary scale is the expectation of Y M EY 0P2 dam aq2 6100 q 2106161 The population mean I has been expressed as deviation from the actual midpoint Thus the actual population mean should be M midpoint Example dwar ng gene in the mouse Assume that the frequency of allele is p 09 and that ofpg allele is q 01 We have Map q2pqd4X09 0l2X09X0lx2356 The actual population mean isM midpoint 356 10 1356 Average effect of gene Genotypes are not transmitted from generation to generation it is the gene that is inherited from parent to offspring Average effect of a gene is the mean deviation from the population mean of individuals which received that gene from one parent the gene received from the other parent having come at random from the population First let us look at the average effect of allele A1 Consider one allele beingll and the other allele being randomly sampled from the population The probability that the other allele is A1 equals p If this happens the genotype will be A1141 with a genotypic value a On the other hand the probability that the other allele is A2 equals a Ifthe other allele is sampled then the genotype will be A1142 with a genotypic value 51 So in the population containing individuals with one A1 allele being fixed a proportion of p will be A1141 and a proportion ofq will be A1142 Define the mean ofthis population by M Al we have M A1 ap dq We then express this mean by the deviation from the population mean M resulting in the defined average e ect of genell all MA1Mqadqp The average ef ect of A2 is similarly defined by first obtaining M A pd qa and then 0 2 MA M padqp Average effect of gene substitution In a biallelic system the average effect of gene substitution is more informative than the average effect of gene The average effect of gene substitution is defined by a a1 a2 adq p The average gene effects and average effect of gene substitution can be derived using the conditional distribution and conditional mean approach Let us define a 2X2 table as Amp AM Amp A1A1apz A1A2d pq a A2Q 14214103 7 14214200 92 0 2 0L1 0L2 M A1 2 ap d apdq P P 001MAfM apdqap q2pqd qadqp Appendix E Linear Combination Quadratic Forms and Covariance Matrix Linear combination Let a be an ngtltl vector of constants Xan ngtltl vector of variables The scalar l aTX is called a linear combination ofX For example x1 13x1 4x2 5x3 3 4 5 x2 aTX x3 3 x1 where a 4 andX x2 5 x3 Quadratic forms LetA be an 71er constant matrix usually symmetrical X be an ngtltl vector of variables then Q X TAX is a quadratic form of X For example let x1 an a12 a13 x x2 A 6121 6122 6123 a 31 a 32 a 3 33 x1 all all 6113 X x2 and A all 6122 6123 x3 6131 6132 6133 the quadratic form is an all an 1 3 3 QXTAXC1 x2 x3 6121 6122 6123 2 ZZaUx1xj 11 1 a3 l X X X 3 Variance covariance matrix Let X x1 xn T be an ngtltl vector of multiple variables Denote the variance 2 and covariance by 61 Varxland GU C0vxlxy respectively for 1 l n The variancecovariance matrix of X is de ned as El 2 612 62 39 39 39 6m x VarX Var xn 6m 6H2 39 39 39 n VarX is a compact way of writing an array of variances and covariances Let Xx1xnT a vector 71 variables and Y y1ymT be a vector ofm variables De ne COVx1y1 C0Vx1y2 COVx1 ym Covx Covx Covx m CMXJT zyl 2y2 2y COVOCWJl OVOCWJz COVOCWJm W as the covariance matrix betweenX and Y We can de ne the following partitioned matrix X VarX E CovX Y T Var J E Y CovYXT VarY where VarX is an n X n variance matrix VarY is an m X m variance matrix and CovYXT CovXYT T is an m X n covariance matrix Expectation of linear combination Let Xx1xnT and Ex1 H1 fori ln De ne u1 HAT then x1 190 H1 EXE x E99 2 p 96 Exn H If a a1 any is a vector of constants then EaTX aTEX Let Y y1 ynT be another vector of variables we have EXYEXEY An example E2
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https://www.semanticscholar.org/author/Bobby-DeMarco/3028897 | math | For a graph G, denote by t(G) (resp. b(G)) the maximum size of a triangle-free (resp. bipartite) subgraph of G. Of course t(G) ≥ b(G) for any G, and a classic result of Mantel from 1907 (the first case of Turán's Theorem) says that equality holds for complete graphs. A natural question, first considered by Babai, Simonovits and Spencer about 20 years ago… (More)
Answering a question of Kolaitis and Kopparty, we show that, for given integer q > 1 and pairwise nonisomorphic connected graphs G ξ k) is asymptotically uniformly distributed on Z k q . | s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280310.48/warc/CC-MAIN-20170116095120-00432-ip-10-171-10-70.ec2.internal.warc.gz | CC-MAIN-2017-04 | 557 | 2 |
http://mathhelpforum.com/discrete-math/128377-conditional-proof.html | math | Use a conditional proof to prove the following argument:
Only a fool would lie about one of Elaine's sorority sisters to her. A classmate of
Elaine's lied about Joanne to her. Therefore, if none of Elaine's classmates are fools, then Joanne is not a sorority sister of Elaine. (F(x) = x is a fool; L(x,y,z) = x lies
about y to z ; C(x,y) = x is a classmate of y; S(x,y) = x is a sorority sister of y;
e = Elaine ; j = Joanne)
Any help? Thanks! | s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122619.60/warc/CC-MAIN-20170423031202-00485-ip-10-145-167-34.ec2.internal.warc.gz | CC-MAIN-2017-17 | 443 | 6 |
http://gmatclub.com/forum/m08-q3-131935.html | math | "If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month"
=> 220 tickets sold this month yield 10% greater revenue compared to the last month
=> As this is compared against the last month's value, base value is that of last month
=> Let us take the tickets sold last month as X. As a 10% increase results in 220 in this month, (220-X)/X = 10% = 10/100
=> on solving , X = 200
(or we can simply guess 200 as 10% of it 20 and 200+20 = 220)
"If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue"
=> This time the comparison is based on this month's value
=> base value should be this month's
=> suppose last month's value is 100, this month's value must be 105, as there is 5% hike
=> To get the % of decrease in the last year in comparison with this year, go for a reverse calculation
=> (105-100) decrease from 105 => 5*100/105 % = 100/21 %
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http://theracingline.net/2018/race-car-tech/race-tech-explained/tyres-combined-tyre-forces/ | math | [su_list icon=”icon: angle-double-right” icon_color=”#3498db”]
- Part 1 – Tyre as a vertical spring
- Part 2 – Road Interaction & Contact Patch Grip
- Part 3 – Longitudinal Forces
- Part 4 – Lateral Forces
- Part 5 – Load Sensitivity
We have now analyzed a bit of the main aspects of tyres behavior, including how a tyre produces longitudinal and lateral forces and load sensitivity.
However, a question still remains: how does a tyre behave, when it had to exchange with the road lateral and longitudinal forces at the same time?
Any time a tyre interacts with the road with a planar force having both a lateral and a longitudinal component, we talk about combined grip.
A typical situation where combined grip is used by the driver is when he/she starts to steer, while still pushing on the brake pedal (trail braking), or when he/she accelerates out of a corner while the car has not yet completely been realigned. Both of these situations take place regularly on a track if a driver explores the full potential of car and tyres.
In general, it is common for the car to negotiate a section of a track and experience both a lateral and longitudinal acceleration, exchanging with the road forces with both a lateral and a longitudinal component. From a pure mathematical perspective, a force can be represented by a vector, which is an entity defined by a magnitude (force’s intensity) and a direction (if we talk about planar forces, a combination of a lateral and longitudinal portion). A vector (and, hence, a force) is normally represented graphically with an arrow, this making much easier also for who is not too versed with mathematic to grasp its meaning.
The picture above describes a pure braking situation on the left side and a pure cornering situation, on the right side.
From a more rigorous perspective, we can imagine that the two vectors/forces refers to a known and fixed vertical load.
In both of these cases, the tyre can exploit its full potential in one direction only, hence maximizing either car’s lateral or longitudinal acceleration.
Since we now know that tyre forces can be represented as vectors, we can also conclude that, in cases where a combination of a lateral and a longitudinal force are exchanged with the road, the magnitude of the combined force can be obtained combining (with a vector sum) lateral and longitudinal components.
In a first approximation, useful here to explain the concept of combined grip, we can imagine the maximum possible magnitude of lateral and longitudinal force that a tyre can exchange with the road (for a fixed vertical load) to be the same. This will also mean that if we ask the tyre to provide at the same time a lateral and a longitudinal force, the resultant force vector (which is, as we saw, the vector sum of lateral and longitudinal component) cannot have a bigger magnitude than the one of the pure lateral / longitudinal force maximum magnitude.
If all of this is true, we can then define the maximum combined force for a given vertical load by using a circle, with its radius given by the maximum pure longitudinal /pure lateral force:
This means, on one side, that the magnitude of our maximum combined force is the same as the maximum magnitude of the pure lateral or longitudinal force. But this also means that, in combined grip situations, the maximum allowed lateral and longitudinal forces will be smaller than in pure cornering or in pure braking:
The circle defining the maximum combined force the tyre can exchange with the road is often called the friction circle.
The reality of things is actually a bit more complex that what we explained, as very often, for a given vertical load, the maximum magnitude of the longitudinal force a tyre can achieve is not necessarily the same as the maximum magnitude of the lateral one. This is why engineers very often talks about friction ellipse, instead of friction circle.
Another important point to mention is that, depending on tyre construction and the goals that want to be achieved with a certain design, it is possible that the shape of the envelope defining the maximums, is not a regular shape and cannot be defined either with a circle or an ellipse. However, this goes beyond the scope of this short overview.
It is also interesting to analyze how a slip curve changes its shape, in a combined grip situation.
As we have seen, anytime we have a non-zero slip ratio and slip angle at the same time, the amount of longitudinal and lateral force that the tyre can produce drops.
The shape of a plot of longitudinal force with respect to slip ratio, when the tyre also experiences a slip angle, depends very much on tyre construction. In general, anyway, the bigger the slip angle, the smaller the available longitudinal force for a given slip ratio.
This effect of having a bigger slip angle is stronger at smaller slip ratios and tends to lose intensity as we move toward bigger and bigger slip ratios, up to 1 (or -1).
We can identify a similar trend if we look at the plot of lateral force with respect to slip angle, when the tyre also experiences a slip ratio.
For a given slip angle, the tyre will produce smaller and smaller cornering forces, as the slip ratio gets bigger.
It is also interesting to cross these plots, looking for example at how the curve of lateral force with respect to slip ratio looks like, for growing slip angles:
We see the same tendencies we already identified, with the lateral force (at a given slip angle) dropping as the slip ratio increase. This plot gives maybe a better idea of how much cornering potential the tyre loses if the slip ratio increases, with the lateral forces coming very close to zero if the slip ratio gets to the value of one.
Similar tendencies can be seen if we look at the plot of longitudinal force with respect to slip angle, with varying slip ratio.
It is interesting to notice that the longitudinal force drops much slower with respect to the slip angle, compared to what the lateral force does with respect to the slip ratio. This tells us that, while it is difficult to steer when a front tyre experiences high slip ratios (or, in an extreme case, is locked), it is still possible brake the car (up to a point) even when the front tyres are steered. The reason for this is that, normally, pretty small slip ratios are required to produce high braking forces.
The final part next week will look at cambers, temperatures and pressures. | s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655896905.46/warc/CC-MAIN-20200708062424-20200708092424-00308.warc.gz | CC-MAIN-2020-29 | 6,462 | 32 |
https://www.topperlearning.com/answer/draw-two-line-segments-and-s/n6gqtkioo | math | Draw two line segments and state features of a line segment in terms of
(a) Its endpoints
(b) Extension on both sides
Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM
PN and CD are the required line segments.
(1) It has two distinct endpoints.
(2) A line segment does not extend endlessly on both sides.
Answered by | 4th Jun, 2014, 03:23: PM
- Draw a line l take any three points A B and c on it measure the length AB BC and AC using a ruler verify that A b + BC= AC A c- A B =bc AC - bc =AB
- State two features of a point?
- Answer the following for two lines shown below (a) What are the points that lie on the two lines? Whether the lines would intersect?
- Answer the following questions for the given figure. (a) What are lines p, q, and r called? (b) What is the point at which they meet called? Label it on the figure. (c) How many lines can pass through the labeled point?
- What are parallel lines? Does the distance between them vary over their length?
- Categorize the following in terms of line, line segment, ray, point, point of intersection on the basis of the following figure (a) LM (b) MR, OP, ON (c) LR (d) O (e) O, L, M, R
- Draw a rough figure and label the following a. Line l contains point A but not B b. Lines p and q intersect at point o c. Rays PQ and QR meet to form angle PQR
- Answer the following questions with the help of the figure given below : (i) name the transversal (ii) identify any two vertically opposite angles (iii) name any two corresponding angles (iv) name any two alternate angles
- 1) Write the pairs of parallel lines in the above figure. 2) Which is the point of intersection of the 3) Write down all the points of intersection of the lines in the figure.
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Enter the OTP sent to your number | s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655890105.39/warc/CC-MAIN-20200706042111-20200706072111-00194.warc.gz | CC-MAIN-2020-29 | 1,890 | 24 |
http://howeverythingworks.org/wordpress/1997/01/27/question-799/ | math | In class, you sat motionless on a cart with a ball in your lap. You said that your momentum was zero. You then threw the ball in one direction and you began moving in the other direction. You said that your momentum was still zero. How can your momentum be zero if you are moving?
In both cases, I was referring to the total momentum of the ball and me. The total momentum of the ball and me was zero before I threw the ball and it was still zero after I threw the ball. However, before I threw the ball nothing was moving and after I threw the ball the two of us were moving in opposite directions. It was our total momentum that was zero after the throw, not our individual momenta. While the ball and I each had a nonzero momentum after the throw, our momenta were equal in amount but opposite in direction—the ball’s momentum was exactly opposite mine. If you were to add our momenta together, they would sum to zero. Since momentum is conserved and we couldn’t exchange momentum with anything around us, the ball and I began and ended with the same total amount of momentum: zero. | s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247483873.51/warc/CC-MAIN-20190217233327-20190218015327-00057.warc.gz | CC-MAIN-2019-09 | 1,091 | 2 |
https://www.timeshighereducation.com/books/points-on-the-continuum/161521.article | math | This is an ambitious and substantial book on a classical subject area that has been extensively covered in the past. The authors are well-known mathematicians; Rubinstein pere is the father figure of moving boundary problems and his son has a substantial reputation. Such a book invites comparisons with its predecessors, such as Courant and Hilbert's standard work. What do the present authors have to add?
The authors set out their programme in the preface. They intend to study partial differential equations as arising naturally out of continuum models of physical processes. Moreover, they will give a rigorous treatment of "classical" methods, which they imply have been somewhat unjustly neglected by "modern mathematical education". And since that education often contains little or no physical background, they will begin with a description of commonly occurring models in the natural sciences, and their formulation in terms of partial differential equations.
Finally, they intend their book to be used by graduate students in mathematics, engineering and natural sciences. They begin, then, with a chapter on the ideas of continuum modelling. Several consistent features of the book are immediately clear. The first is, quite simply, that there is an enormous amount of information. After a discussion of the basics of models of continuous media, we find outlines of the usual models for linear elasticity, viscous and inviscid fluids, electrostatics and electrodynamics, chemical kinetics, equilibrium thermodynamics, thermodynamics of irreversible processes, together with a preliminary discussion of conservation laws. All this, in 28 pages. Second, there is no lack of rigour. The tone is set by the definition of a continuum, on page one; the comments on thermodynamics indicate that the authors have an inclination to a "rational mechanics" approach.
It is perhaps no coincidence that the notation is rather dense - altogether, there is more than a whiff of the formidable and comprehensive Soviet school of textbook writing. Finally, there is a degree of idiosyncrasy in the subject matter and the way it is treated. This has positive and negative aspects.
On the downside, one could cite their definition of a rotational fluid flow as one in which the velocity is the curl of a vector potential (thereby making stationary fluids rotational, and forcing all rotational flows to have zero divergence), their use of the notation (Greek) nu(x) for the Heaviside function, or their frankly eccentric preference for a version of the Laplace transform that is p times the usual definition. On the other hand, subjects such as chemical kinetics, electrodiffusion, the Buckley- Leverett equation and the Stefan problem (which, of course, reflect the particular interests of the authors) make a welcome appearance.
There follows a chapter in which the relationship between continuum models and partial differential equations is further developed -- and then we come to the heart of the matter, a detailed analysis, in the classical style, of the mathematical properties of some of these equations. The ordering is quite conventional, beginning with quasilinear and nonlinear first-order equations (there is a nice treatment of the latter but, oddly, Charpit's equations are not named as such, and neither are obvious applications such as geometric optics or the ship wave equation cited). The classification of second-order quasilinear equations is followed by about 50 pages on hyperbolic equations, 100 on second-order elliptic equations (but not the biharmonic equation), and nearly 200 on the parabolic case. We are led through extremely (perhaps overly) detailed treatments of the main classical theorems of the linear classical theory, and there is a more sporadic treatment of selected nonlinear problems.
The final section turns to some more practical matters, with chapters on Fourier series, integral transforms and asymptotic analysis. The material of the first two of these has largely been better presented elsewhere, while in the third the authors more or less admit that they cannot cover the subject adequately. Lastly, a clutch of appendices about routine methods includes some interesting specialised applications to heat and mass transfer.
There is no doubt that this is a work of considerable and thorough erudition. But the rather distinctive slant and style of the book has consequent drawbacks. One is that not many students will find it easy to develop their intuition for the central ideas. This is partly because informal - intuitive - treatments are largely absent, but also the theory of distributions has been, perhaps rather mistrustfully, relegated to a minor role. (The delta function is not even mentioned in the treatment of Green's functions for elliptic equations.) A second is that the enormous literature on functional-analytic approaches to applied mathematics might almost not exist, if we read only this book.
A more balanced treatment would spell out the comparison; the reader could then judge whether the emphasis on classical methods was justified.
On the positive side, in addition to, and hidden away in, the vast body of information are some fascinating topics that are impossible to find elsewhere. What we need is a user's guide to help us to find them.
Sam Howison is a lecturer in applied mathematics, University of Oxford.
Partial Differential Equations in Classical Mathematical Physics
Author - Isaak Rubinstein and Lev Rubinstein
ISBN - 0 521 41058 4
Publisher - Cambridge University Press
Price - £60.00
Pages - 676 | s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583511122.49/warc/CC-MAIN-20181017090419-20181017111919-00448.warc.gz | CC-MAIN-2018-43 | 5,582 | 17 |
https://nrich.maths.org/public/leg.php?code=31&cl=1&cldcmpid=8036 | math | Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?
Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Find the next number in this pattern: 3, 7, 19, 55 ...
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Can you make square numbers by adding two prime numbers together?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.
On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?
How would you count the number of fingers in these pictures?
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?
If the answer's 2010, what could the question be?
Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?
On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?
Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
Are these domino games fair? Can you explain why or why not?
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Can you substitute numbers for the letters in these sums?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.
If you have only four weights, where could you place them in order to balance this equaliser?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs? | s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187827662.87/warc/CC-MAIN-20171023235958-20171024015958-00528.warc.gz | CC-MAIN-2017-43 | 6,488 | 50 |
https://vivu.tv/what-is-a-critical-angle-easy-definition/ | math | What is a critical angle easy definition?
critical angle, in optics, the greatest angle at which a ray of light, travelling in one transparent medium, can strike the boundary between that medium and a second of lower refractive index without being totally reflected within the first medium.
What is critical angle for class 10th?
The critical angle is the angle of incidence, for which the angle of refraction is 90°. If light enters a denser medium from a comparatively rarer medium, then the direction of light changes and the light ray bends towards the normal.
What is critical angle and its formula?
Critical Angle can be described as the angle of incidence that offers an angle of refraction of 90 degrees. Remember that the critical angle is defined as an angle of incidence value. The critical angle will be 48.6 degrees for water-air boundaries and 61.0 degrees for crown glass-water boundary.
What is critical angle GCSE?
The angle of incidence when the angle of refraction is 90 o, and the ray changes from just refracting to total internal reflection, is called the critical angle.
What is meant by critical angle quizlet?
What is meant by critical angle? The critical angle is the minimum angle of incidence inside a medium at which a light ray is reflected back into the the medium. When light is incident on the surface of the medium past the critical angle the light is totally reflected back into the medium.
What is meant by critical angle in fibers?
Waves going from a dense medium to a less dense medium speed up at the boundary between them. This causes light rays to bend when they pass from glass to air at an angle other than 90°. This is refraction. Beyond a certain angle, called the critical angle, all the waves reflect back into the glass.
What is critical angle Shaalaa?
It is the angle of incidence in the denser medium corresponding to which the angle of refraction in the rarer medium is 90°.
How do you find a critical angle?
The critical angle can be calculated from Snell’s law by setting the refraction angle equal to 90°. For any angle of incidence less than the critical angle, part of the incident light will be transmitted and part will be reflected.
What occurs when the critical angle is exceeded?
The angle of incidence in a denser medium, at an interface between the denser and less dense medium, at which the light is refracted along the interface. When the critical angle is exceeded, the light is totally reflected back into the denser medium.
What is the best way to calculate the critical angle?
– a glass to water interface – a diamond to water interface – a diamond to glass interface
Could you explain the critical angle?
This angle of incidence is called the critical angle. The critical angle is the angle of incidence where the angle of refraction is 90 °. The light must travel from an optically more dense medium to an optically less dense medium. Figure 5.15: When the angle of incidence is equal to the critical angle, the angle of refraction is equal to 90 °.
How does a critical angle and a refractive index relate?
The speed of light varies in different transparent materials.
What is the critical angle of total internal reflection?
Total Internal Reflection (TIR) When a ray of light goes from denser to rarer medium it bends away from the normal and as the angle of incidence in denser medium increases, the angle of refraction in rarer medium also increases and at a certain angle, angle of refraction becomes 90°, this angle of incidence is called critical angle (C). | s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500074.73/warc/CC-MAIN-20230203185547-20230203215547-00738.warc.gz | CC-MAIN-2023-06 | 3,550 | 26 |
https://mathsblog.co.uk/2010/09/13/year-6-maths-worksheet-calculator-patterns-and-recurring-decimals/ | math | The calculator can prove to be a great tool for those who are fascinated by numbers and these pages give us just one example of this.
It uses simple division sums to produce interesting recurring decimals. For example:
1/9 is 0.111111
2/9 is 0.22222
3/9 is 0.33333
and so on.
It also asks children to use their knowledge of equivalent fractions to see if they can come up with other division questions which also create these patterns. As 1/9 is equivalent to 2/18 then this fraction will also create the same pattern.
A further extension is to ask why this happens and this can be answered by doing the division by written methods where it will soon be noticed that the same remainder keeps recurring, hence the recurring or never ending answer. The numbers can also be continued: 10/9 = 1.111111 etc. Fascinating!!
(A philosophical extra to ask is why doesn’t 9/9 give 0.999999?)
These pages can be found in our Using and Understanding Maths section for Year 6. | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296818999.68/warc/CC-MAIN-20240424014618-20240424044618-00333.warc.gz | CC-MAIN-2024-18 | 965 | 10 |
http://www.maa.org/programs/students/student-resources/high-school?device=mobile | math | The Mathematical Association of America (MAA) is the largest mathematical society in the world that focuses on mathematics for students, faculty, professional mathematicians, and all who are interested in the mathematical sciences; that is, mathematics at the undergraduate level. Our members include university, college, and high school teachers; high school, undergraduate and graduate students; and others in academia, government, business, and industry. Our core interests are Education, Research, Professional Development, Public Policy, and Public Appreciation. The student web pages cover topics in academics, careers, research/summer opportunities, meetings for students, and more. If you are not yet a member, we urge you to consider joining and ask you to visit our membership page. As a member, you can help the MAA fulfill our goals to benefit you, the student.
For information about Dolciani Mathematics Enrichment Grants (DMEG), for projects designed to develop mathematical enrichment programs for talented students in middle school or high school, please click here.
If you are a high school or middle school student thinking of majoring in mathematics, you have come to the right place.
If you are a high school or middle school student not thinking of majoring in mathematics, but you really enjoy math, you are still at the right place.
If you are a high school or middle school math teacher, possibly involved in your school's Math Club, you are also at the right place and we need your help.
Hopefully, your school already has a math club or mathlete team. If they don't, try and start one. You may be surprised how quickly an organization can come together. A good place to start with some ideas on putting a math club together is at the Texas State University - San Marcos page on starting a club. UNC Charlotte has tips for recruiting members and running a club.
Mu Alpha Theta is a high school honor society for math students. Think about how cool it will be to graduate with a Mu Alpha Theta Honor Cord on your gown! Learn about what they do and how to set up a chapter in your school.
The American Mathematics Competitions is a friendly problem contest sponsored by the MAA. There are five main competitions for high school students:
The overall goal is to use these contest to strengthen the mathematical capabilities of young people. Middle school students can also look at MathCounts.
There are a wide variety of summer programs available for talented high school math students. First off, take a look around you and talk to your teachers. There may be something going on at a campus near you. Otherwise, the following partial list of summer programs may help.
Actually, that's a question only you can answer. Some people have a passion for the intellectual challenge: solving difficult problems and proving conjectures are true. Others understand the versatility of a degree in math. If you decide to major in math, the question you will most be asked is, "What will you do with your degree, teach?" For many math majors, teaching is their goal. If you want to know what else is out there, take a look at the MAA Career Page.
A couple of statistics: In The Jobs Rated Almanac 1999, "mathematician" ranked #5 out of 250 job studied in terms of income, stress, physical demands, potential growth, job security, and work environment; The National Association of Colleges and Employers 2005 Salary Survery states that mathematicians earned a starting salary 37.7% above the national average. A 2009 study showed that the top three best jobs in terms of income and other factors were careers suited for math majors.
What classes are out there for a math major? Well, every math major takes a three-semester sequence in calculus. Afterwards there are classes in discrete math, differential equations, linear algebra, abstract algebra, and real analysis to take. Electives can include operations research, topology, cryptography, number theory, geometry, probabililty theory, statistics, and numerical analysis. Many school ask their students to do a senior research project or take a capstone course.
Outside of class in college, there are often MAA student chapters or math clubs. Some schools sponsor their students to take the Putnam Exam, administered by the MAA . Usually to get ready for the Putnam, prospective test takers go over past problems and discuss strategy at a weekly meeting. Faculty supervised student research is an exciting way to delve further into a topic you find exciting. Such work may be for college credit, or as an extra-curricular activity. Researchers have plenty of opportunities to give a talk either at their home institution, at MAA Sectional Conferences, Regional Undergraduate Conferences, or at MathFest. Also, students can present their findings on a poster at the Joint Mathematics Meeting. | s3://commoncrawl/crawl-data/CC-MAIN-2016-36/segments/1471982937576.65/warc/CC-MAIN-20160823200857-00182-ip-10-153-172-175.ec2.internal.warc.gz | CC-MAIN-2016-36 | 4,855 | 14 |
http://nrich.maths.org/public/leg.php?code=-68&cl=3&cldcmpid=876 | math | A right-angled isosceles triangle is rotated about the centre point
of a square. What can you say about the area of the part of the
square covered by the triangle as it rotates?
This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
To avoid losing think of another very well known game where the
patterns of play are similar.
A cheap and simple toy with lots of mathematics. Can you interpret
the images that are produced? Can you predict the pattern that will
be produced using different wheels?
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
Place a red counter in the top left corner of a 4x4 array, which is
covered by 14 other smaller counters, leaving a gap in the bottom
right hand corner (HOME). What is the smallest number of moves. . . .
P is a point on the circumference of a circle radius r which rolls,
without slipping, inside a circle of radius 2r. What is the locus
This is a simple version of an ancient game played all over the world. It is also called Mancala. What tactics will increase your chances of winning?
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being
visible at any one time. Is it possible to reorganise these cubes
so that by dipping the large cube into a pot of paint three times
you. . . .
A game for 2 players
Find the ratio of the outer shaded area to the inner area for a six
pointed star and an eight pointed star.
A 10x10x10 cube is made from 27 2x2 cubes with corridors between
them. Find the shortest route from one corner to the opposite
A spider is sitting in the middle of one of the smallest walls in a
room and a fly is resting beside the window. What is the shortest
distance the spider would have to crawl to catch the fly?
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
Show that all pentagonal numbers are one third of a triangular number.
Glarsynost lives on a planet whose shape is that of a perfect
regular dodecahedron. Can you describe the shortest journey she can
make to ensure that she will see every part of the planet?
Discover a way to sum square numbers by building cuboids from small
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A rectangular field has two posts with a ring on top of each post.
There are two quarrelsome goats and plenty of ropes which you can
tie to their collars. How can you secure them so they can't. . . .
Two boats travel up and down a lake. Can you picture where they
will cross if you know how fast each boat is travelling?
This article for teachers discusses examples of problems in which
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to think deeply about the context and extend their ability to. . . .
This task depends on groups working collaboratively, discussing and
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A visualisation problem in which you search for vectors which sum
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Can you find a rule which relates triangular numbers to square numbers?
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Two angles ABC and PQR are floating in a box so that AB//PQ and BC//QR. Prove that the two angles are equal.
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The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?
A cube is made from smaller cubes, 5 by 5 by 5, then some of those
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ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP
: PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED.
What is the area of the triangle PQR?
Seven small rectangular pictures have one inch wide frames. The
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of. . . .
Bilbo goes on an adventure, before arriving back home. Using the
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The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.
A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.
Can you find a rule which connects consecutive triangular numbers?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
I found these clocks in the Arts Centre at the University of
Warwick intriguing - do they really need four clocks and what times
would be ambiguous with only two or three of them?
Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.
Find the point whose sum of distances from the vertices (corners)
of a given triangle is a minimum.
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?
Two intersecting circles have a common chord AB. The point C moves
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coordinates (a,b) and (c,d), respectively. What are the coordinates
of the vertices B and D? What is the area of the square?
A bicycle passes along a path and leaves some tracks. Is it
possible to say which track was made by the front wheel and which
by the back wheel?
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Simple additions can lead to intriguing results...
A bus route has a total duration of 40 minutes. Every 10 minutes,
two buses set out, one from each end. How many buses will one bus
meet on its way from one end to the other end? | s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368697442043/warc/CC-MAIN-20130516094402-00078-ip-10-60-113-184.ec2.internal.warc.gz | CC-MAIN-2013-20 | 6,835 | 94 |
https://datascience.stackexchange.com/questions/28716/human-height-estimation-using-walking-stride/28726 | math | Are there any papers or research showing a correlation between walking stride and human height? My purpose is to estimate height from walking stride of a person.
I did not find scientific data, but interesting ratio is mentioned on several sports sites like this:
Women have ratio 0.413 and men 0.415 and it is used by multiplying height with ratio and we get the stride length.
My lenght 182cm, ratio 0.415 stride length 182 x 0.415 = 75.53cm | s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540496492.8/warc/CC-MAIN-20191207055244-20191207083244-00088.warc.gz | CC-MAIN-2019-51 | 443 | 4 |
https://www.math.snu.ac.kr/board/index.php?mid=seminars&document_srl=636033&sort_index=room&order_type=desc&l=ko | math | Gromov showed that one way to obtain a word-hyperbolic group is to choose a presentation "at random". I will survey random group properties in Gromov's model at various values of the density parameter. We will then focus on Ollivier-Wise cubulation of random groups for density parameter <1/5. I will indicate how to construct new walls that work at higher densities. This is joint work with John Mackay. | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816586.79/warc/CC-MAIN-20240413051941-20240413081941-00678.warc.gz | CC-MAIN-2024-18 | 404 | 1 |
https://www.groundai.com/project/ward-identity-and-homes-law-in-a-holographic-superconductor-with-momentum-relaxation/ | math | Ward Identity and Homes’ Law in a Holographic Superconductor with Momentum Relaxation
We study three properties of a holographic superconductor related to conductivities, where momentum relaxation plays an important role. First, we find that there are constraints between electric, thermoelectric and thermal conductivities. The constraints are analytically derived by the Ward identities regarding diffeomorphism from field theory perspective. We confirm them by numerically computing all two-point functions from holographic perspective. Second, we investigate Homes’ law and Uemura’s law for various high-temperature and conventional superconductors. They are empirical and (material independent) universal relations between the superfluid density at zero temperature, the transition temperature, and the electric DC conductivity right above the transition temperature. In our model, it turns out that the Homes’ law does not hold but the Uemura’s law holds at small momentum relaxation related to coherent metal regime. Third, we explicitly show that the DC electric conductivity is finite for a neutral scalar instability while it is infinite for a complex scalar instability. This shows that the neutral scalar instability has nothing to do with superconductivity as expected.
a]Keun-Young Kim, a,b]Kyung Kiu Kim, c]and Miok Park
Ward Identity and Homes’ Law in a Holographic Superconductor with Momentum Relaxation
School of Physics and Chemistry, Gwangju Institute of Science and Technology, Gwangju 61005, Korea
Department of Physics, College of Science, Yonsei University, Seoul 120-749, Korea
School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea
Keywords: Gauge/Gravity duality, Holographic superconductor, Homes’ law
- 1 Introduction
- 2 AC conductivities: holographic model and method
- 3 Conductivities with a neutral scalar hair instability
- 4 Ward identities: constraints between conductivities
- 5 Homes’ law and Uemura’s law
- 6 Conclusion and discussions
- A Two-point functions related to the real scalar operator
Holographic methods have provided novel and effective tools to study strongly correlated systems [1, 2, 3, 4] and they have been applied to many condensed matter problems. In particular, holographic understanding of high superconductor is one of the important issues. After the first holographic superconductor model proposed by Hartnoll, Herzog, and Horowitz (HHH)111The HHH model is a class of Einstein-Maxwell-complex scalar action with negative cosmological constant. [5, 6], there have been extensive development and extension of the model. For reviews and references, we refer to [2, 3, 7, 8].
The HHH model is a translationally invariant system with finite charge density. Therefore, it cannot relax momentum and exhibits an infinite electric DC conductivity even in normal phase not only in superconducting phase. To construct more realistic superconductor models, a few methods incorporating momentum relaxation were proposed. One way of including momentum relaxation is to break translational invariance explicitly by imposing inhomogeneous (spatially modulated) boundary conditions on a bulk field [9, 10, 11, 12, 13]. Massive gravity models [14, 15, 16, 17, 18, 19, 20] give some gravitons mass terms, which breaks bulk diffeomorphism and translation invariance in the boundary field theory. Holographic Q-lattice models [21, 22, 23, 24, 25] take advantage of a global symmetry of the bulk theory. For example, a global phase of a complex scalar plays a role of breaking translational invariance. Models with massless scalar fields linear in spatial coordinate [26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36] utilize the shift symmetry. Some models with a Bianchi VII symmetry are dual to helical lattices [37, 38, 39]. Based on these models, holographic superconductor incorporating momentum relaxation have been developed [40, 41, 42, 43, 44, 45, 46, 47, 48, 49].
In this paper, we study the HHH holographic superconductor model with massless scalar fields linear in spatial coordinate , where the strength of momentum relaxation is identified with the proportionality constant to spatial coordinate. The property of the normal phase of this model such as thermodynamics and transport coefficients were studied in [30, 26, 50, 28, 29, 51, 52]. The superconducting phase was analysed in [43, 44]. In particular, optical electric, thermoelectric and thermal conductivities of the model have been extensively studied in [29, 44, 51, 52]. Building on them, we further investigate interesting properties related to conductivities and momentum relaxation. There are three issues that we want to address in this paper: (1) conductivities with a neutral scalar hair instability, (2) Ward identities: constraints between conductivities, (3) Homes’ law and Uemura’s law. We explain each issue in the following.
(1) In a holographic superconductor model of a Einstein-Maxwell-scalar action [6, 7], a superconducting state is characterized by the formation of a complex scalar hair below some critical temperature. In essence, the complex scalar is turned on by coupling between the maxwell field and complex scalar through the covariant derivative. Interestingly, it was also observed [6, 7] that a different mechanism for the instability forming neutral scalar hair222A neutral scalar may arise from a top-down setting [53, 54]. is possible. This instability was not associated with superconductivity because it does not break a symmetry, but at most breaks a symmetry . Therefore, in this system with a neutral scalar hair, it is natural to expect that DC electric conductivity will be finite contrary to the case with a complex scalar hair (superconductor). However, to our knowledge, it has not been checked yet. In the early models without momentum relaxation, this question is not well posed since electric DC conductivity is always infinite due to translation invariance and finite density. In this paper, in a model with momentum relaxation, we show that DC electric conductivity is indeed finite with a neutral scalar hair.
(2) It was shown [3, 55], in normal phase without momentum relaxation, there are two constraints relating three transport coefficients: electric conductivity(), thermoelectric conductivity() and thermal conductivity(). The constraints can be derived by the Ward identity regarding diffeomorphism. Thanks to these two constraints, and can be obtained algebraically once is computed numerically. This is why only is presented in the literature . In our model, there is an extra field, a massless scalar for momentum relaxation, and it turns out there are three Ward identities of six two-point functions: , and and three more two-point functions related to the operator dual to a scalar field. Therefore, the information of alone cannot determine and . If we know three two-point functions then the Ward identities enable us to compute the other three two-point functions. In this paper, following the method in , we first derive the Ward identities for two-point functions analytically from field theory perspective. Next, we confirm them numerically from holographic perspective. This confirmation of the Ward identities also demonstrates the faithfulness of our numerical method.
(3) Homes’ law and Uemura’s law are empirical and material independent universal laws for high-temperature and some conventional superconductors [56, 57]. The law states that, for various superconductors, there is a universal material independent relation between the superfluid density () at near zero temperature and the transition temperature () multiplied by the electric DC conductivity () in the normal state right above the transition temperature .
where , and are scaled to be dimensionless, and is a dimensionless universal constant: or . They are computed in from the experimental data in [56, 57]. For in-plane high superconductors and clean BCS superconductors . For c-axis high superconductors and BCS superconductors in the dirty limit . Notice that momentum relaxation is essential here because without momentum relaxation is infinite. There is another similar universal relation, Uemura’s law, which holds only for underdoped cuprates [56, 57]:
where is another universal constant. In the context of holography Homes’ law was studied in [58, 45]. It was motivated by holographic bound of the ratio of shear viscosity to entropy density () in strongly correlated plasma and its understanding in terms of quantum criticality or Planckian dissipation ,where the time scale of dissipation is shortest possible. Since Homes’ law also may arise in systems of Planckian dissipation there is a good chance to find universal physics in condensed matter system as well as in quark-gluon plasma. In Homes’ law was observed in a holographic superconductor model in a helical lattice for some restricted parameter regime of momentum relaxation, while Uemura’s law did not hold in that model. However, physic behind Homes’ law in this model has not been clearly understood yet. For further understanding on Homes’ law, in this paper, we have checked Homes’ law and Uemuras’ law in our holographic superconductor model. We find that Homes’ law does not hold but Uemura’s law holds at small momentum relaxation region, related to coherent metal regime.
This paper is organised as follows. In section 2, we introduce our holographic superconductor model incorporating momentum relaxation by massless real scalar fields. The equilibrium state solutions and the method to compute AC conductivities are briefly reviewed. In section 3, the conductivities with a neutral scalar instability are computed and compared with the ones with a complex hair instability. In section 4, we first derived Ward identities giving constraints between conductivities analytically from field theory perspective. These identities are confirmed numerically by holographic method. In section 5, after analysing conductivities at small frequency, we discuss the Home’s law and Uemura’s law in our model. In section 6 we conclude.
2 AC conductivities: holographic model and method
2.1 Equilibrium state
In this section we briefly review the holographic superconductor model we study, referring to [26, 29, 51, 52, 61] for more complete and detailed analysis. We consider the action333The complete action includes also the Gibbons Hawking term and some boundary terms for holographic renormalization, which are explained in [26, 29, 51, 52, 61] in more detail.
where and is the holographic direction. is the Ricci scalar and is the cosmological constant with the AdS radius . We have included the field strength for a gauge field , the complex scalar field with mass , two massless scalar fields, . The covariant derivative is defined by with the charge of the complex scalar field. The action (2.1) yields equations of motion
for which we make the following ansatz:
In the gauge field, encodes a finite chemical potential or charge density and plays a role of an external magnetic field. is dual to a superconducting phase order parameter, condensate. Near boundary , with two undetermined coefficients and , which are identified with the source and condensate respectively. The dimension of the condensate is related to the bulk mass of the complex scalar by . In this paper, we take and to perform numerical analysis. is introduced to give momentum relaxation effect where is the parameter for the strength of momentum relaxation. For , the model becomes the original holographic superconductor proposed by Hartnoll, Herzog, and Horowitz (HHH) [5, 6].
First, if (no condensate), the solution corresponds to a normal state and its analytic formula is given by
where is the location of the black brane horizon defined by , , and is interpreted as charge density. It is the dyonic black brane modified by due to . The thermodynamics and transport coefficients(electric, thermoelectric, and thermal conductivity) of this system was analysed in detail in . In the case without magnetic field, see . Next, if , the solution corresponds to a superconducting state with finite condensate and its analytic formula is not available444A nonzero induces a nonzero , which changes the definition of ‘time’ at the boundary so field theory quantities should be defined accordingly.. For , the solutions are numerically obtained in for and in for . For example we display numerical solutions for some cases in Figure 1, where we set and plot dimensionless quantities scaled by : , , and .
2.2 AC conductivities
The purpose of this subsection is to briefly describe the essential points of a method to compute the AC thermo-electric conductivities. For more details and clarification regarding our model at , see [52, 51] for normal phase and for superconducting phase. At see for normal phase.
In order to study transport phenomena holographically, we introduce small bulk fluctuations around the background obtained in the previous subsection. For example, to compute electric, thermoelectric, and thermal conductivities it is enough to consider
where for and is enough for thanks to a rotational symmetry in space. For the sake of illustration of our method, we consider the case for and refer to for . In momentum space, the linearized equations of motion around the background are555For case, the bulk fluctuations to direction should be turned on so the number of equations of motion are doubled too.
Near boundary () the asymptotic solutions are
The on-shell quadratic action in momentum space reads
Here is the coefficient of when is expanded near boundary and is charge density. The index in and are suppressed.
The remaining task for reading off the retarded Green’s function is to express in terms of . It can be done by the following procedure. First let us denote small fluctuations in momentum space by collectively. i.e.
Near black brane horizon (), solutions may be expanded as
which corresponds to incoming boundary conditions for the retarded Green’s function and is some integer depending on specific fields, . The leading terms are only free parameters and the higher order coefficients such as are determined by the equations of motion. A general choice of can be written as a linear combination of independent basis , (), i.e. . For example, can be chosen as
Every yields a solution , which is expanded near boundary as
where and the leading terms are the sources of -th solutions and are the corresponding operator expectation values. and can be regarded as regular matrices of order , where is for row index and is for column index. A general solution may be constructed from a basis solution set :
with arbitrary constants ’s. For a given , we always can find 666There is one subtlety in our procedure. The matrix of solutions with incoming boundary condition are not invertible and we need to add some constant solutions, which is related to a residual gauge fixing .
so the corresponding response may be expressed in terms of the sources
3 Conductivities with a neutral scalar hair instability
By the numerical method reviewed in the previous subsection, the electric, thermoelectric and thermal conductivities of the model (2.1) have been computed in various cases [29, 52, 44]. As an example, in Figure 2, we show the results for , which is reproduced here for easy comparison with new results in this paper.
Figure 2 shows AC electric conductivity (), thermoelectric conductivity (), and thermal conductivity () for and at different temperatures. The colors of curves represent the temperature ratio, , where is the critical temperature of metal/superconductor phase transition. for dotted, red, orange,green, and blue curves respectively. In particular, the dotted curve is the case above and the red curve corresponds to the critical temperature. The first row is the real part and the second row is the imaginary part of conductivities.
One feature we want to focus on in Figure 2 is pole in Im below the critical temperature. There is no pole above the critical temperature. By the Kramers-Kronig relation, the pole in Im implies the existence of the delta function at in Re. It means that in superconducting phase the DC conductivity is infinite while in normal phase the DC conductivity is finite due to momentum relaxation.
Unlike the studies in , here we set . Between finite and zero , there is a qualitative difference in the instability of a Reissner-Nordstrom AdS black hole . The origin of the superconductor (or superfluidity) instability responsible for the complex scalar hair may be understood as the coupling of the charged scalar to the charge of the black hole through the covariant derivative . In other words, the effective mass of defined by can be compared with the Breitenlohner-Freedman (BF) bound. The BF bound for AdS is . The effective mass may be sufficiently negative near the horizon to destabilize the scalar field since becomes bigger at low temperature777As the temperature of a charged black hole is decreased, develops a double zero at the horizon.. Based on this argument one may expect that when the instability would turn off. However, it turns out that a Reissner-Nordstrom AdS black hole may still be unstable to forming neutral scalar hair, if is a little bit bigger than the BF bound for AdS. It can be understood by the near horizon geometry of an extremal Reissner-Nordstrom AdS black hole. It is AdS R so scalars above the BF bound for AdS may be below the bound for AdS. These two instability conditions can be summrized by one ineqaulity
which reproduces the result for in
Here, we see can be below the BF bound when .
However, it was discussed in [6, 7] that the instability to forming neutral scalar hair for is not associated with superconductivity because it does not break a symmetry, but at most breaks a symmetry . Therefore, it would be interesting to see if the DC conductivity is infinite or not in the background with a neutral scalar hair.888We thank Sang-Jin Sin for suggesting this. Without momentum relaxation () this question is not well posed since the DC conductivity is always infinite with or without a neutral scalar hair due to translation invariance and finite density. Now we have a model with momentum relaxation (), we can address this issue properly.
To have an instability at we choose the same parameters as Figure 2: and . For , , which is below the BF bound (3.1). Figure 3 shows our numerical results of conductivites, where all temperatures are below : for red, orange,green, and blue curves respectively. A main difference of Figure 3 from Figure 2 is the disappearance of pole in Im below . It confirms that the neutral scalar hair has nothing to do with superconductivity as expected.
In Figure 3 it is not easy to see the conductivities in small regime, so we zoom in there in Figure 4. Contrary to the conductivity of normal component in superconducting phase, the DC electric conductivity is not so sensitive to temperature and increases as temperature decreases, which is the property of metal. The thermoelectric and thermal conductivities decrease as temperature increases except a small increase of thermoelectric conductivity near the critical temperature. As a cross check, we have also computed these DC conductivities analytically by using the black hole horizon data according to the method developed in . Since there is no singular behavior in the conductivities as we may regard the real scalar field here as the dilaton in and the conductivities read
where , and are the entropy density, charge density and temperature in the dual field theory. They are given by , and . The analytic values are designated by the red dots in Figure 4 and they agree to the numerical values very well. For a special case with , in Figure 5, we see that , different from superconducting case ( shown in ), but , same as superconducting case.
3.1 Superfluid density with a complex scalar hair
We have found that for there is no pole in Im, of which strength corresponds to superfluid density. To understand it better, we derive an expression for superfluid density for . Let us start with the Maxwell equation,
Once we assume that all fields depend on and and the fluctuations are allowed only for the -direction, the -component of the Maxwell equation reads
The integration of (3.5) from horizon to boundary gives the boundary current
By hydrodynamic expansion for small , it turns out that the first term and the second term goes to zero as
while the last term goes to constant. Here we used the expansions of the fileds near horizon
where is a constant residual gauge parameter fixing , and , and can be expanded as
With the following source-vanishing-boundary conditions
except , the current (3.6) can be interpreted as
This shows how the hairy configuration contributes to . If , vanishes, which confirms our numerical analysis.
4 Ward identities: constraints between conductivities
In this section, we first analytically derive the Ward identities regarding diffeomorphism from field theory perspective. It gives constraints between conductivities() and two-point functions related to the operator dual to the real scalar field. Next, these identities are confirmed by computing all two-point functions numerically from holographic perspective.
4.1 Analytic derivation: field theory
To derive the Ward identities, we closely follow the procedure in 999See for a holographic derivation. and extend the results therein to the case with real and complex scalar fields, which are and in (4.1). Our final results are (4.44)-(4.45) and (4.56)-(4.58).
Let us start with a generating functional for Euclidean time ordered correlation functions:
where , , , , and are the non-dynamical external sources of the stress-energy tensor , current , real scalar operators , and complex operators respectively. We define the one-point functions by functional derivatives of :
where these expectation values are not tensors but tensor densities under diffeomorphism. One more functional derivatives acting on one-pint functions give us Euclidean time ordered two-point functions:
We consider the generating functional invariant under diffeomorphism, , and the variation of the fields can be expressed in terms of a Lie derivative with respect to the vector field
For diffeomorphism invariance, the variation of should vanish:
which, after integration by parts, yields the Ward identity for one-point functions regarding diffeomorphism.
By taking a derivative of (4.18) with respect to either , , or , we obtain the Ward identities for the two-point functions: | s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986693979.65/warc/CC-MAIN-20191019114429-20191019141929-00554.warc.gz | CC-MAIN-2019-43 | 22,667 | 78 |
https://www.encyclopediaofmath.org/index.php/Spearman_coefficient_of_rank_correlation | math | Spearman coefficient of rank correlation
A measure of the dependence of two random variables and , based on the rankings of the 's and 's in independent pairs of observations . If is the rank of corresponding to that pair for which the rank of is equal to , then the Spearman coefficient of rank correlation is defined by the formula
or, equivalently, by
where is the difference between the ranks of and . The value of lies between and ; when the rank sequences completely coincide, i.e. , ; and when the rank sequences are completely opposite, i.e. , . This coefficient, like any other rank statistic, is applied to test the hypothesis of independence of two variables. If the variables are independent, then , and . Thus, the amount of deviation of from zero gives information about the dependence or independence of the variables. To construct the corresponding test one computes the distribution of for independent variables and . When one can use tables of the exact distribution (see , ), and when one can take advantage, for example, of the fact that as the random variable is asymptotically distributed as a standard normal distribution. In the latter case the hypothesis of independence is rejected if , where is the root of the equation and is the standard normal distribution function.
Under the assumption that and have a joint normal distribution with (ordinary) correlation coefficient ,
as , and therefore the variable can be used as an estimator for .
The Spearman coefficient of rank correlation was named in honour of the psychologist C. Spearman (1904), who used it in research on psychology in place of the ordinary correlation coefficient. The tests based on the Spearman coefficient of rank correlation and on the Kendall coefficient of rank correlation are asymptotically equivalent (when , the corresponding rank statistics coincide).
|||C. Spearman, "The proof and measurement of association between two rings" Amer. J. Psychol. , 15 (1904) pp. 72–101|
|||M.G. Kendall, "Rank correlation methods" , Griffin (1962)|
|||B.L. van der Waerden, "Mathematische Statistik" , Springer (1957)|
|||L.N. Bol'shev, N.V. Smirnov, "Tables of mathematical statistics" , Libr. math. tables , 46 , Nauka (1983) (In Russian) (Processed by L.S. Bark and E.S. Kedrova)|
|[a1]||J. Hájek, Z. Sidák, "Theory of rank tests" , Acad. Press (1967)|
|[a2]||M. Hollander, D.A. Wolfe, "Nonparametric statistical methods" , Wiley (1973)|
Spearman coefficient of rank correlation. A.V. Prokhorov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Spearman_coefficient_of_rank_correlation&oldid=15078 | s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256163.40/warc/CC-MAIN-20190520222102-20190521004102-00373.warc.gz | CC-MAIN-2019-22 | 2,643 | 14 |
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https://www.worldhistoryedu.com/archimedes-biography-scientific-accomplishments-inventions-principle/ | math | Archimedes: Biography, Scientific Accomplishments, Inventions, & Principle
Born in Sicily, Magna Graecia, Archimedes was a critically acclaimed Greek scientist who attained so many feats in a host of scientific disciplines like astronomy, physics, mathematics, mechanics and engineering. He is famed for coming out with the Archimedes principle upon which fluid dynamics as a discipline partly rests on.
Another spectacular accomplishment of him came in his accurate approximation of the mathematical constant pi (π), which he calculated to fall between 3 10/77 and 3 1/7. The fact that many of his inventions – like the Archimedes screw – are still in use to this day makes him an even more remarkable scientist of the classical age.
Here is a complete biography, scientific contributions and major achievements of Archimedes of Syracuse (c. 287 bc – c. 212 bc), one of the most influential scientists in world history and a colossal Greek mathematician of the highest order.
Birth and early life
Archimedes’ place of birth, Syracuse, at the time was a buzzing city filled with many renowned scholars and artists. The city also benefited from its extensive trade ties with merchants from Greece, Phoenicia and Egypt. According to many historians and scholars in antiquity, Syracuse was at the time one of the most famous cities in the known world.
Although not much is known about the early life of this great mathematician, many historians that came after him proposed that he most likely spent his early years in Egypt, particularly in the city of Alexandria. It was during this time that he invented a device known as the Archimedes’ screw (more on that later).
The only thing we know about his family is that he was the son of Phidias, a renowned astronomer. One of his colleagues known as Heracleides is said to have written a biography about him. However, none of those biographies remain to this day.
Archimedes and King Hieron II, the king of Syracuse
What seems to be apparently clear is that he spent a huge chunk of his life in the Greek city-state of Syracuse on the island of Sicily. While in Sicily, he became a close friend of Hieron II (308-215 BC), the tyrant and later king of Syracuse.
A number of accounts have stated that he helped Hieron II in his court. In one particular case he was able to calculate the proportion of silver and gold in a jewelry that had been gifted to King Hieron.
This third century BC Sicilian-born scientist probably received much of his education in Alexandria in Egypt, where he studied geometry and astronomy from/with scholars and successors of Euclid. Alexandria at the time was perhaps the hub of the intellectual world as it housed a wide variety of scholars from different parts of the world.
Archimedes’ Greatest Contributions
Archimedes, a Greek mathematician, inventor, and scholar of critical acclaim, is praised as one of the greatest mathematicians of all time. He is praised due to his remarkable contributions to a host of disciplines such as mechanics, astronomy, geometry, arithmetic, and physics.
Fictional stories about Archimedes
Being an important figure from the classical age, his story and achievements often suffers a lot as the line between myth and factual detail gets blurred.
“Heurēka!” (“Eureka! Eureka!”)
Did Archimedes actually jump out of his bath and run out naked into the streets shouting “Heurēka!” (“I have found it!”)? Many claim that the story was anything but an exaggeration. That probably never happened when Archimedes conceived the principle of buoyant force. Like many scientists that make a breakthrough, Archimedes most likely would have been over the moon over his discovery of how to determine the proportion of silver and gold; however, it is unlikely that he stormed out of the bathroom stark naked into the streets.
Similarly, it is highly doubtful that the Syracuse-based mathematician uttered the sentence: “Give me a lever and a place to stand and I will move the Earth”. To this day, there is no historical evidence to support such claim. Such a statement is demonstrative of the immense power of levers.
Another made-up story is the one which says that he used a set of mirrors to reflect the sun’s rays to burn a number of Roman ships during the siege of Syracuse in 212 BC. Archimedes did indeed contribute immensely in producing war machines to defend Syracuse during the siege; however, he did not deploy some sort of sun ray-killing machines.
Finally, the story that Archimedes met his end at the hands of a Roman soldier after he refused to abandon a mathematical diagram that he had been working on seems a bit too far-fetched.
Although history has come to judge Archimedes as one of the greatest mathematician and inventors of all time, Archimedes never thought highly of some of his inventions. According to Plutarch, it was for the above reason why the mathematicians chose not leave written records of those works.
However, he took an enormous amount of pride in his work in On the sphere and Cylinder, which shows the mathematical relationship between the volume of a sphere and the cylinder in which it is inscribed. He purposely instructed that his tomb carry image of a sphere inscribed in a cylinder.
Archimedes thus was more pleased by his works in the development of mathematical theorems and proofs than his mechanical inventions. During his time, however, his fame predominantly came as a result of his mechanical inventions.
READ MORE: 12 Greatest Ancient Greek Inventions
Major achievements of Archimedes
For someone to be described by ancient historians and modern historians alike as the greatest mathematician of all time means that Archimedes was truly indeed a gifted-mathematician.
Below is a quick presentation of the major achievements of Archimedes:
Archimedes’ Law of the Lever
To demonstrate just how powerful levers can be, there have been some historians that claimed that the statement “Give me a lever and a place to stand, and I will move the world” was uttered by Archimedes. Regardless of whether he uttered it or not, the fact is that Archimedes made tremendous contributions to lever technology. He discovered that the same or even more work could be done when trade-offs are made between force and distance.
Area, surface area and volume of sphere
He used a method of integration to calculate the areas, surface areas and volumes of spheres and other shapes. His works are credited with laying the pillar for calculus, which would later be improved upon by modern mathematicians like Leibniz, Newton and Kepler.
Nine of Archimedes’ treatise survived, including On the Sphere and Cylinder which showed that the surface area of any sphere of radius (r) is four times the value of the greatest circle. This theorem, which is contained in the treatise On the Sphere and Cylinder, can be expressed mathematically as S = 4πr2
Also in the work, the mathematician showed that the volume of the circumscribing cylinder is 2πr3
His mathematical theorem showed that the volume of a sphere is two-thirds that of the cylinder in which it is inscribed. This can be expressed as V = 4/3πr3
Approximation of the value of pi (π)
Another significant contribution of Archimedes to mathematics was the value of pi (π). The mathematician calculated that pi fell between 3 10/71 and 3 1/7. He is said to have used a very innovative technique to get the value. That technique was used until the 15th century CE.
In addition to calculating pi, he also accurately approximated square roots.
The mathematician also developed his system of showing large numbers mathematically.
The Archimedes’ principle
In addition to developing a host of theorems in mechanics, including in works related to the centre of gravity of solids and plane figures (in the treatise On Plane Equilibriums), he developed a law of buoyancy which is commonly known as Archimedes’ principle. The principle covers the weight of a body that is immersed in a liquid.
Archimedes’ Principle, also known as the Law of Buoyancy, states that an object immersed in fluid will have an upward force equal to the weight of the displaced fluid.
Archimedes’ Principle allows for the calculation of the volume or average density of an object immersed in a fluid. The principle is famed for helping measure the volume of irregular objects, such as jewelry, cutlery, and many others. In addition to that, it allows scantiest to understand how objects behave when immersed in any fluid. With Archimedes principle, one can explain how hot air balloons stay in the air, or how ships float.
Applications of the Archimedes principle is vast and wide, including in disciplines like entomology, engineering, geology, medicine, dentistry, and engineering, among others. For example, in the medical field, the principle comes in useful when determining the densities of teeth and bones.
The Archimedes screw
The screw that Archimedes invented came to be known as the Archimedes’ screw. The screw, which is enclosed in a pipe, is used to lift water from one level to another. The Archimedes’ screw came in very handy when seamen removed water from their ship’s hull.
He touched a bit on integral calculus
His contributions to geometry were unparalleled. He even went as far as anticipating the method of exhaustion which is rudimentary form of modern-day calculus.
Archimedes worked on finding the volumes of the segments of solids that emerged from the revolution of shapes such as circles, ellipse, hyperbola or parabola. This work of his, which is contained in the treatise On Conoids and Spheroids, fall under calculus in our modern time.
His use of method of exhaustion (modern calculus) allowed him to come out with more mathematical theorems.
The compound pulley
This invention of Archimedes ended up bringing the scientist immense praise as it revolutionized the way large objects were lifted. According to Plutarch, the mathematician demonstrated this invention of his to King Hieron by effortless pulling a ship in a straight line.
Archimedes’ passion and associations with other mathematicians of his era
Archimedes was said to be completely devoted to the pursuit of scientific knowledge, particularly mathematics and mechanics. He often did this at a huge expense to his health as he neglected food and drink and basic personal hygiene so he could focus solely on his experiments and studies.
Many of the critically acclaimed works of Archimedes came via his correspondence with mathematicians and colleagues of his in Alexandria, including Eratosthenes of Cyrene and Conon of Samos.
A defense contractor for the city of Syracuse
His knowledge in engineering and mechanics enabled him to come out with a number of inventions that he used to defend the city of Syracuse against the Romans in 213 BC. According to Plutarch, his close friend King Hieron was the one who encouraged him to build those war machines.
His engines of war gave him more acclaim that his mathematical theorems. That comes as no surprise considering the fact that it was a BC era, an era when warfare was an extremely important. His war machines received enormous praise for being able to keep the Roman forces at bay for almost two years.
Many of Archimedes works were theoretical in nature. Much of his work in mathematics was perhaps fanned on by his passion for mechanics.
It’s been stated that his works in theoretical mechanics and hydrostatics enabled him to come out a number of mathematical theorems. As it is seen in his treatise Method Concerning Mechanical Theoremis, Archimedes used much of what he knew in mechanics to advance his knowledge in mathematics.
Famous works of Archimedes that survived
Many of his theorems in mechanics, including those on the center of gravity of plane figures, are contained in the treatise On Plane Equilibriums. In the treatise Quadrature of the parabola, Archimedes calculates the area of a segment of a parabola that had been cut off by any chord.
Archimedes is credited with producing many works. Although many of them were lost, nine of his treaties survived. They are as follows:
- On Floating Bodies
- On Spirals
- On Conoids and Spheroids
- Measurement of a circle
- The Sandreckoner
- Quadrature of the Parabola
- On Plane Equilibriums
- On the Sphere and cylinder
In the treatise The Sandrekoner, the mathematician shows how a number system could accommodate astonishing numbers of up to 8 x 1063. He goes on to say that with that number system, he could count every grain of sand which the universe could hold.
He was one of the few scientists of his era that actually thrived to put his mathematical theorems into practice. This is one of the reasons why his works had/and continue to have a huge impact in the world of science.
Archimedes favored the viewing his scientific experiments, including engineering problems, using the lens of mathematical theorems. His passion for mathematics is what led him to deploy mechanical experiments to gain greater understanding of mathematical theorems.
The mathematician and inventor Archimedes of Syracuse died in 212 or 211 BC in Syracuse on the island of Sicily. He was killed during Roman siege (214-212 BC) on the city of Syracuse (during the Second Punic War). He was most likely in his mid-70s.
Out of the strong respect and admiration General Marcus Claudius Marcellus had for Archimedes, he ordered that the scientist be giving a burial with honor. Marcellus had hoped to capture Archimedes alive so that he could perhaps benefit from the genius of the scientist.
According to the Greek historian Plutarch, Archimedes was busy going about with some very important works in mathematics when a Roman soldier struck him down. The historian goes on to say that Archimedes, in spite of the order from the soldier, refused to halt his work.
Another version of how Archimedes died (also from Plutarch) states that Roman soldiers wrongly thought that the mathematician carried on him a bag that contained gold. Unbeknownst to those soldiers, the bag actually contained mathematical instruments, spheres and angles that the mathematician was sending to Marcellus.
Read More: 10 Most Famous Ancient Greeks and their Achievements
More Archimedes Facts
The story of Archimedes running naked into the crowded streets of Syracuse shouting “Eureka! Eureka!” was first written down by a Roman scholar and architect named Vitruvius. According to the accounts, the scientist had discovered the principle of buoyancy in order to help him assess whether King Hieron’s golden crown was pure gold or not.
According to Greek historian Plutarch, Archimedes was probably related to Heiron II, the king of Syracuse. This point could be supported by the fact that he dedicated his treatise The Sandreckoner to Gelon, the son of Hieron.
While in Alexandria, Egypt, he studied with a number of followers of the famous mathematician Euclid. He often corresponded with fellow mathematicians Conon of Samos and Eratosthenes of Cyrene, both lived in Alexandria.
After realizing that some of his friends began to take credit for his mathematical proofs, he desisted from including proofs to theorems in his correspondence with mathematicians in Alexandria.
Compared to other scientists and mathematicians of his, Archimedes has quite a lot more anecdotal details about his life.
Much of what we know about the life and works of Archimedes comes from the accounts of Plutarch (c. 46-119 CE), the Greek historian and biography. Other sources came from the likes of Livy and other Greek historians.
The roman general by the name of Marcus Claudius Marcellus – was saddened by his death as he intended to bring Archimedes into his service. The general was impressed by the machines that Archimedes built to defend the city from the Romans
Following Rome’s siege of Syracuse in 212 BC, Roman General Marcellus is believed to have taken two spheres made by Archimedes back to Rome. The spheres were basically about the various planetary objects as well as their motions.
Like many scientists and geniuses that came after Archimedes, the likes of Galileo and Newton were big admirers of the Sicilian scientist and mechanical engineer.
Following his death, his mathematical works and treatise did not gain large acclaim as compared to the ones of the mathematician and geometer Euclid. Regardless, there were still a good number of mathematicians in Alexandria that were devout followers of his works. Those scholars included Theon, Pappus, and Heron.
When the Roman statesman and scholar Cicero travelled to Sicily in 75 BC he searched for the tomb of Archimedes. Cicero found the tomb to be covered on all side by weeds. | s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224646457.49/warc/CC-MAIN-20230531090221-20230531120221-00685.warc.gz | CC-MAIN-2023-23 | 16,720 | 91 |
https://www.pdfsdownload.com/download-pdf-for-free/a+mean+variance+skewness+portfolio+optimization+mo | math | a mean variance skewness portfolio optimization mo PDFs / eBooks
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(1995) show an efficient algorithm to optimize a mean-variance-skewness model. By definition, the portfolio optimization problem proposed by Markowitz (1952) is multi- Alfaro-Cid, E., Baixauli, J.S. and Fernandez-Blanco, M.O. (2008). | s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304686.15/warc/CC-MAIN-20220124220008-20220125010008-00108.warc.gz | CC-MAIN-2022-05 | 2,679 | 17 |
https://pari.math.u-bordeaux.fr/archives/pari-dev-1210/msg00056.html | math | |Bill Allombert on Fri, 26 Oct 2012 22:50:33 +0200|
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|Re: %Ps of t_REAL|
On Thu, Oct 25, 2012 at 11:26:17PM +0200, Bill Allombert wrote: > Hello PARI developers, > > ? \p10000 > realprecision = 10018 significant digits (10000 digits displayed) > ? a=Pi; > ? \p38 > realprecision = 38 significant digits > ? printf("%s",a) > 3.1415926535897932384626433832795028842 > > I know this is the documented behaviour but I cannot say I ever liked it. > I would much prefer to get 10018 digits. (If I wanted 38 digits, I would > do the computation to 38 digits, or I would write %.38s). > > It is worse in library mode where you do not have any control over > realprecision. It is especially painful with err_printf which is > used for debugging, when the interesting digits are discarded. We discussed about changing the behaviour, but there are two problems: 1) %g convert the data to t_REAL: ? printf("%g",12) 12.000000000000000000000000000000000000 2) "%s" does not allow to specify a precision. Instead: * s: Convert to a character string. If a precision is given, no more than the specified number of characters are written. ? printf("%.8s",[Pi,23]) [3.14159 So we are stuck. Cheers, Bill. | s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232259452.84/warc/CC-MAIN-20190526185417-20190526211417-00260.warc.gz | CC-MAIN-2019-22 | 1,264 | 4 |
https://ufn.ru/en/articles/1980/10/d/ | math | H--like impurity centers and molecular complexes created by them in semiconductors
This review analyzes the status of the problem of H$^-$-like centers and the molecular complexes that they form in doped semiconductors. The study of these centers is closely associated with the general problem of the localization of electrons in disordered systems. The existing experimental data are discussed from a unitary standpoint. Models of various impurity complexes are discussed and the pertinent estimates are given. We show that all the fundamental observed regularities at low and moderate impurity concentrations are explained by the formation of either isolated H$^-$-like centers or of complexes of the H$^-$--H$^+$-type. At higher impurity concentrations, the number of H$^-$--H$^+$-type complexes declines, impurity clusters are formed, and then a conducting impurity band arises from the H$^-$-like states. | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950373.88/warc/CC-MAIN-20230402012805-20230402042805-00099.warc.gz | CC-MAIN-2023-14 | 909 | 2 |
http://scientificpearlsofwisdom.blogspot.com/2009/10/universe-as-computer.html | math | Sunday, October 18, 2009
What Language Does Our Universe "Speak"?
Many profound physicist have come to think of physics at the very tiniest length scale (the Planck length) as a computer or information processor. To name a few: John A. Wheeler, Richard Feynman, Roger Penrose, Gerard 't Hooft. Wheeler expressed this view as "it from bit".
One of the main reasons for this view is the realization that physics at that scale will have to be discrete. If not, it becomes very hard to reconcile relativity and quantum mechanics into one theory. In the continuous domain calculation simply blow up: they cannot be re-normalized. In addition to that, the uncertainty principle of quantum mechanics demands that we can not even pinpoint things down to such precision without creating a black hole which would immediately render any measurement at a scale smaller than its horizon impossible....So these physicist think that physics at that scale is some sort of cellular automaton.
Around the end of every century some people seem the need to make the rather absurd claim that science is coming to an end (I believe we have barely started, but anyway). This century this view is expressed in the book: "The End Of Science: Facing The Limits Of Knowledge In The Twilight Of The Scientific Age" by John Horgan. He argues that there are four recent theories that have shown the fundamental limitations of science:
1. Relativity: anything inside the horizon of a black hole will never get out. So we cannot study the inside of a black hole.
2. Quantum Mechanics: the world is irreducibly random.
3. Chaos: The dynamics of many real physical phenomenon displays extreme sensitivity to initial conditions.
4. Complexity Theory: Godel's theorem of incompleteness of formal systems.
Let's see how these theories would fare in the face of a fundamental theory of "Physics as Computation" (PAC). I think the black hole issue is already close to being resolved. A quantum mechanical treatment of BHs will involve BH-radiation (or Hawking radiation). As such, in-falling matter will cause disturbances on the surface of the BH-horizon that encodes the information of the in-falling matter and which will eventually be radiated out again. No information is lost in the process. (Every BH will eventually die in an explosion that is more violent than the most energetic supernova, but it takes a while..) For the observer that stays outside the BH, the BH horizon is the edge of the universe in a very real sense. It will see his colleague that falls into the BH freeze onto the horizon, get disintegrated and eventually be radiated out again in bits and pieces. For the in-falling observer the edge of the universe is not the BH horizon, but a singularity at the center of the BH. In this case we have to deal with a singularity but it seems evident to me that the final PAC theory will describe that singularity not as an infinitely dense point but rather a sensible finite object.
How the irreducibility of quantum mechanics may be resolved in terms of a cellular automaton was described in my previous blog on "Quantum Mechanics is not the Final Theory".
The phenomenon of chaos in nonlinear dynamical systems makes claims on unpredictability of a more every day nature: for instance the weather patterns are unpredictable because a small error in the initial conditions may result in large differences a few days later (except in California where we don't need weather forecasting). The canonical example is this: x[t+1]=2*x[t] mod 1. This means that at every iteration we move all digits one decimal place to the left and set the number to the left of the dot to 0: 0.12345...
Finally Godel's theorem. It says that within any sufficiently complex formal system there will be true theorems that cannot be proved. I am still thinking about these issues, but I seem to have an issue with the notion of "a true theorem". True can only acquire meaning as an interpretation of the formal system (say mapping sequences to mathematical or physical "truths"). But mathematics is itself a formal system. Truth does not exist outside any axiomatic system and the interpretation that Godel's theorem shows that truth is bigger than formal reasoning just doesn't sit well with me. Anyway, some future blogs will unquestionably be devoted to these deep issues.
It will be very interesting to be able to answer the question: "what is the complexity class of the sequences generated by the cellular automaton that governs our universe". Or phrased more informally: "What language does our universe speak". Here is my prediction: Dutch ;-) (or maybe a language of the same complexity). It seems that Dutch is more complex than context-free languages due to cross-referencing but still decidable in polynomial time. It represents a possible level of complexity where things are not too regular but also not too unwieldy. Anyway, my prediction here should be taken with a huge grain of salt of course.
Soooo, the universe is a huge computer that is computing "something". It is our task as scientists to figure what and how it is computing. Actually, we already know the answer: 42 ;-). But what was the original question? Let's leave that to religion. | s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794872114.89/warc/CC-MAIN-20180528072218-20180528092218-00122.warc.gz | CC-MAIN-2018-22 | 5,219 | 15 |
http://iembra.org/confidence-interval/calculate-the-bootstrap-standard-error-of-the-75th-percentile.php | math | Calculate The Bootstrap Standard Error Of The 75th Percentile
Generated Wed, 05 Oct 2016 18:12:46 GMT by s_hv997 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.8/ Connection For our purposes here, these will be the 2.5th and 97.5th percentile, though generically these are the a/2 and 1-a/2 percentiles. We will be using the hsb2 dataset for all of the examples on this page. If we were calculating 95% confidence limits on the mean, SPSS could tell us that those limits were 61.01 and 68.19. check my blog
Even if the population is not normal, the Central Limit Theorem tells us that the sampling distribution will be at least approximately normal, so we don't worry too much. Notice that it has a range of about 60 milliseconds, with a mean of about 65 milliseconds (the median was 62). Your cache administrator is webmaster. The median is not as well behaved as the mean relative to the central limit theorem, which does not apply to medians.
Bootstrap Percentile Confidence Interval
install.packages("boot") library(boot) hsb2<-read.table("http://www.ats.ucla.edu/stat/data/hsb2.csv", sep=",", header=T) Using the boot commandThe boot command executes the resampling of your dataset and calculation of your statistic(s) of interest on these samples. Preview this book » What people are saying-Write a reviewWe haven't found any reviews in the usual places.Selected pagesPage 13Title PageTable of ContentsIndexReferencesContentsChapter 1 Graphical Methods 1 Chapter 2 Regression 23 Chapter 3 The system returned: (22) Invalid argument The remote host or network may be down. dch: David C.
However, there are two important features of this approach. How to cite this page Report an error on this page or leave a comment The content of this web site should not be construed as an endorsement of any particular The percentile method would take these to be the upper and lower cutoffs for the 95% confidence interval. The Bootstrap Method Of Constructing Confidence Intervals Can Be Used To Estimate To get the standard error of the median, we have to have the empirical standard deviation of a bunch of medians.
Howell University of Vermont [email protected]Welcome to the Institute for Digital Research and Education Institute for Digital Research and Education Home Help the Stat Consulting Group by giving Better intervals I could say the same things here that I said for confidence limits on the mean, with respect for corrections for bias and acceleration. Then do your resampling. The system returned: (22) Invalid argument The remote host or network may be down.
But we need one more thing--we need the standard error of the median that corresponds to the standard error of the mean in the traditional formula. Bootstrap Confidence Interval Calculator Diagram of the bootstrapped t method: Original Sample: 2 2 3 4 5 5 5 6 7 9 --> Med Sample 1: 2 2 2 5 6 6 6 7 7 The second argument can be an index vector of the observations in your dataset to use or a frequency or weight vector that informs the sampling probabilities. This book is meant for graduate students in statistics, economics, policy analysis, and social sciences, especially, but certainly not exclusively, those interested in the challenges of economic development in the Third
Percentile Method Confidence Intervals
However, SPSS cannot give us limits on the median If we use our program to calculate confidence limits on the median, we obtain the following results. We will demonstrate a few of these techniques in this page and you can read more details at its CRAN package page. Bootstrap Percentile Confidence Interval Generated Wed, 05 Oct 2016 18:12:46 GMT by s_hv997 (squid/3.5.20) Bootstrap Confidence Interval Example I will use the data from the condition in which 5 comparison digits were first presented, and the test stimulus actually was one of those digits.
From these samples, you can generate estimates of bias, bootstrap confidence intervals, or plots of your bootstrap replicates. http://iembra.org/confidence-interval/calculate-confidence-intervals-from-mean-and-standard-error.php Your cache administrator is webmaster. Generated Wed, 05 Oct 2016 18:12:46 GMT by s_hv997 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.6/ Connection His Handbook on Poverty and Inequality (with Shahidur Khandker) was published by the World Bank in 2009, his articles have appeared in over 30 scholarly journals, and he has written numerous Bootstrap Percentile Confidence Interval In R
error t1* 0.6174493 -0.004455323 0.04169738While the printed output for bootcorr is brief, R saves additional information that can be listed:summary(bootcorr) Length Class Mode t0 1 -none- numeric t 500 -none- The system returned: (22) Invalid argument The remote host or network may be down. When the sampling distribution is perfectly symmetric, the percentile method is quick, easy to comprehend, and accurate. news There is nothing sacred about these values, but they should give you the general idea.
This method computes . What Is The Mean Difference In Credit Card Debt Of The Two Groups In The Original Data? This is analogous to what we did with the mean. Med1a, Med1b, Med1c, etc--inner set of bootstrapped medians, which will be used to calculate t*1.
Let B represent the number of bootstrap samples we calculate in the outer loop, and let b represent the number of bootstrap samples we draw based on each outer bootstrap samples.
Generated Wed, 05 Oct 2016 18:12:46 GMT by s_hv997 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.5/ Connection The procedures for bootstrapping almost any statistic follow a very predictable pattern, and I am not going to repeat much of that here. This is based on a study by Sternberg (1966), in which he asked subjects to view a set of digits for a brief time (measured in milliseconds) and then see a Bootstrap Confidence Interval R Her major areas of interest are applied statistics, statistics and marketing, the analysis of living standards surveys, data mining, and model selection.
Your cache administrator is webmaster. Your cache administrator is webmaster. Then our confidence limits become. Notice that these limits are somewhat narrower (57.5 and 65.0) and that they are slightly asymmetric around the sample median.
Each new sample contains n elements. We would expect a positive skew because of the nature of the task. This is a book that can serve as a reference work, to be taken down from the shelf and perused from time to time. Additionally, the book will be useful to academics and practitioners who work closely with survey data.
IDRE Research Technology Group High Performance Computing Statistical Computing GIS and Visualization High Performance Computing GIS Statistical Computing Hoffman2 Cluster Mapshare Classes Hoffman2 Account Application Visualization Conferences Hoffman2 Usage Statistics 3D It is not the standard error of the median. Please try the request again. Before using commands in the boot package, you must first download the package and load it in your workspace.
The system returned: (22) Invalid argument The remote host or network may be down. Your cache administrator is webmaster. A fifth type, the studentized intervals, requires variances from each bootstrap sample. Dominique is a Fellow of the American Statistical Association.Jonathan Haughton (Ph.D.
The system returned: (22) Invalid argument The remote host or network may be down. Having drawn B bootstrap samples, we sort them as before from low to high. A specialist in the areas of economic development, international trade, and taxation, and a prize-winning teacher, he has lectured, taught, or conducted research in over a score of countries on five We can illustrate the result of this method using an example that I have used elsewhere.
We can obtain an estimate of that by taking the medians of our B samples, and simply calculating the standard deviation of that distribution. Harvard 1983) is Professor of Economics at Suffolk University, and Senior Economist at the Beacon Hill Institute for Public Policy, both in Boston. The only method that I have programmed as of the time of this original writing is "Lunneborg's" method. | s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487622234.42/warc/CC-MAIN-20210616063154-20210616093154-00628.warc.gz | CC-MAIN-2021-25 | 8,445 | 21 |
https://www.hackmath.net/en/word-math-problems/ratio?tag_id=154&page_num=2 | math | Ratio + expression of a variable from the formula - math problems
Number of problems found: 109
Perimeter of rectangle is 48 cm. Calculate its dimensions if they are in the ratio 5:3 (width:height)
- Ratio in trapezium
The height v and the base a, c in the trapezoid ABCD are in the ratio 1: 6: 3, its content S = 324 square cm. Peak angle B = 35 degrees. Determine the perimeter of the trapezoid
Mother divided her three children's oranges in a ratio of 6:5:4. Two children gave 45 oranges. How many oranges were there?
- Ratio of sides
Calculate the area of a circle with the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
- Cone and the ratio
Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
- The circumference
The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm2. What is its length?
- Ratio of squares
A circle is given in which a square is inscribed. The smaller square is inscribed in a circular arc formed by the side of the square and the arc of the circle. What is the ratio of the areas of the large and small squares?
- If the 3
If the 6th term of a GP is 4 and the 10th is 4/81, find common ratio r.
- What is 10
What is the 5th term, if the 8th term is 80 and common ratio r =1/2?
- Squares ratio
The first square has a side length of a = 6 cm. The second square has a circumference of 6 dm. Calculate the proportions of the perimeters and the proportions of the contents of these squares? (Write the ratio in the basic form). (Perimeter = 4 * a, conte
- Rectangular garden
The sides of the rectangular garden are in ratio 1: 2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden.
- The perimeter 3
The perimeter of a rectangle is 35 cm. The ratio of the length to its width is 3:2. Calculate the dimensions of the rectangle
- Cuboid edges in ratio
Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm3.
- Collection of stamps
Jano, Rado, and Fero have created a collection of stamps in a ratio of 5: 6: 9. Two of them had 429 stamps together. How many stamps did their shared collection have?
- Surface of cubes
Peter molded a cuboid 2 cm, 4cm, 9cm of plasticine. Then the plasticine split into two parts in a ratio 1:8. From each piece made a cube. In what ratio are the surfaces of these cubes?
- Rhombus and diagonals
The a rhombus area is 150 cm2 and the ratio of the diagonals is 3:4. Calculate the length of its height.
- ISO triangle
Calculate the area of an isosceles triangle KLM if its sides' length is in the ratio k:l:m = 4:4:3 and has perimeter 377 mm.
- Right triangle
Legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
- Divide money 2
Ben and Dan had the same amount of money at the start. When Ben gave 300 to Dan, the ratio of Ben 's money to Dan's money became 2:3. How much money did each have at first?
The money - coins are minted from the hardest bronze, which contains copper and tin in a ratio of 41: 9. How much copper and tin are in 2kg of bronze money?
Check out our ratio calculator. Ratio - math word problems. Expression of a variable from the formula - math word problems. | s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610704828358.86/warc/CC-MAIN-20210127152334-20210127182334-00679.warc.gz | CC-MAIN-2021-04 | 3,444 | 40 |
http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-amcv17i4p455bwm | math | This paper provides an optimal approximation of the fundamental linear fractional order transfer function using a distribution of the relaxation time function. Simple methods, useful in systems and control theories, which can be used to approximate the irrational transfer function of a class of fractional systems fora given frequency band by a rational function are presented. The optimal parameters of the approximated model are obtained by minimizing simultaneously the gain and the phase error between the irrational transfer function and its rational approximation. A simple analog circuit, which can serve as a fundamental analog fractional system is obtained. Illustrative examples are presented to show the quality and usefulness of the approximation method. | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817780.88/warc/CC-MAIN-20240421132819-20240421162819-00238.warc.gz | CC-MAIN-2024-18 | 767 | 1 |
https://finance.icourban.com/articles/cbse-class-10-maths-chapter-4-important-questions-with-solutions-1669196308-1 | math | CBSE Class 10 Maths Chapter 4 Important Questions: In this article, we will go through the important questions from Chapter 4 Quadratic Equations of CBSE Class 10. For the candidates of CBSE Class 10 board examinations, this will serve as the checklist of various questions with varying difficulty that could be asked from this chapter.
Chapter 4 Quadratic Equations is a part of the second unit Algebra which has a total weightage of 20 marks.
The prescribed topics to be covered under Quadratic equations are: Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula. Relationship between discriminant and nature of roots.
Students can view the detailed CBSE Class 10 Maths Syllabus 2022-2023 by clicking on the link below:
MULTIPLE CHOICE QUESTIONS ( 1 MARK)
SHORT ANSWER TYPE QUESTIONS (2 MARKS)
SHORT ANSWER TYPE QUESTIONS (3 MARKS)
LONG ANSWER TYPE QUESTIONS (4 MARKS)
To view the solutions to these important question from CBSE Class 10 Maths Chapter 4, click on the link below:
|Solutions to CBSE Class 10 Maths Chapter 4 Quadratic Equations Important Questions|
There are a total of fifteen chapters in CBSE Class 10 Mathematics syllabus which are divided under seven different units. Quadratic Equations is a part of the second unit Algebra. Unit 2 also deals with Polynomials, Linear Equations in two variables and Arithmetic Progressions.
Practise makes a man perfect. This saying also applies to students - specially Maths students! Apart from enabling students to master their mistakes, practising also helps them speed up their process of solving each question and even helps them memorise important formulae.
These practise papers have been specially designed by subject experts for the students of CBSE class 10 in academic year 2022-23. Give these a try to see your preparation level and strengthen your chances of scoring higher.
All the best! | s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710916.40/warc/CC-MAIN-20221202183117-20221202213117-00873.warc.gz | CC-MAIN-2022-49 | 1,972 | 14 |
http://ismaelrperiod4.blogspot.com/2013/10/sv4-unit-i-concept-2-graphing.html | math | Sunday, October 27, 2013
SV#4: Unit I Concept 2: Graphing Logarithmic Functions & Indentifying Key Parts
In order to understand how to solve the problem, the viewer must pay special attention to the sentence: "The LOG's Xylophone was Happy and Rich." This means that the graph of a logarithmic function has an asymptote of x=h, and that there are no restrictions on its range. Another thing that the viewer should take note of is the use of the Change of Base Formula throughout the problem. This is crucial because it enables one to correctly input logarithmic functions into a graphing calculator. | s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590169.5/warc/CC-MAIN-20180718115544-20180718135544-00342.warc.gz | CC-MAIN-2018-30 | 599 | 3 |
https://getacho.com/8-3-study-guide-and-intervention-special-right-triangles/ | math | What is a Special Right Triangle?
A special right triangle is a right triangle with side lengths that are in a particular ratio. There are three types of special right triangles: 30°-60°-90° triangles, 45°-45°-90° triangles, and the 3-4-5 right triangle. These triangles have special features that make them easier to work with in solving problems. For example, the side lengths of a 45°-45°-90° triangle can be found by multiplying the length of the shorter leg by the square root of two.
Using the Pythagorean Theorem to Solve Problems
The Pythagorean Theorem is a mathematical rule that states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side. This theorem is used for solving problems involving special right triangles. By plugging in the length of the two shorter sides of the triangle, the length of the longest side can be determined. This can be done for all types of special right triangles.
Solving for Unknown Side Lengths
One of the most common uses of special right triangles is to solve for unknown side lengths. By using the properties of special right triangles, you can determine the length of the missing side. For instance, if you know the length of the shorter leg of a 30°-60°-90° triangle, you can use the special ratio to calculate the lengths of the other two sides. You can also use the Pythagorean Theorem to determine the length of the longest side.
Using Special Right Triangles to Find Angles
Special right triangles can also be used to find angles. By plugging in the known side lengths of a triangle into the Pythagorean Theorem, you can find the angle measures of the triangle. For instance, if you know the length of the two shorter sides of a 45°-45°-90° triangle, you can use the Pythagorean Theorem to determine the length of the longest side. From there, you can find the angles of the triangle by dividing the length of the longest side by the length of the shorter sides.
Special right triangles can be used to solve many types of problems. By understanding the properties of these triangles, you can find side lengths and angles with ease. Using the Pythagorean Theorem and the special ratios of the sides, you can find unknown side lengths and angles in special right triangles. Special right triangles are an invaluable tool in mathematics. | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949533.16/warc/CC-MAIN-20230331020535-20230331050535-00216.warc.gz | CC-MAIN-2023-14 | 2,364 | 9 |
http://skechersconnect.com/45177.php | math | Geometry Book Answers Pdf
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https://hunterriverpei.com/4-10-as-a-percent/ | math | It"s very common once learning around fractions to want to know how convert a fraction like 4/10 right into a percentage. In this step-by-step guide, we"ll display you how to turn any fraction into a percent really easily. Let"s take it a look!
Want to quickly learn or show students exactly how to transform 4/10 to a percentage? play this really quick and also fun video now!
Before we gain started in the fraction to portion conversion, let"s walk over some really quick portion basics. Remember the a numerator is the number over the fraction line, and the denominator is the number below the portion line. We"ll use this later in the tutorial.
You are watching: 4/10 as a percent
When we are using percentages, what we room really speak is that the percent is a portion of 100. "Percent" way per hundred, and also so 50% is the very same as saying 50/100 or 5/10 in portion form.
So, because our denominator in 4/10 is 10, we could adjust the portion to do the denominator 100. To execute that, we divide 100 by the denominator:
100 ÷ 10 = 10
Once we have that, we deserve to multiple both the numerator and denominator through this multiple:
4 x 10/10 x 10=40/100
Now we deserve to see that our fraction is 40/100, which way that 4/10 together a percent is 40%.
We can likewise work this out in a simpler method by first converting the fraction 4/10 to a decimal. To carry out that, we just divide the numerator by the denominator:
4/10 = 0.4
Once we have the price to that division, we have the right to multiply the prize by 100 to do it a percentage:
0.4 x 100 = 40%
And over there you have actually it! Two various ways to convert 4/10 to a percentage. Both are pretty straightforward and also easy come do, however I personally favor the convert to decimal method as the takes much less steps.
I"ve viewed a the majority of students get perplexed whenever a concern comes up about converting a portion to a percentage, yet if you follow the measures laid out here it have to be simple. The said, you might still need a calculator because that more complicated fractions (and friend can constantly use ours calculator in the type below).
If you desire to practice, grab you yourself a pen, a pad, and also a calculator and try to convert a few fractions to a percentage yourself.
Hopefully this tutorial has actually helped you come understand exactly how to transform a portion to a percentage. You can now go forth and convert fractions to percentages as much as your little heart desires!
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See more: What Is 08 As A Fraction
What is 4/10 as a percentage?. hunterriverpei.com. Retrieved from https://hunterriverpei.com/calculator/fraction-as-percentage/what-is-4-10-as-a-percentage/. | s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662562106.58/warc/CC-MAIN-20220523224456-20220524014456-00512.warc.gz | CC-MAIN-2022-21 | 3,314 | 24 |
https://psychology.164news.com/gender-and-geographical-disparity-in-editorial-boards-of-journals-in-psychology-and-neuroscience-nature-com/ | math | Editorial board analysis
Our first analysis considered gender representation in psychology. The sample included a total of 2,864 editors. Overall, there were significantly more male (n = 1,706) than female (n = 1,157) editors (Table 1 and Fig. 1a). This was primarily driven by the larger categories, namely category 2 (associate and section editors) and category 3 (advisory and editorial board members). There was no significant difference in gender representation among category 1, the smallest and most senior category (editors-in-chief and their deputies), although men (n = 49) outnumbered women (n = 37) in that category too. Data from 2017, 2 years before the data presented here, indicated that approximately 45% of full professors, 53% of associate professors and 65% of assistant professors in psychology in the USA were female33. The proportion of female editors (all categories) was significantly lower than expected based on the proportion of female faculty (χ2(1) = 10.39, P = 0.001). The proportion of female editors-in-chief was not statistically different from the proportion of female full professors (χ2(1) = 0.16, P = 0.688).
Table 1 Overall proportion of editors who were male and female in the top 50 journals in the field of psychology, and in each of the three subcategories: (1) editors-in-chief and their deputies, (2) associate and section editors and (3) advisory and editorial boards
Fig. 1: Overall proportion of male and female editors in the top 50 journals in psychology and neuroscience.
a,b, The overall proportion of editors who were male and female in the top 50 journals in psychology (a) and neuroscience (b), and in each of the three subcategories: (1) editors-in-chief and their deputies, (2) associate and section editors and (3) advisory and editorial boards.
The above analysis did not consider variability in the proportion of male and female editors at the individual journals. To quantify this, we calculated what percentage of journals had proportions of male and female editors in ten-point percentage increments. For over three-quarters of psychology journals (76%), more than half of editors were male, while for only 20% of journals were the majority of editors female (Fig. 2a). The interested reader can refer to Supplementary Data 1 for the specific journals in each position, denoted by number. Over half of the journals (54%) had more than 60% ……. | s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233508959.20/warc/CC-MAIN-20230925083430-20230925113430-00169.warc.gz | CC-MAIN-2023-40 | 2,411 | 6 |
https://brainly.in/question/96759 | math | mass attached to the spring,
Now if spring is cut into half its spring-constant, k, doubles.
Hence time period, T, is decresed by
The above explanation is valid only if spring is ideal, i.e. massless.
A more general formula is
mass of spring.
I believe you can find the modified time-period. | s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560279169.4/warc/CC-MAIN-20170116095119-00464-ip-10-171-10-70.ec2.internal.warc.gz | CC-MAIN-2017-04 | 291 | 7 |
https://www.jstage.jst.go.jp/article/kikaic1979/58/549/58_549_1366/_article/-char/ja/ | math | 1992 年 58 巻 549 号 p. 1366-1370
This paper deals with a mathematical model of the mechanics of rigid bodies connected by rotary joints. The method is based on the Lagrangian formulation. The kinetic energy is written in terms of the angular velocities. The expression for the kinetic energy has a homogeneous quadratic form in the angular velocity, the coefficient matrix of which is given by the products of triangular matrices. The equations of motion are derived from the Lagrange's equations for the quasi-coordinates, the angular velocities of the bodies. The equations of motion become recursive forms due to the structure of the expression of the kinetic energy of the system. The algorithm of the inverse dynamics, which follows from the equations of motion, becomes also a recursive form like the algorithm based on the Newton-Euler equations of motion. Since the algorithm is based on the Lagrangian formulation, it can be extended to more complex systems that include flexible bodies, the constraints of which limit the motion of the systems, and so on. | s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988955.89/warc/CC-MAIN-20210509032519-20210509062519-00028.warc.gz | CC-MAIN-2021-21 | 1,069 | 2 |
https://www.usingenglish.com/forum/threads/94758-quot-appropriate-quot-quot-right-quot-or-quot-suitable-quot | math | Student or Learner
Please tell me if "appropriate" is OK in the following:
Write the answers in the appropriate boxes, using the necessary punctuation marks.
(there is a table with questions written under the heading QUESTIONS on the left and empty boxes coming under ANSWERS on the right)
The same for:
Put a tick in the appropriate box. (or "right" box?)
I need to know whether "appropriate and "right" are synonymous in these contexts.
Appropriate means: "Suitable for a particular person or place or condition etc" The word 'appropriate' has the meaning 'right and suitable'.
By the expression 'Tick the appropriate box' you mean 'the corresponding box to your question'. It is close to 'right box', but in these cases we use 'appropriate' and it gives the best understanding to the person(s) communicated; as mentioned above, it means: the right and suitable box.
We use 'right' in the same way in other situations: e.g. He is the right man; ask him.
I'm hopeful that if you go through some examples in the good dictionaries you'll get my point much clearly.
Last edited by abdmlkbd; 22-Apr-2009 at 15:34. | s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719463.40/warc/CC-MAIN-20161020183839-00070-ip-10-171-6-4.ec2.internal.warc.gz | CC-MAIN-2016-44 | 1,110 | 12 |
https://www.test-guide.com/ap-calculus-ab-practice-exam.html | math | Full-Length AP Calculus AB Test
Take our AP calculus AB practice exam. You can take our full-length exam (simulated like the actual exam) or just answer smaller batches of questions (if you are in a hurry).
What is the AP Calc Exam?
The AP calculus exam is an exam that you take to earn college credit. You will have the opportunity to take the AP calculus exam after completing your AP calculus class.
Most students take an AP calculus class in their junior or senior year of high school. The exam is completely optional, but it is highly recommended that you take the exam.
You will need to score a 3 or better on the exam to earn your college credit.
AP Calculus AB Description
There are actually two AP calculus exams, so before you go any further, make sure you are going to be taking the AP calc AB exam and not the BC exam.
There are eight units covered on the AP calculus AB exam and in your AP calculus class. Your teacher may choose to group them together differently or teach them in a different order, but you should be able to familiarize yourself with these topics:
- Unit One: Limits and Continuity: Examine various graphs of functions and forms of the conceptual basis of calculus limits (10-12%)
- Unit Two: Differentiation: Definition and Fundamental Properties: Explore how limits change over small intervals and understand how derivatives are a tool to measure the rate of change from one variable to another (10-12%)
- Unit Three: Differentiation: Composite, Implicit, and Inverse Functions: Understand the differentiation of implicit and inverse functions and apply the chain rule to find derivates of composite functions (9-13%)
- Unit Four: Contextual Applications of Differentiation: Apply lessons from previous units to real-life scenarios and approximate values and limits of certain functions (10-15%)
- Unit Five: Analytical Applications of Differentiation: Discover abstract structures and formal conclusions of differentiation and come to analytic conclusions by reasoning definitions and theorems (15-18%)
- Unit Six: Integration and Accumulation of Change: Learn about the relationship between differentiation and integration and understand integration as the total of change over an interval instead of instant change at a point (17-20%)
- Unit Seven: Differential Equations: Explore slope fields to discover the infinite general solutions to a differential equation (6-12%)
- Unit Eight: Applications of Integration: Continue work with integrals to uncover a function’s average value, model particle motion, and calculate net change (10-15%)
As you can see, you will need to be able to read graphs and formulate answers that are well-supported by what you analyze from graphs and understand multiple types of graphs with various equations on them.
AP Calculus AB Exam Overview
The AP calc AB exam is split into 4 sections. The table below breaks down how the exam is split up:
|Section 1, Part A
|Section 1, Part B
|Section 2, Part A
|Section 2, Part B
How to Use an AP Calculus Practice Exam
We suggest the following when using our AP calculus AB exam:
- Find a Quiet Room & Set Aside Some Time: Make sure you are in a quiet environment and have set aside ample time to take the practice exam. You will need to focus when taking the exam.
- Take the Exam Like You Would on Test Day: Do not use a calculator on sections you are not allowed. Do not cheat and check your notes. Take the exam like you would on the test day to see how you would score.
- Utilize Answer Explanations: Use our detailed answer explanations to learn how to solve the problems and learn important concepts.
- Answer Our Practice Sets: The practice sets were designed to help you study in a stress free environment. There is no timer, and you can see the answers after each question.
How Do I Study for the AP Calculus AB Exam?
Here are some tips you can use when studying for the AP calculus AB exam:
- Pay Attention in Class: This is an obvious one, but so many students skip this part. If you pay attention in class, you will pick up on so many little details that will help you.
- Take a Practice Exam: Take our practice exam above. Use it to gauge where you stand.
- Pinpoint Struggle Areas: Find areas that you struggle with. A great way to do this is by taking our practice exam above and noting which questions give you the most trouble.
- Seek Help with Struggle Areas: Once you have figured out which areas you struggle with the most, you can seek out help. Your teacher is a great place to start. If this is not an option, a classmate is another great resource.
Frequently Asked Questions
Is the AP calc AB exam easy?
The AP calculus AB exam is not something that should be taken lightly. Around 61% of test takers pass the exam (scoring a three or higher), but you do need to be properly prepared before the exam to increase your chances of passing.
What percent is 5 on the AP calc AB?
To score a 5 on the AP calc AB exam, you will need to answer 70% to 75% of the questions correctly.
Is your exam realistic?
Our simulated practice exam was designed to mimic the actual AP calculus AB exam. We have the same number of questions, time limits, question types, and topics tested. | s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707948234904.99/warc/CC-MAIN-20240305092259-20240305122259-00079.warc.gz | CC-MAIN-2024-10 | 5,201 | 43 |
https://books.google.es/books?id=ZSYLAAAAMAAJ&pg=PA302&focus=viewport&vq=greatest+elongation&dq=editions:ISBN0554617749&lr=&hl=es&output=html_text | math | « AnteriorContinuar »
globe to the latitude thereof, 25 deg. where fix the quadrant of altitude, and place it so as to make an angle with the meridian of 43 deg. in the horizon, and observe where the edge of the quadrant interseets the parallel of 30 deg. south latitude, for that is the place of the port B. Then count the number of degrees on the edge of the quadrant intersected between the two ports, and there will be found 73 deg. which, multiplied by 60, gives 4380 miles for the distance sailed. As the two ports are now known, let each be brought to the meridian, and observe the difference of longitude in the equator respectively, which will be found 50 deg.
N. B. Had this problem been solved by loxodromics, or sailing on a rhumb, the difference of longitude would then have been 52 deg. 30 min. between the two ports,
PROBLEM XLV. Given the difference of latitude and distance run, to find the difference of longitude and angle of the course.
Example. Admit a ship sails from a port A, in latitude 50 deg. to another port B, in latitude 17 deg. 30 min. and her distance run be 2220 miles. Rectify the globe to the latitude of the place A, then the distance run, reduced to degrees, will make 37 deg. which are to be reckoned from the end of the quadrant lying over the port A, under the meridian ; then is the quadrant to be moved, till the 37 degrees coincide with the parallel of 17 deg. 30 min. north
latitude ; then will the angle of the course appear in the arch of the horizon, intercepted between the quadrant and the meridian, which will be 32 deg. 40 min.; and by making a mark on the globe for the port B, and bringing the same to the meridian, you will observe what number of degrees pass under the meridian, which will be twenty, the difference of longitude required.
PROBLEM XLVI. Given the difference of longitude and course, to find the difference of latitude and distance sailed.
Example. Suppose a ship sails from A, in the latitude 51 deg. on a course making an angle with the meridian of 40 deg. till the difference of longitude be found just 20 degrees ; then rectifying the globe to the latitude of the port A, place the quadrant of altitude so as to make an angle of 40 deg. with the meridian; then observe at what point it intersects the meridian passing through the given longitude of the port B, and there make a mark to represent the said port; then the number of degrees intercepted between that and the port A, will be 28, which will give 1680 miles for the distance run: and the said mark for the port B, being brought to the meridian, will have its latitude there shewn to be 27 deg. 40 min.
Given the course and distance sailed, to find the difference of longitude, and difference of latitude.
Example. Suppose a ship sails 1800 miles from a port A, 51 deg. 15 min. south-west, on an angle of 45 deg. to another port B.
Having rectified the globe to the port A, fix the quadrant of altitude over it in the zenith, and place it to the south-west point in the horizon ; then upon the edge of the quadrant under 30 deg. (equal to 1800 miles from the port A) is the port B; which bring to the meridian, and you will there see the latitude; and, at the same time, its longitude on the equator, in the point cut by the meridian.
In all these cases, the ship is supposed to be kept upon the arch of a great circle, which is not difficult to be done, very nearly, by means of the globe, by frequently observing the latitude, measuring the distance sailed, and (when you can) finding the difference of longitude ; for one of these being given, the place and course of the ship is known at the same time; and therefore the preceding course may be altered, and rectified without any trouble, through the whole voyage, as often as such observations can be obtained, or it is found necessary. Now if any
of these data are but of the quantity of four or five degrees, it will suffice for correcting the ship’s course by the globe, and carrying her directly to the intended fort, according to the following problem.
PROBLEM XLVIII. To steer a ship upon the arch of a great circle by the given difference of latitude, or difference of longitude, or distance sailed in a given time.
Admit a ship sails from a port A, to a very distant port Z, whose latitude and longitude are given, as well as its geographical bearing from A; then,
First, having rectified the globe to the port A, lay the quadrant of altitude over the port Z, and draw thereby the arch of the great circle through A and Z; this will design the intended path or track of the ship.
Secondly, having kept the ship upon the first given course for some time, suppose by an observation you find the latitude of the present place of the ship, this added to, or subducted from the latitude of the port A, will give the present latitude in the meridian ; to which bring the path of the ship, and the part therein, which lies under the new latitude, is the true place B of the ship in the great arch. To the latitude of B rectify the globe, and lay the quadrant over Z, and it will shew in the horizon the new course to be steered.
Thirdly, suppose the ship to be steered upon this course, till her distance run be found 300 miles, or 5 degrees ; then, the globe being rectified to the place B in the zenith, laying the quadrant from thence over the great arch, make a mark at the 5th degree. from B, and that will be the present place of the ship, which call C; which being brought to the meridian,
its latitude and longitude will be known. Then rec. tify the globe to the place C, and laying the quadrant from thence to Z, the new course to be steered will appear in the horizon.
Fourthly, having steered some time upon course, suppose, by some means or other, you come to know the difference of longitude of the present place of the ship, and of any of the preceding places, C, B, A ; as B, for instance; then bring B to the meridian, and turn the globe about, till so many degrees of the equator pass under the meridian as are equal to the discovered difference of longitude; then the point of the great arch cut by the meridian is the present place D of the ship, to which the new course is to be found as before,
And thus, by repeating these observations at proper
will find future places, E,F,G, &c. in the great arch; and by rectifying the course at each, your ship will be conducted on the great circle, or the nearest way from the port A to Z, by the use of the globe only | s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107878662.15/warc/CC-MAIN-20201021235030-20201022025030-00715.warc.gz | CC-MAIN-2020-45 | 6,472 | 22 |
https://pendulumedu.com/qotd/odd-one-out-wheat-maize-groundnuts-cotton | math | Three of the following words are alike in a certain way and one is different. Pick the odd word out?
Correct Answer : a ) WheatExplanation :
According to the question
The common logic applied here is
Maize, Ground Nut, and Cotton are the Kharif crops
While Wheat is a Rabi crop
Hence, (a) is the correct answer. | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100172.28/warc/CC-MAIN-20231130062948-20231130092948-00727.warc.gz | CC-MAIN-2023-50 | 311 | 7 |
https://swmath.org/software/11038 | math | Eulerian tour algorithms for data visualization and the PairViz package. 𝙿𝚊𝚒𝚛𝚅𝚒𝚣 is an R package that produces orderings of statistical objects for visualization purposes. We abstract the ordering problem to one of constructing edge-traversals of (possibly weighted) graphs. 𝙿𝚊𝚒𝚛𝚅𝚒𝚣 implements various edge traversal algorithms which are based on Eulerian tours and Hamiltonian decompositions. We describe these algorithms, their 𝙿𝚊𝚒𝚛𝚅𝚒𝚣 implementation and discuss their properties and performance. We illustrate their application to two visualization problems, that of assessing rater agreement, and model comparison in regression.
Keywords for this software
References in zbMATH (referenced in 3 articles )
Showing results 1 to 3 of 3.
- Hurley, C. B.; Oldford, R. W.: Graphs as navigational infrastructure for high dimensional data spaces (2011)
- Hurley, C. B.; Oldford, R. W.: Eulerian tour algorithms for data visualization and the (\mathttPairViz) package (2011)
- Wilhelm, Adalbert F. X. (ed.); Linsen, Lars (ed.): Special issue: Data viz VI (2011) | s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572077.62/warc/CC-MAIN-20220814204141-20220814234141-00234.warc.gz | CC-MAIN-2022-33 | 1,119 | 7 |
http://corporate.morningstar.com/us/asp/subject.aspx?xmlfile=2979.xml | math | |Executive Director of Research and Development|
Wolfram Research, Inc.
|Founded by physicist Stephen Wolfram in 1987, Wolfram Research creates advanced technologies such as Mathematica computational software and the Wolfram|Alpha online resource. |
| Think big|
A project as ambitious as Wolfram|Alpha needs data as broad as the world’s imagination. This groundbreaking online resource aims to answer questions not by surfacing information from the Internet, but by building its own encyclopedic database that makes it possible for anyone to compute virtually anything. Its creator, Wolfram Research, Inc.—a pioneer accustomed to developing what it needs in-house—found the integrity and depth of financial data it was looking for in Morningstar® Data for stocks.
Search for data experts
Wolfram Research knows data. “We have 20 years of expertise in financial computation and engineering,” says Peter Overmann, who led the integration of financial data into Wolfram|Alpha.
|While collecting and curating other data types, Overmann decided to keep the project on a fast track by seeking out financial data providers. That’s when he contacted Morningstar. |
Source precise information
Wolfram Research considered every leading data provider, performing extensive quality checks and comparisons on their data samples. “Financial data is fundamentally difficult to deal with compared to other areas,” describes Overmann. “Following a stock over 30 years is a challenge, and Morningstar has done a good job processing data and delivering it in a useful form.”
Compute millions of queries
The depth of Morningstar’s data helps Wolfram|Alpha anticipate the millions of financial inquiries it receives.
|“Wolfram|Alpha knows about 600-700 properties from each company’s balance sheet—sourced from Morningstar,” says Overmann. “The data includes everything we and our users expect to have.” Overmann envisions incorporating additional data from Morningstar. “There are many opportunities for our companies to expand together.”| | s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917120206.98/warc/CC-MAIN-20170423031200-00464-ip-10-145-167-34.ec2.internal.warc.gz | CC-MAIN-2017-17 | 2,059 | 13 |
https://proremodeler.com/foolproof-markup-math | math | Most remodeling contractors quickly learn to estimate project costs accurately, but they often have trouble when it comes to setting a selling price for their work. They know they need to charge more than the actual cost to build the project, but they don’t have a good handle on what their actual overhead costs are. Many simply add 10% or 15% and hope for the best. Others may have heard that a remodeling company should earn at least 30% to cover overhead and profit. It seems high, but they want to be successful, so they mark up the job by multiplying estimated direct costs by 1.3 .
Multiplying direct costs by 1.3 amounts to a 30% markup, but it does not yield a 30% margin. If this is the way you’re doing it, you’re losing money on every job.
Wait, what happened? Why does that 30% markup ($3,000) amount to just a 23.1% margin? It’s because markup is a percentage of costs (3,000 ÷ 10,000 = 30.0%), whereas margin is a percentage of the selling price (3,000 ÷ 13,000 = 23.1%). To achieve a 30% margin, you need a markup of 42.8% .
Margin is a percentage of the selling price. To achieve a 30% margin, you have to add 42.8% to estimated costs.
Whether you need a 30% margin to cover actual overhead and profit is a topic for another time (you may need more). But assuming you do and that estimated costs for this hypothetical job are accurate, if you do things #TheRightWay and sell the job for $14,280, you earn $3,567 to cover overhead, plus $713 in profit.
But if you sell the job for $13,000, you lose big. Your $3,000 markup leaves you $567 in the hole—money that comes out of your pocket to cover overhead expenses—plus, you don’t get the $713 in profit. On bigger jobs, the lost dollars add up fast .
Confusing a 30% markup with a 30% margin leads to a selling price that fails to cover overhead expenses and wipes out profit.
Divide and Conquer
You can also find the proper selling price by dividing instead of multiplying. Subtract your target margin from one, then divide estimated costs by the result. For example, to find the selling price at a 30% margin, divide by 0.7 (1.00 – 0.3) .
Another way to find the selling price is to subtract the decimal value of your target margin from one, then divide that number into estimated costs.
Both methods work equally well, and since most contractors have a smartphone in their pocket, doing the actual math is pretty simple either way. To make things even easier, whether you multiply or divide you can look up the correct markup factor on a chart .
Selling at the right price is a good start, but you have to produce the job on budget to earn your margin. If you’re still losing money, the most common culprits are failing to account for all overhead costs or undercharging for labor, two topics we’ll address in a future article.
To use the Markup Multiplier chart, look up your target margin percentage (overhead plus profit) in the left-hand column. Then use the corresponding number in the right column to multiply estimated costs. For example, to find the selling price at a 30% margin, you would multiply estimated costs by 1.43.
To use the Markup Divisor chart, divide estimated costs by the number in the right-hand column. For example, for a 30% margin, divide costs by 0.70. | s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334591.19/warc/CC-MAIN-20220925162915-20220925192915-00456.warc.gz | CC-MAIN-2022-40 | 3,277 | 14 |
https://www.physicsforums.com/threads/when-to-use-cos-or-sin-in-physics-problems.279220/ | math | Hi, I get really confused when to use the cos function or the sin function. for example, I was looking at this yesterday and thought the other way around of the correct answer. Why did it chose sin function for tension and cos function for the normal force? This problem doesn't explain why it chose the trigometric function for each question. Thank You. | s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823236.2/warc/CC-MAIN-20181210013115-20181210034615-00323.warc.gz | CC-MAIN-2018-51 | 354 | 1 |
https://slideplayer.com/slide/1544970/ | math | Presentation on theme: "Introduction to Electrical Machines"— Presentation transcript:
1 Introduction to Electrical Machines Mechanical and Electrical Systems SKAA 2032Introduction to Electrical MachinesDr. Asrul Izam AzmiFaculty of Electrical EngineeringUniversiti Teknologi Malaysia
2 IntroductionOne of energy can be obtained from the other form with the help of converters.Converters that are used to continuously translate electrical input to mechanical output or vice versa are called electric machines.The process of translation is known as electromechanical energy conversion.
3 Conversion from mechanical to electrical: generator Electrical systemMechanical systemElectric Machinee, iT, nMotorEnergy flowGeneratorAn electrical machine is link between an electrical system and a mechanical system.Conversion from mechanical to electrical: generatorConversion from electrical to mechanical: motor
4 DC machines (generators or motors) if the electrical system is DC. Induction machineElectrical MachinesSynchronous machineAC machineMachines are called AC machines (generators or motors) if the electrical system is AC.DC machines (generators or motors) if the electrical system is DC.
5 Coupling magnetic fields Electrical systemMechanical systemCoupling magnetic fieldse, iT, nTwo electromagnetic phenomena in the electric machines:When a conductor moves in a magnetic field, voltage is induced in the conductor.When a current-carrying conductor is placed in a magnetic field, the conductor experiences a mechanical force.
6 AC Rotating Machines DC machine Induction machine Electrical Machines Synchronous machineAC machine
8 Basic Idea A motor uses magnets to create motion. The fundamental law of all magnets:Opposites attractLikes repel.Inside an electric motor, these attracting and repelling forces create rotational motion
9 Basic Idea Magnetic field of a straight conductor The magnetic field lines around a long wire which carries an electric current form concentric circles around the wire.Right hand rule-1
10 Basic Idea Magnetic field of a circular conductor Right hand rule-1 gives the direction of the magnetic field inside and outside a current-carrying loop.
11 Basic Idea Magnetic field of a coil of wire A solenoid is a long coil of wireThe field inside a solenoid can be very uniform and very strong.The field is similar to that of a bar magnet.
12 Basic Idea The use of soft metal increases the magnetic field strength Use right hand rule-2 / eye rule to determine direction of magnetic field in a coil
13 Basic Idea Fleming’s left hand rule for motors Don’t be confused with Fleming’s right hand rule for generator
14 Working Principle Elementary AC motor Consider a rotor → formed by permanent magnet.Consider a stator → formed by coil of conductor to create AC electromagnetic field
15 Working PrincipleAn AC Current flowing through conductors energize the magnets and develop N and S poles.The strength of electromagnets depends on current.First half cycle current flows in one direction.Second half cycle it flows in opposite direction.
16 Working PrincipleConsider the AC voltage at 0 degrees, then, no current will flow, and there is no magnetism.Supplied voltageInitial position of the rotor
17 Working PrincipleAs voltage increases, current starts to flow and electromagnets gain strength and North and South poles appear.The rotor magnet is pushed CW, and the rotor and motor starts to rotate.
18 Working PrincipleWhen voltage decreases, the current decreases also, the electromagnet loses the strength, and when V=0 there is no magnetism.
19 Working PrincipleNow, AC voltage builds up as part of the negative cycle.Then, current flows in opposite direction, and the magnets reverse polarity.Therefore, the CW rotation continues.
25 Practical AC MotorWe can see that the poles rotate around the circumference of the motor.The rotor, no matter how it is positioned at rest, will be locked-in with the magnetic field and will turn in one direction only.(Same rotation as the poles).
26 Induction Motor Most AC motors are induction motors Induction motors are favored due to their ruggedness (no brush), simplicity and cheap.90% of industrial motors are induction motor.Application(1-phase): washing machines, refrigerators, blenders, juice mixers, stereo turntables, etc.(2-phase) induction motors are used primarily as servomotors in a control system.(3-phase): pumps, compressors, paper mills, textile mills, etc.
27 Induction MotorThe single-phase induction motor is the most frequently used motor in the worldMost appliances, such as washing machines and refrigerators, use a single-phase induction machineHighly reliable and economical
28 Induction MotorFor industrial applications, the three-phase induction motor is used to drive machinesLarge three-phase induction motor. (Courtesy Siemens).
29 Construction of Induction Motor An induction motor is composed of a rotor, (armature)A stator containing windings connected to a poly-phase energy sourceThe pair of coils correspond to the phases of electrical energy available.Each pair connected in series creating opposite poles:1 pole for North and 1 pole for South.
30 Induction Motor Stator with (a) 2-phase and (b) 3-phase windings. Stator frame showing slots for windings.
31 Induction Motor It has a stator and a rotor like other type of motors. 2 different type of rotors:Squirrel-cage winding,Wound-rotorBoth three-phase and single-phase motors are widely used.Majority of the motors used by industry are squirrel-cage induction motorsA typical motor consists of two parts:An outside stationary stator having coils supplied with AC current to produce a rotating magnetic field,An inside rotor attached to the output shaft that is given a torque by the rotating field.
32 Squirrel-cage Rotor Rotor is from laminated iron core with slots. Metal (Aluminum) bars are molded in the slots instead of a winding.Two rings short circuits the bars.–Most of single phase induction motors have Squirrel-Cage rotor.One or 2 fans are attached to the shaft in the sides of rotor to cool the circuit.
33 Wound Rotor It is usually for large 3 phase induction motors. Rotor has a winding the same as stator and the end of each phase is connected to a slip ring.Three brushes contact the three slip-rings to three connected resistances (3-phase Y) for reduction of starting current and speed control.Compared to squirrel cage rotors, wound rotor motors are expensive and require maintenance of the slip rings and brushes, so it is not so common in industry applicationsWound rotor induction motor was the standard form for variable speed control before the advent of motor
34 SlipsIt is virtually impossible for the rotor of an AC induction motor to turn at the same speed as that of the rotating magnetic field.If the speed of the rotor were the same as that of the stator, no relative motion between them would exist, and there would be no induced EMF in the rotor.Without this induced EMF, there would be no interaction of fields to produce motion. The rotor must, therefore, rotate at some speed less than that of the stator if relative motion is to exist between the two.The percentage difference between the speed of the rotor and the speed of the rotating magnetic field is called slip.The smaller the percentage, the closer the rotor speed is to the rotating magnetic field speed.
35 Slips The synchronous speed (NS) of a motor is given by: where NS : synchronous speed or the rotating magnetic field (rpm)NR : rotor speed (rpm)The synchronous speed (NS) of a motor is given by:whereF : frequency of the rotor current (Hz)NP : number of poles
36 Example ProblemA two pole, 60 Hz AC induction motor has a full load speed of 3554 rpm. What is the percent slip at full load?NP
37 Torque Torque is a rotational force. The torque of an AC induction motor is dependent upon the strength of the interacting rotor and stator fields and the phase relationship between them.whereT : torqueK: constantΦ: stator magnetic flux (Wb)IR : rotor current (A)cos θR : power factor of rotor
38 Voltage and frequency induced in the rotor The voltage and frequency induced in the rotor both depend on the slip. They are given by the following equation.f2 = s fE2 = s Eoc (approx.)f2 = frequency of the voltage and current in the rotor [Hz]f = frequency of the source connected to the stator [Hz]s = slipE2 = voltage induced in the rotor at the slip sEoc = open-circuit voltage induced in the rotor when at rest [V]
39 Active Power in a Induction Motor Efficiency () =PoutputPinput
40 Example 1Calculate the synchronous speed of a 3-phase induction motor having 20 poles when it is connected to a 50 Hz source.120 fpns =120 x 5020=300 r/minSource frequency = 50 Hz, number of poles = 20Synchronous speed ns =
41 Example 2A 0.5 hp, 6-pole induction motor is excited by a 3-phase, 60 Hz source. If the full-load is 1140 r/min, calculate the slip.Source frequency = 60 Hz, number of poles = 6Full load/rotor speed = 1140 r/min120 fpns =120 x 606=1200 r/minSynchronous speed ns =
42 Induction Motor Slip speed: ns – nR = 1200 – 1140 = 60 r/min Slip: s = (ns - nR) / ns= 60/1200= 0.05 or 5%
43 Example 3A single phase, 4 poles induction motor gives the following data:Output 373 W ; 230 VFrequency : 50 Hz., Input current 2.9 APower factor: 0.71 ; Speed: 1410 r.p.m.a) Calculate the efficiency of the motorb) Determine the slip of the motor when deliveringthe rated output | s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573533.49/warc/CC-MAIN-20190919142838-20190919164838-00009.warc.gz | CC-MAIN-2019-39 | 9,451 | 38 |
https://www.newschoolers.com/forum/thread/588286/Are-these-skis-mounted-forward-of-centre- | math | in the last picture it looks like justin dorey's skis (on the left) are mounted further forward than centre. ive heard jon olsson is famous for doing this but i dont understand it. isnt the point of centre mounting so that you get equal swing weight? doesn't it make the ski unstable at speed if you're mounted forward of centre? and doesn't it defeat the shape of the ski, even if its a symmetrical ski? | s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806030.27/warc/CC-MAIN-20171120111550-20171120131550-00769.warc.gz | CC-MAIN-2017-47 | 404 | 1 |
http://www.jiskha.com/members/profile/posts.cgi?name=toni | math | revise thesis statement Thesis sentence: When I order the liquors for my business I believe it is a useless expense of using the online service, because I have to order certain quantities from the liquor commission, but when parties are given for our clientele, I find out that...
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https://advancesindifferenceequations.springeropen.com/articles/10.1186/1687-1847-2014-149 | math | - Open Access
Finite time synchronization problems of delayed complex networks with stochastic perturbations
© Cui et al.; licensee Springer. 2014
- Received: 10 November 2013
- Accepted: 20 March 2014
- Published: 19 May 2014
The paper is concerned with the finite-time synchronization problem of delayed complex networks with stochastic perturbations. Based on the finite-time stability theorem, some sufficient conditions are obtained to ensure finite-time synchronization for the Markovian jump complex networks with time delays and partially unknown transition rates. Finally, the effectiveness of the proposed method is demonstrated by illustrative examples.
- stochastic perturbations
- complex networks
- time delays
Over the past decades, the dynamics analysis of complex networks has witnessed rapidly growing research interests since the pioneering work of Watts and Strogatz . On the one hand, complex networks exist in our daily life with examples including the Internet, the World Wide Web, food webs, electric power grids, cellular and metabolic networks, etc. . And on the other hand, the dynamical behaviors of complex networks have found numerous applications in various fields such as physics, technology, and the life sciences . In fact, synchronization is a basic motion in nature that has been studied for a long time [4–6]. Recently, synchronization of complex networks has received increasing research attention [7–10].
It is important to note that most of the above research results on network synchronization are based on the asymptotic process of an infinite time. That is, network synchronization only occurs when the time tends to infinity. Thus in theory, it is impossible for a network to achieve synchronization in a limited time. However, in actual physical or engineering systems, complex networks usually achieve synchronization state in a limited time, which is finite-time synchronization. On the one hand, in the existing literature on finite time synchronization is not treated often. And on the other hand, finite-time synchronization is a very important bridge for a complex network to succeed in the actual application. In addition, more and more researchers begin to realize the important role of finite-time synchronization, and there are some related research results [11–14].
Time delays often occur in complex networks because of the limited speed of signals traveling through the links and the frequently delayed couplings in biological neural networks, gene regulatory networks, communication networks, and electrical power grids [9, 10]. It has been well known that time delays can cause complex dynamics such as periodic or quasi-periodic motions, Hopf bifurcation, and higher-dimensional chaos. It should be noted that [11, 12] and did not consider the time-delay problem. Although there are some works that have been reported on the finite synchronization on delayed networks systems, they are mainly concerned with the finite-time boundedness . It is checked that the finite-time boundedness is conservative rather than the finite time convergence. In addition, stochastic perturbation becomes one of the main sources for causing instability and poor performance of networks .
In reality, it has been revealed that a neural network sometimes has finite modes, so that switching from one to another at different times may occur [10, 16]. And such a switching (or jumping) can be governed by a Markovian chain [17, 18]. This is partly because a Markovian jump is a suitable mathematical pattern to represent a class of complex networks subject to random abrupt variations in the structures . Moreover, Markovian jump complex networks can be regarded as a special class of stochastic network systems. So a great number of significant results on synchronization of Markovian switching networked systems have been available in the literature [8, 10, 16]. Unfortunately, almost all of the above mentioned works on the synchronization problem of complex networks are built upon the assumption that switching probabilities are known precisely. However, in most cases the transition probabilities of Markovian jump systems or networks are not exactly known [19–21]. Moreover, the estimated values of the mode transition rates may also lead to instability or at least degraded system performance as the partially unknown mode transition rates in system matrices do . Some extended results concerning the uncertain transition probabilities have been reported in [22, 23]. However, such uncertainties require the knowledge of a bound or structure of uncertainties, which is conservative to some extent.
Although the finite-time stability or stabilization problems of the control systems has received much attention [15, 24, 25], finite-time synchronization of the delayed complex networks has attracted comparatively less attention primarily due to the lack of an appropriate control method, and secondly due to the difficulty residing in the mathematical derivation. Besides, how to tackle the coexistence of finite-time synchronization and the other two typical networked-induced constraints, stochastic disturbance and time delays in Markovian jump complex networks with partially unknown transition rates, still remains open.
In this paper, finite-time synchronization problems are studied for the delayed complex networks with stochastic perturbations and incomplete description of their transition rates. The main features of this paper are twofold: (1) Based on the finite-time stability theorem, some sufficient conditions are obtained to ensure finite-time synchronization for the Markovian jump complex networks with time delays and partially unknown transition rates. (2) For finite-time synchronization research, the model in this paper is more practical, because the network model involves time delays and stochastic perturbations.
Notation Throughout this paper, and denote, respectively, the n-dimensional Euclidean space and the set of all real matrices. The superscript ‘T’ denotes the transpose and the notation (respectively, ) where X and Y are symmetric matrices, means that is positive semi-definite (respectively, positive definite); I is the identity matrix with compatible dimension. refers to the Euclidean vector norm; the notation stands for the Kronecker product of matrices A and B. If A is a matrix, denotes the minimum eigenvalue. stands for a block-diagonal matrix E. means the expectation of the random variable x. Matrices, if their dimensions are not explicitly stated, are assumed to be compatible for algebraic operations.
with , and . Here, is the transition rate from to if , while .
where ‘?’ represents the unknown transition rate. For notational clarity, , we denote with , .
where , .
The diffusive couplings mean that the coupled networks (1) are decoupled when the systems are synchronized. So, the coupling terms satisfy , , where denotes zero matrix of n dimension.
where is the particular solution of the system (3).
We need the following assumption to study the finite-time synchronization of the complex network (1).
, , .
where , , , .
Assumption 3
where denotes the set of continuous functions mapping the interval into .
Before ending this section, let us recall the following results, which will be used in the next section.
Lemma 1 (Finite-time stability theorem )
Suppose that function is differentiable (the derivative of at 0 is in fact its right derivative) and , where and . Then will reach zero at finite time and for all .
Lemma 2 (Jesen inequality )
If are positive number and , then .
Lemma 3
If and , then .
In this section, we deal with the synchronization problem in finite time for the Markovian jump complex networks with time delays by designing pinning controller. By constructing new stochastic Lyapunov-Krasovskii functionals and using the finite-time stability theorem, sufficient conditions for the finite-time synchronization control problems are derived.
where , , .
where and , , otherwise, , , . and is the sign function, , the real number β satisfies , .
where and , , otherwise, , , . , .
where , , , , . , is the initial condition satisfying Assumption 2.
According to , for (), it is easy to get .
According to (12), one obtains . For any , there is . Therefore, . By Lemma 1, converges to zero in a finite time, and the finite time is estimated by .
Hence, the error vector () will stochastically converge to zero within . According to the Definition 1, the coupled complex network (1) is finite-time synchronization in the finite time . The proof is hence completed. □
Investigated the finite-time boundedness synchronization problems for complex networks with time delays. Different from this literature, this paper studied the network synchronization to achieve in a finite time. Therefore, the result of this paper shows more advantages.
where , , , otherwise, , . , . We can obtain the following corollary.
where is the diagonal matrix, , , then, under the set of controllers (20), the complex network (1) () is synchronization at finite time , where , , and , . , is the initial condition satisfying Assumption 2 of , .
In this section, the example is given to demonstrate the effectiveness of the proposed approach.
This paper has introduced a general delayed complex networks model with stochastic perturbations and the finite-time synchronization problem of Markovian switching complex networks with stochastic disturbance. Based on the finite-time stability theorem and inequality technique, easily testable conditions have been established to ensure finite-time synchronization for the addressed complex networks. Moreover, conditions that guarantee the finite-time synchronization of the delayed complex networks without switching have also been established. With variable time delays or random delays or mixed delays, finite-time synchronization research of Markovian switching complex network remains open. And it is hard for us to solve such problems, which is our future research.
The work was supported by the Education Commission Scientific Research Innovation Key Project of Shanghai under Grant 13ZZ050, the Science and Technology Commission Innovation Plan Basic Research Key Project of Shanghai under Grant 12JC1400400.
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This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. | s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578532050.7/warc/CC-MAIN-20190421180010-20190421202010-00234.warc.gz | CC-MAIN-2019-18 | 16,154 | 77 |
https://www.amtraktrains.com/threads/bn-amtraks-train-numbering-systems.79899/ | math | I have noticed that during time changes in the year they add a 10 to the symbol, for example: 7 would be 1007 and 8 would be 1008. I know that BN used to use this system in their day to not confuse the Empire Builders with Freight trains 7 & 8. But I have heard crews call it 1007 or 1008, not on daylight savings time and they cycle crews pretty often here so it wasn't habit from the BN days. I noticed that they stopped calling it 1007 or 1008 around 2016. I also have noticed crews calling trains 1004 and 1003 on SWC. Does anyone know why they stopped adding a 10 to the start of the symbol? | s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362969.51/warc/CC-MAIN-20211204094103-20211204124103-00367.warc.gz | CC-MAIN-2021-49 | 596 | 1 |
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https://www.ucasprogress.com/course/2295107/a-level-mathematics | math | A Level Mathematics at Chiltern Hills Academy
Year 1 AS Level
The course consists of three branches of Mathematics that are examined via separate one and a half hour examinations.
C1 Core Mathematics Algebra and functions, coordinate geometry in the (x,y) plane, sequences and series, differentiation, integration
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https://www.helpwithassignment.com/Solution-Library/hypothesis-testing-on-mean-difference-between-men-and-women-running-marathon | math | You are testing a claim that (for a certain year) the mean time required by men to run the Boston Marathon race was less than the mean time required by women to run the race. For that year, two random samples were taken from those who participated in the Boston Marathon: a sample of 20 men and sample of 30 women. For those sampled, the mean time for the men to run the race was 132 minutes and the mean time for the women to run the race was 151 minutes. Previous data has shown that the standard deviation for male race times is 29 minutes, and for females it is 36 minutes. Based on this information, using a level of significance of 0.03, test your hypothesis. Show all steps of the hypothesis process.
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http://www.slideshare.net/Dr-Agarwals-Eye-Hospital/ptosis | math | Introduction• Ultrasound biomicroscopy (UBM) provides high- resolution imaging of the anterior segment in a noninvasive fashion.• In addition to the tissues easily seen using conventional methods (ie, slit lamp), such as the cornea, iris, and sclera, structures including the ciliary body and zonules, hidden from clinical observation, can be imaged and their morphology assessed.• Pathophysiologic changes involving anterior segment architecture can be evaluated qualitatively and quantitatively.
INTRODUCTION• Recent technique to visualize anterior segment with the help of high frequency ultra sound transducer.• UBM (anterior segment ultrasonography) is performed with a 50 Mhz probe.• The resolution of 50 MHz probe is 40 microns and the depth is 4 mm
• UBM is done with the patient in the supine position and the eye is open.• Since the piezoelectric crystal of the transducer is open it should not come in direct contact with the eye to prevent injury to the cornea
• There is a special cup which fits in between the eyelids, keeping them open• The eye cup is filled with saline or sterile methylcellulose.• The crystal of the transducer is placed in saline approximately 2 mm from the eye surface. (This distance of 2 mm prevents injury to the cornea and also helps as a fluid standoff.)• The eye is scanned in each clock hour from the center of the cornea to the ora serrata
Iridociliary cyst The most common clinical presentation of an irido-ciliary cystis a peripheral iris elevation - the typical UBM finding of a thinwalled structure with no internal reflectivity is diagnostic.
• UBM is useful in opaque media• The most important limitation of UBM is depth. UBM cannot visualize structures deeper more that 4 mm from the surface.• The other limitation is that UBM cannot be performed in presence of an open corneal or scleral wound.• It is time consuming
• Tomographic techniques generate slice images of three-dimensional objects.• Optical tomographic techniques are of particular importance in the medical field, because these techniques can provide non- invasive diagnostic images
• Optical coherence tomography is a non- contact, real-time technique that uses low infrared laser energy to image structures.
• Optical coherence tomography imaging is based on measuring the delay of light (typically infrared) reflected from tissue structures.• Because light travels extremely fast, it is not possible to directly measure the delay at a micron resolution. Therefore, OCT employs low-coherence interferometry to compare the delay of tissue reflections against a reference reflection.
• To obtain an OCT image, the instrument scans a light beam laterally, creating a series of axial scans (A-scans), after which it combines these A-scans into a composite image.• Each A-scan contains information on the strength of reflected signal as a function of depth.
• The more commonly used retinal OCT uses 820-nm light, which allows for excellent tissue penetration to the level of the retina.• The anterior segment OCT utilizes 1310- nm light, which has greater absorption resulting in limited penetration.
• This allows for increased intensity of the light as decreased amounts reach the retina.• The light is 20 times more intense, giving a much greater signal-to-noise ratio.• This increased intensity allows for increasing the speed in imaging 20 times, with decreased motion artifact.
• Compared with other imaging modalities, OCT has a higher-depth resolution.• Resolution is determined by the wavelength and the spectral bandwidth of the light source, Shorter wavelengths and wider bandwidths provide better resolution.
Types of oct system There are two principles of image acquisition and data processing in anterior segment OCT:• Time domain and• Fourier domain algorithms.
• In time domain OCT, there is a mechanical moving part that performs the A-scan, Thus, the rate of the scan is limited by the movement of the part.• In Fourier domain OCT, the information in an entire A-scan is acquired by a charge-coupled device (CCD) camera simultaneously. As there is no mechanical movement, the scan time in Fourier domain OCT is faster. This is an important advancement because faster acquisition time means lesser variability in the result due to the patient’s eye movements.
Scans• Anterior Segment Scan (16 x 6 mm)• Single, Dual or Quad lines• 256 A scans / .125 sec acquisition per line• High Resolution Scan (10 x 3 mm)• Single or Quad• 512 A-scans / .25 sec acquisition per line• Pachymetry Scan (10 x 3 mm)• 8 radial lines• 128 A scans / 0.5 sec total acquisition time• All Scans adjustable in orientation and direction
PHAKIC IOL PRE OP PLANNING POST OP OBSERVATIONACD PCIOL DEPTH AND CENTRATIONANGLE TO ANGLE IRIS POSITIONANTERIOR CHAMBER ANGLE CRYSTALLINE LENS VAULTIRIS OR CRYSTALLINE LENS ENDOTHELIAL SAFETY DISTANCEPOSITIONACCOMADITVE ANALYSIS ACCOMADITIVE ANALYSIS
Advantages of AS OCT• Technicians can do the scanning• Imaging flexibility• Faster imaging reduces error• Image through an opaque cornea• Its easy to image accommodative changes• Scans can be taken immediately after surgery
Limitations• Pigmentation on the posterior side of the iris blocks the penetration of infrared light.• Trabecular meshwork/ ciliary body not seen• Manual angle measurement
History• History of present illness• Associated history• Past history• Family history
History• History of present illness :age of onset• Associated history duration• Past history one/both eye• Family history variability
History• History of present illness• Associated history : diplopia• Past history odynophagia• Family history muscle weakness cardiac problem night blindness
History• History of present illness• Associated history• Past history : trauma/ surgery• Family history contact lens lid edema allergy dry eyes
History• History of present illness• Associated history• Past history• Family history
evaluation of ptosis• head posture,Eyebrow position, eyelid masses, inflammation, proptosis• pupillary size, reaction, heterochromia• Best corrected Visual Acuity: In infants, make sure infant can fix and follow light with each eye• Cycloplegic Refraction
In children• Presence or absence of Lid fold• Head tilt• Iliff test
Measurements• Vertical fissure height• Margin reflex distance• LPS action• Lid crease level• Lid level on down gaze
Vertical fissure height• The distance between the upper and lower eyelid in vertical alignment with the center of the pupil in primary gaze, with the patient’s brow relaxed.• Normal – 9-10mm in primary gaze• Should be seen in up gaze, down gaze and primary gaze• Amount of ptosis = difference in palpebral apertures in unilateral ptosis or Difference from normal in bilateral ptosis
Grading of severity of ptosis < or = 2mm : mild ptosis = 3 mm : moderate ptosis = or > 4 mm : severe ptosis
MRD• Margin-to-reflex distance 1 (MRD1) : is the distance from the central pupillary light reflex to the upper eyelid margin with the eye in primary gaze.• A measurement of 4 - 5 mm is considered normal.• If the margin is above the light reflex the MRD 1 is a +ve value.• If the lid margin is below the corneal reflex in cases of very severe ptosis the MRD 1 would be a –ve value.
MRD• Margin-to-reflex distance 2 (MRD2) : is the distance from the central pupillary light reflex to the lower eyelid margin with the eye in primary gaze. . • The MRD1 plus the MRD2 should equal the palpebral fissure measurement
Levetor function• is the distance the eyelid travel from downgaze to upgaze while the frontalis muscle is held inactive at the brow.• The normal levator function is between 13- 17mm
• Lid excursion is a measure of the levator function. The frontalis action is blocked by keeping the thumb tightly over the upper brow and asking the patient to look up from down gaze and measuring the amount of upper lid excursion at the center of the lid.
Grading of levator action< 4mm – poor levator function5-7 mm – fair levator function8-12 mm – good levtor function
Lid crease• Position is the distance from the crease to lid margin• Normal – 8 to 10mm in primary gaze• An absent lid crease is often accompanied by poor levator function.• If a lid crease is present but is higher than normal and if a deeper upper lid sulcus is found on that side, note these as signs of a levator aponeurosis disinsertion.
Phenyl ephrine test• Patients with minimal ptosis (2 mm or less) should have a phenylephrine test performed in the involved eye or eyes• Either 2.5 or 10% phenylephrine is instilled in the affected eye or eyes. Usually two drops are placed and the patient is reexamined 5 minutes later. • The MRD1 is rechecked in the affected and unaffected eyes .• A rise in the MRDl of 1.5 mm or greater is considered a positive test. This indicates that Müllers muscle is viable | s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719045.47/warc/CC-MAIN-20161020183839-00469-ip-10-171-6-4.ec2.internal.warc.gz | CC-MAIN-2016-44 | 9,027 | 36 |
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- free trial of algebra answers | s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439740423.36/warc/CC-MAIN-20200815005453-20200815035453-00116.warc.gz | CC-MAIN-2020-34 | 118,479 | 2,360 |
https://www.coursehero.com/file/23936699/131/ | math | 1. Assume that, at the beginning of 2016, Resnick sold half of its shares of the Vallejo Company stock for $30 per share plus $600 in brokerage selling fees. Prepare the journal entry to record the sale of the Vallejo Company stock. If no adjustments are to be made, then the initial investment placed for half of the Vallejo company shares needs to be calculated. Stock Purchase Price = ( Quantity of Shares ) ∗ ( Price per Share ) + Brokerage Fee Vallejo Stock PurchasePrice = ( 800 Shares ) ∗ 1 2 ∗ ( $ 22.50 1 Share ) + $ 1,200 ∗ 1 / 2 = $ 9,600 Then the gain from the Vallejo stock sale needs to be calculated with a similar formula; the resulting quantity needs to then be compares to the Vallejo stock investment cost in order to yield the gain or loss on sale of the investment. Stock Sale Price = ( Quantityof Shares ) ∗ ( Price per Share ) + Brokerage Fee Vallejo Stock PurchasePrice = ( 800 Shares ) ∗ 1 2 ∗ ( $ 30.00 1 Share ) + $ 600 = $ 12,600 Gain ∨ Loss onSale of Investment = ( Vallejo Stock Sale Price ) −( Vallejo Purchase Price ) Gain ∨ Loss onSale of Investment = $ 12,600 − $ 9,600 = $ 3,000 ( Gain )
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- Summer '09
- Vallejo Stock, net unrealized fair | s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141204453.65/warc/CC-MAIN-20201130004748-20201130034748-00097.warc.gz | CC-MAIN-2020-50 | 1,264 | 5 |
https://talk.collegeconfidential.com/high-school-life/1094596-how-do-you-tell-if-you-like-math.html | math | Every career that I choose and am interested in is heavily involved when it comes to mathematics, same with pretty much every other job that is seen as top tier and prestigious. I myself want to be a shallow banker in NY with a degree in economics (HS Soph at the moment) and economics is pretty much all about mathematics, even though I believe it is classified as a social studies pathway. It would be too much to list every major career that involves math, so I will say the only one that I think does not is LAW, which I am not interested in.
I am not natural at math. I manage to get A's in my advanced math classes, but it takes a lot of hard work for me, while some others breeze through it. I am also severely handicapped when it comes to stuff like mental math. I literally do all of my calculations with a calculator. So, for me, math equates to a lot of hard work and, when it comes to homework, tedious and tiring work as well. I always get frustrated because they put the hardest problems at the end, when you are the most exhausted and do not have the drive to put in tons of time on just one problem.
Lastly, I don't understand how people say they like mathematics. I genuinely do not understand the concept of it. I don't exactly hate math because I know it drives our world, but I physically cannot process how someone would enjoy doing math and do it for fun.
I don't want to limit myself when it comes to my future careers because I know whatever it ends up to be, it will involve math, but at the same time, I don't really look forward to being behind and enduring hardship just because I am not naturally apt when it comes to mathematics.
P.S. A little about myself in case it helps develop my persona a little easier for analysis, so that you guys could advise me on if I would struggle with my career paths:
I am extremely based on logic and rationality, and am detail-oriented. One of my major extracurriculars is debate: even though I dislike politics, I like the intellectual battle of wits that it poses.
When it comes to all of my classes, I make my grades with an insane work ethic; I only have one natural talent that I enjoy and that I excel at, and that is writing.
Rank: top 3%/820. | s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912201329.40/warc/CC-MAIN-20190318132220-20190318154220-00389.warc.gz | CC-MAIN-2019-13 | 2,215 | 8 |
https://testmaxprep.com/lsat/community/1988-breaking-my-brain | math | Christopher on September 14, 2016
I can normally get myself to the point that I see why the answer is what it is, but this one is stumping me. I don't feel as though any answer is more right than the correct answer, but maybe a walk through of the answers would help on this one.
Collin on September 7, 2019
on January 6, 2021 | s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710462.59/warc/CC-MAIN-20221128002256-20221128032256-00792.warc.gz | CC-MAIN-2022-49 | 326 | 4 |
http://flylah.com/lounge/topic1082.html | math | Hello~ I'm going to give few very very difficult IQ questions. Please try to solve it. Have fun~ xD
1)Some months have 30 days, some haves have 31 days. How many months have 28 days?
2)If a doctor give you 3 pills and tells you to take one pill every half hour, how long would it be before all the pills had been taken?
3)I went to bed at 8 o'clock in the evening and wound up my clock and set the alarm to sound at 9 o'clock in the morning. How many hours sleep I would get before being awaken by the alarm?
4)Divide 30 by half and add ten. What do you get?
5)Take 2 apples from 3 apples. What do you have?
6)If you drove bus with 39 people on board from Kuala Lumpur and stopped at Malacca to pick up 4 more people and drop off 5 passengers at Seremban and at Perak drop off 9 passengers and pick up 7 more and eventually arrive at Perak 20 hours later, What's the name of the driver?
7)Fill in the circles from 1 to 12. The final answer for each side will be the same when 3 numbers plus together...
8) How you explain the missing piece? | s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223206147.1/warc/CC-MAIN-20140423032006-00603-ip-10-147-4-33.ec2.internal.warc.gz | CC-MAIN-2014-15 | 1,040 | 9 |
https://www.powerfulintentions.org/members/MeowAuan | math | What are your Powerful Intentions?
I'm beautiful.. worthy and good enough.. My life is FANTASTIC.. I'm one of the happiest girls in da world :-)
What are your Intended Results in joining this community?
hmm.. will tell u later
Do you feel you have been attracted to be here in an inspired and positively enthusiastic way? If the answer is no, you are in the wrong place! :-} If the answer is yes, Welcome Aboard! | s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711069.79/warc/CC-MAIN-20221206024911-20221206054911-00810.warc.gz | CC-MAIN-2022-49 | 412 | 5 |
https://www.easycalculation.com/maths-dictionary/median.html | math | It is the middle value located in a group of ordered numbers. Median splits the higher number with the lowest number. It is also termed as middle value in a collection of numbers.
Learn what is median. Also find the definition and meaning for various math words from this math dictionary. | s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998913.66/warc/CC-MAIN-20190619043625-20190619065625-00180.warc.gz | CC-MAIN-2019-26 | 288 | 2 |
https://mattcoaty.com/tag/equivalent-fractions-math-project/ | math | A few days ago I started gathering resources to supplement a math unit on fractions. The classroom was studying equivalent fractions and I thought there might be a variety of resources available on a few of the blogs that I regularly visit. I generally follow the #mathchat hashtag and find/share ideas that relate to mathematics. While reading a few math blogs on fractions, I came across John Golden’s site that has some amazing ideas that can be used in math classroom. His triangle pattern template sparked my interest.
John provided a template that’s available on his site. I printed out the template and began filling out each triangle with fractions. I ended up with a sheet that looked like this.
So what happened?
First a lot of brainstorming and error checking. Then I decided to have students cut out the triangles and compile equivalent fractions. This is what happened …
Students in fourth grade cut out each triangle and combined them to make equivalent fraction squares. Students worked in collaborative pairs during the project. I observed students using math vocabulary and having constructive conversations with each other to finish the assignment.
Before giving the assignment to a fifth grade class I decided to eliminate two triangles on the sheet above. It was the job of the student to find what triangles were missing and create equivalent fractions to complete the squares. The students were engaged in this activity from start to finish. Some students even wrote the equivalent decimal next to each square.
Overall this project took approximately 45 minutes to complete and it was worth every minute. Students used the terms fraction, improper fraction, mixed number, numerator, denominator, multiplication, division, and pattern throughout the project.
Just as I did, feel free to tweak this project to best meet the needs of your students. | s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224650620.66/warc/CC-MAIN-20230605021141-20230605051141-00535.warc.gz | CC-MAIN-2023-23 | 1,873 | 8 |
https://www.itia.ntua.gr/en/docinfo/1908/ | math | M. Nezi, Multivariate statistical analysis of extreme rainfall and runoff in a sample of 400 river basins over USA from database MOPEX, Diploma thesis, 103 pages, Department of Water Resources and Environmental Engineering – National Technical University of Athens, Athens, October 2018.
The analysis of extreme rainfalls requires a multidimensional approach with a high level of uncertainty. The most commonly used probabilistic distribution for describing the annual maxima of daily rainfall is the Generalized Extreme Value (GEV) distribution. Based on the extreme value theory, the GEV distribution combines the three limiting-type family distribution (a) Gumbel Type I, (b) Fréchet Type II and (c) Weibull Type III. The regime of the annual maximum rainfall variable is affected by myriad of factors. In this diploma thesis we investigate the influence of soil moisture, as it is expressed by the observed accumulative daily rainfall before the extreme rainfall and streamflow scenarios occurred. This analysis is performed in 400 catchments in USA and uses the Generalized Extreme Value distribution fitted by the methods of L-moments, in an attempt to calculate the statistical parameters of the extreme annual rainfall, cumulative rainfall and extreme annual streamflow time series. In this statistical study, the temporal range of previous daily rainfall data is initially estimated in various time steps, starting from five until thirty days before the extreme observation. The analysis focuses on the correlation coefficient between the time series and which of the accumulated rainfall has the strongest statistical impact upon the maximum annual rainfall and streamflow time series. Additionally, by using the L-moment method, the study extracts the generalized extreme distribution for these time series, aiming to better understand the statistical correlation between them and their statistical behavior. We focus on the behavior of the shape parameter of the GEV distribution for detecting which of the previous extreme value distributions fits better to the specific sample of variables. It seems that our samples are better approached by the Fréchet distribution. In the end, we research the effectiveness of the catchment’s hydroclimatic and geographical characteristics upon the statistical parameters of the GEV distribution and correlation coefficient. By creating spatial probabilistic maps, we observe the vulnerability of the statistical parameters in a more spherical way. | s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057039.7/warc/CC-MAIN-20210920131052-20210920161052-00460.warc.gz | CC-MAIN-2021-39 | 2,504 | 2 |
http://saveberlin.com/contingency-table-analysis-diy-project-download/ | math | Sal uses the contingency table chi-square test to see if a couple of different herbs prevent people from getting sick. Which test. There are three ways to compute a P value from a contingency table. Fisher’s test is the best choice as it always gives the exact P value, while the chi-square test only calculates an approximate P value. For example, Table 1 shows the data from the Mediterranean Diet and Health case study.
Sampling Scheme 1: The total number of data values in the contingency table (N) is fixed, but none of the row or column totals are fixed. To produce the plot shown in Example of a Contingency Table, follow the instructions in Example of Contingency Analysis. Example of a Contingency Table. Analysis of risk factors for unfavorable outcomes (odds ratio, relative risk, difference in proportions, absolute and relative reduction in risk, number needed to treat). Quantities Derived from the 2-by-2 Contingency Table.
A contingency table is essentially a display format used to analyse and record the relationship between two or more categorical variables. It is the categorical equivalent of the scatterplot used to analyse the relationship between two continuous variables. Contingency Table Analysis. Methods and Implementation Using R. Pages 17-61. Analysis of Two-way Tables. Response Variable Analysis in Contingency Tables Maria Kateri. Calculate the odds ratio and confidence interval for a 2 X 2 contingency table. To perform a simple correspondence analysis in Minitab, choose Stat Multivariate Simple Correspondence Analysis.
Prophet Statguide: Contingency Table Analysis
Loglinear Models in Contingency Table Analysis. HARRY H. KU AND SOLOMON KULLBACK. 1. Introduction. In recent statistical literature dealing with the. | s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189903.83/warc/CC-MAIN-20170322212949-00041-ip-10-233-31-227.ec2.internal.warc.gz | CC-MAIN-2017-13 | 1,755 | 5 |
https://collegeprep.uworld.com/sat/math-section/ | math | About SAT® Math Section
The SAT® Math section only tests your proficiency in some aspects of mathematics. It focuses on topics that prove math readiness for future college math courses. In this section, you will find multi-step problems with math scenarios in science, social science, work environments, and other real-life situations. To solve these questions, you need math problem-solving skills, conceptual understanding, and general fluency in math. This comprehensive guide will provide everything about the SAT Math syllabus, format, scoring, and question types. We will also discuss the level of math that you may see on the test and share some review tips to help you prepare better.
SAT Math Format and Syllabus
The paper and pencil SAT Math test is divided into two parts, lasting 80 minutes. However, with the SAT going digital, several changes regarding format, question types, and test duration will be seen. Click on the tabs below to understand the structure of the Math section on both paper and pencil as well as the digital SAT.
On the paper and pencil format, the SAT Math Test is divided into two parts – a “calculator” portion and a “no calculator” portion, with a total of 58 questions to be completed in 80 minutes. A 5-minute break is provided between the calculator and no-calculator portions of the math test. Here is a breakdown of the number of questions in each portion and the time allotted to answer them.
What type of math questions are on the SAT?
You will find two types of questions in the SAT Math section – Multiple-Choice Questions (MCQs) and Grid-in Questions for which students have to produce their own responses. Out of 58 questions, 45 are MCQs with four answer choices and 13 are grid-ins that require students to produce their own responses.
What topics are on the SAT Math?
The math section on the paper and pencil test will focus on four key areas highlighted in the table below:
|No. of Questions
|Percentage of Test
|Heart of Algebra
|Problem Solving and Data Analysis
|Passport to Advanced Math
|Additional Topics in Math
Let’s learn about each of these key areas in detail.
Heart of Algebra
These questions focus on systems of linear equations and functions asking you to solve equations which represent a situation plus establish connections between different representations of linear equations.
Problem Solving and Data Analysis
These questions focus on ratios, percentages, and proportional reasoning asking you to analyze graphical and statistical data, evaluate reports, make inferences, and draw conclusions.
Passport to Advanced Math
These questions focus on the level of math that you will study in higher education courses such as science, economics, math, technology, and engineering.
Additional Topics in Math
These questions focus on geometry, trigonometry, radian measure, complex numbers, and applications of surface area and volume.
Study at your pace at an affordable price.
We have everything you need to score a 750+!
SAT Math Review Tips
We know that preparing for the SAT Math test can seem overwhelming, but with the right guidance, you will be ready to take the test with confidence. Here are a few things to keep in mind:
- Learn what is on the Math test. It is important to know the format, question types, and duration of the test. Knowing all the basics is a good way to kickstart your test prep.
- Practice as much as you can. There is no better way of improving your math skills than practicing. Learning how to apply all the formulas and developing a thorough understanding of the topics on the test are essential for a strong performance. You can find a compiled list of all the formulas useful for solving the math questions on our SAT Math formula sheet.
- Time yourself. You must practice time management. When you time yourself, it will also help you determine your concentration and testing endurance level while under pressure. This may help decrease test day anxiety as well as boost your performance.
- Focus on your weak points. By analyzing which areas you are struggling with, you can study efficiently. Improving your weaknesses and locking down your strengths will increase your success on the math SAT section.
Lastly, it is crucial to make an effective study plan to complete your preparation on time. Our SAT Math study guide can help you with this and also give you tips on approaching different questions on the test. You can perfect your math skills by using UWorld’s SAT Math practice test. Our in-depth answer explanations and performance-tracking tools will help you get closer to your targeted score. | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817206.54/warc/CC-MAIN-20240418124808-20240418154808-00261.warc.gz | CC-MAIN-2024-18 | 4,624 | 33 |
https://tapintoteenminds.com/3acts-by-author/danmeyer/ | math | 3 Act Math Tasks For:
3 Acts Real World Math Tasks by Dan Meyer
The following list of 3 Acts Real World Math Problems were created by Dan Meyer.
Consider adding your own 3 Acts Real World Math Tasks to our Math Problem Database to make math classes a little more enjoyable for students worldwide.
Refine Your 3 Act Task Search Criteria | s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232255837.21/warc/CC-MAIN-20190520081942-20190520103942-00227.warc.gz | CC-MAIN-2019-22 | 335 | 5 |
https://research.caluniv.ac.in/publication/analytical-study-of-d-dimensional-fractional-kleingordon-equation | math | D-dimensional fractional Klein–Gordon equation with fractional vector and scalar potential has been studied. Both fractional potentials are taken as attractive Coulomb-type with different multiplicative parameters, namely v and s. Jumarie-type definitions for fractional calculus have been used. We have succeeded in achieving Whittaker-type classical differential equation in fractional mode for the required eigenfunction. Fractional Whittaker equation has been manipulated using the behaviour of the eigenfunction at asymptotic distance and origin. This manipulation delivers fractional-type confluent hypergeometric equation to solve. Power series method has been employed to do the task. All the obtained results agree with the existing results in literature when fractional parameter α is unity. Finally, we furnish numerical results with a few eigenfunction graphs for different spatial dimensions and fractional parameters. © 2020, Indian Academy of Sciences. | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100626.1/warc/CC-MAIN-20231206230347-20231207020347-00667.warc.gz | CC-MAIN-2023-50 | 971 | 1 |
https://www.nist.gov/publications/model-based-uncertainty-analysis-inter-laboratory-studies | math | Model Based Uncertainty Analysis in Inter-Laboratory Studies
Blaza Toman, Antonio M. Possolo
Statistical analysis of key comparison and inter-laboratory experiments is required to produce an estimate of the measurand called a reference value and further, measures of equivalence of the participating laboratories. Methods of estimation of the reference value have been proposed that rest on the idea of finding a so-called consistent subset of laboratories, that is, eliminating outlying participants. In this paper we propose an alternative statistical model, one that accommodates all of the participants data and incorporates the dispersion among the laboratories into the total uncertainty of the various estimates. This model recognizes the fact that the dispersion of values between laboratories often is substantially larger than the measurement uncertainties provided by the participating laboratories. We illustrate the method on data from key comparison CCL-K1.
Conference on Advanced Mathematical and Computational Tools in Metrology and Testing
and Possolo, A.
Model Based Uncertainty Analysis in Inter-Laboratory Studies, Conference on Advanced Mathematical and Computational Tools in Metrology and Testing , Paris, -1, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=900232
(Accessed April 12, 2024) | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816045.47/warc/CC-MAIN-20240412163227-20240412193227-00338.warc.gz | CC-MAIN-2024-18 | 1,330 | 7 |
https://homeworkdoer.co/what-are-the-branches-of-statistics/ | math | One needs to understand and know about the different branches of statistics to correctly understand statistics from a more holistic point of view. Often the kind of work one has involved in hides the other aspects of statistics however it is important to know the overall idea behind statistics to appreciate its importance.
What are the Branches of Statistics?
Statistics are divided into two major divisions: descriptive and inferential. Each of these is important as they offer different techniques that accomplish different objectives. Descriptive statistics describe what is going on in a population while inferential statistics, allows scientists to collect data from a sample group and generalize them to a larger population. They both have important differences.
In this branch of statistics, the goal is to describe. It deals with the collection of data and its presentation in various forms, such as tables, and graphs, and finding averages and other measures which would describe the data. Numerical measures are used to tell about the features of a set of data. Several items belong in this portion of statistics which include:
- The measure of the center of a data set, consisting of the mean, median and
- The spread of a data set measured with the range or standard deviation
- Measurements such as skewness
- The exploration of relationships and correlation between paired data
- The presentation of statistical results in graphical form
These measures are important and useful because they allow scientists to see patterns among data thus making sense of that data. Descriptive statistics can only be used to describe the population or data set under study, but the results cannot be generalized to any other group or population.
Recommended Posts: Statistics Homework Help
Types of Descriptive Statistics
There are two kinds of descriptive statistics:
Measures of central tendency– capture general trends within the data and are calculated and expressed as the mean, median, and mode. A mean tells scientists the mathematical average of a data set, such as the average age at first marriage; the median represents the middle of the data distribution, like the age that sits in the middle of the range of ages at which people first marry; and, the mode might be the most common age at which people first marry.
Measures of spread– describe how the data are distributed and relate to each other, including:
- The range, the entire range of values present in a data set
- The frequency distribution defines how many times a particular value occurs within a data set
- Quartiles are subgroups formed within a data set when all values are divided into four equal parts across the range
- The average of how much each value deviates from the mean
- Standard deviation, which illustrates the spread of data relative to the mean
Measures of spread are often visually represented in tables, pie and bar charts, and histograms to aid in the understanding of the trends within the data.
Inferential statistics are produced through complex mathematical calculations which allow scientists to infer trends about a larger population based on a study of a sample taken from it. Scientists use inferential statistics to examine the relationships between variables within a sample and then make generalizations or predictions about how those variables will relate to a larger population.
It is usually impossible to examine each member of the population individually. So scientists choose a representative subset of the population, called a statistical sample, and from this analysis, they can say something about the population from which the sample came. There are two major divisions of inferential statistics:
- A confidence interval gives a range of values for an unknown parameter of the population by measuring a statistical sample. This is expressed in terms of an interval and the degree of confidence that the parameter is within the interval.
- Tests of significance or hypothesis testing are where scientists claim the population by analyzing a statistical sample. By design, there is some uncertainty in this process. This can be expressed in terms of a level of significance.
Techniques that social scientists use to examine the relationships between variables, and thereby create inferential statistics, include linear regression analyses logistic regression analyses, ANOVA, correlation analyses, structural equation modeling, and survival analysis. When conducting research using inferential statistics, scientists conduct a test of significance to determine whether they can generalize their results to a larger population. Common tests of significance include the chi-square and t-test. These tell scientists the probability that the results of their analysis of the sample are representative of the population as a whole.
Descriptive vs. Inferential Statistics
Although descriptive statistics help learn things such as the spread and center of the data, nothing in descriptive statistics can be used to make any generalizations. In descriptive statistics, measurements such as the mean and standard deviation are stated as the exact number
However, the focus is different for inferential statistics, it uses measurements such as the mean and standard deviation. Inferential statistics start with a sample and then generalize to a population. This information about a population is not stated as a number; instead, these parameters are expressed as a range of potential numbers along with a degree of confidence.
Statistics Homework Help
Do Need help with statistics homework? Get quick & reliable statistics homework help online from our Top statistics homework doers. | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948765.13/warc/CC-MAIN-20230328042424-20230328072424-00674.warc.gz | CC-MAIN-2023-14 | 5,693 | 31 |
https://lessonplanet.com/teachers/favorite-pizza-pie-graph | math | You've heard of a pie graph, but what about a pizza pie graph? Challenge young mathematicians to answer ten questions based on a random survey of people's favorite pizzas. A pie graph displays the percentages of each type of pizza. Some of the questions require pupils to convert percentages into numbers based on a given total amount.
- Use as an instructional tool, independent practice, or quiz
- Distribute calculators for learners to check their answers
- Provide class members with scrap paper for solving and showing their work
- Promotes data analysis and application skills
- Answer key is not included | s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986685915.43/warc/CC-MAIN-20191018231153-20191019014653-00345.warc.gz | CC-MAIN-2019-43 | 611 | 6 |
http://datavision-inc.com/knowledge/openstack-training/ | math | Introduction to OPENSTACK
CLICK HERE TO REVIEW OPENSTACK TRAINING DATES/LOCATIONS
This is a 1-day introductory class, where attendees will be able to understand the different parts that make up OpenStack and learn why it has become such a fundamental piece in Data Center environments. Presented by an experienced instructor with field experience, discussions are guaranteed to be lively and informative.
By taking this course, attendees will be able to:
1. Understand the context where OpenStack is used.
2. Describe the different components that make up OpenStack.
3. Create and manage tenants and users.
4. Discuss how OpenStack can integrate into an SDN solution.
This course is aimed at network engineers and architects, software developers, sales personnel and anyone interested in understanding OpenStack.
Attendees should have a basic understanding of networking and be able to identify the shortcomings of managing a virtualized environment in a Data Center scenario.
Module 1: Introduction/Agenda
• Company introduction
• Attendee introductions
Module 2: Basic tenets of Cloud Computing
• The idea behind Cloud Computing
• The history of Cloud Computing
• Identifying valid use cases for Cloud Computing
Module 3: OpenStack Primer
• The history of the OpenStack Project
• The OpenStack core components
Module 4: OpenStack Identity (Keystone)
• Configuration and configuration file overview
• Using the Keystone userland binary:
• Adding and deleting tenants and users
• Adding, deleting and modifying endpoints
• Working with Keystone’s permission policy engine
Module 5: OpenStack ImageService (Glance)
• Setting up Glance API / Glance Registry
• Adding images to Glance
Module 6: OpenStack Networking (Neutron)
& Software Defined Networking (SDN)
• Cloud networking basics
• Software-defined networking using Open vSwitch
• Configuration and configuration file structure of Neutron
Module 7: OpenStack Volume (Cinder)
• Cinder basic functionality
• Configuration file structure
• Available Cinder backends
Module 8: OpenStack Compute (Nova)
• OpenStack Nova basic ideas
• Configuration and configuration file structure
• The integration of Nova with the Cinder volume service
Module 9: The OpenStack Dashboard (Horizon) | s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891812579.21/warc/CC-MAIN-20180219091902-20180219111902-00653.warc.gz | CC-MAIN-2018-09 | 2,279 | 43 |
https://altdotaqq.com/qa/quick-answer-what-would-happen-if-zero-didnt-exist.html | math | - Can we live without mathematics?
- What would happen if there were no numbers?
- What will happen to the world of mathematics does not exist?
- Why do we use zero?
- Is 0 a real number?
- What is the biggest number in the world?
- Is 13 a prime number Yes or no?
- Who invented the 0?
- Is 0 real or imaginary?
- Why is 2 A Number?
- Who found zero in India?
- Who is the father of mathematics?
- Do we really need math in life?
- Can the universe exist without math?
- Why is 2 the best number?
- Is zero a number Yes or no?
- Does zero mean nothing?
- Is 2 the only prime number?
- What was used before zero?
- What is the importance of zero in daily life?
- How did the Mayans use zero?
Can we live without mathematics?
Math is needed at every step of life, and we cannot live without it.
It is a subject that is applied to every field and profession.
It tells us how things work, and also allows us to predict certain things, which is how we have progressed so much in life.
It has made our lives easier and uncomplicated..
What would happen if there were no numbers?
Without numbers, people wouldn’t know how to count or measure. There would be many important things we wouldn’t know if it weren’t for numbers. … Without numbers, people wouldn’t know how to count or measure. There would be many important things we wouldn’t know if it weren’t for numbers.
What will happen to the world of mathematics does not exist?
As long as there is space, there is math because math is the foundation of the universe. … Maths has to exist because the universe is goverened by it, if our understanding of maths didn’t exist then nothing would really happen, we would be very limited in terms of technological advancement.
Why do we use zero?
Ancient scholars employed it as a symbol to represent the absence of a number, like the way we use a zero in 101 or 102 to signify that there are no multiples of 10 in the middle position. … However, it took two millennia for zero, with all its mathematical brilliance, to be accepted as a proper number.
Is 0 a real number?
Real numbers consist of zero (0), the positive and negative integers (-3, -1, 2, 4), and all the fractional and decimal values in between (0.4, 3.1415927, 1/2). Real numbers are divided into rational and irrational numbers.
What is the biggest number in the world?
The biggest named number that we know is googolplex, ten to the googol power, or (10)^(10^100). That’s written as a one followed by googol zeroes.
Is 13 a prime number Yes or no?
Here are the first few prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc.
Who invented the 0?
MayansThe first recorded zero appeared in Mesopotamia around 3 B.C. The Mayans invented it independently circa 4 A.D. It was later devised in India in the mid-fifth century, spread to Cambodia near the end of the seventh century, and into China and the Islamic countries at the end of the eighth.
Is 0 real or imaginary?
The real numbers are a subset of the complex numbers, so zero is by definition a complex number ( and a real number, of course; just as a fraction is a rational number and a real number). If we define a pure real number as a complex number whose imaginary component is 0i, then 0 is a pure real number.
Why is 2 A Number?
Two is a prime because it is divisible by only two and one. All the other even numbers are not prime because they are all divisible by two. That leaves only the odd numbers.
Who found zero in India?
AryabhataWhat is widely found in textbooks in India is that a mathematician and astronomer, Aryabhata, in the 5th century used zero as a placeholder and in algorithms for finding square roots and cube roots in his Sanskrit treatises.
Who is the father of mathematics?
ArchimedesArchimedes (287 BC–212 BC) is known as Father of Mathematics. He was born in the seaport city of Syracuse on the greek island of Sicily; his father was an astronomer.
Do we really need math in life?
Unlike literature, history, politics and music, math has little relevance to everyday life. That courses such as “Quantitative Reasoning” improve critical thinking is an unsubstantiated myth. All the mathematics one needs in real life can be learned in early years without much fuss.
Can the universe exist without math?
Many such mathematical constructs exist to explore, but without a physical Universe to compare it to, we’re unlikely to learn anything meaningful about our Universe. … But the Universe is a physical, not mathematical entity, and there’s a big difference between the two.
Why is 2 the best number?
2 (two) is a number, numeral, and glyph. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures.
Is zero a number Yes or no?
Zero is an even number because it is divisible by 2 with no remainder. 0 is neither positive nor negative. Many definitions include 0 as a natural number, in which case it is the only natural number that is not positive. Zero is a number which quantifies a count or an amount of null size.
Does zero mean nothing?
“Zero” is considered to be a number while “nothing” is considered to be an empty or null set. Zero has a numeric value of “0.” Zero is a numerical digit as well as a number and is used to denote that number in numerical values. … However, “nothing” is only a concept depicting a void or absence of anything relevant.
Is 2 the only prime number?
A prime number can have only 1 and itself as factors. … 2 is an even number that has only itself and 1 as factors so it is the only even number that is a prime.
What was used before zero?
Some of the first known zero symbols appear in Babylonian clay tablets of between 400 and 300 B.C.; there the zero was used to clarify the symbols for large numbers. … Brahmagupta was the first to write down the rules for arithmetic with zeros.
What is the importance of zero in daily life?
As a number, zero means nothing – the absence of other values. It plays a central role in mathematics as the identity element of integer, real number, and many other algebraic structures. As a digit, zero is used as a placeholder in the location value system. Historically, this was the last point in use.
How did the Mayans use zero?
The Mayan numeral system was the system to represent numbers and calendar dates in the Maya civilization. It was a vigesimal (base-20) positional numeral system. The numerals are made up of three symbols; zero (shell shape, with the plastron uppermost), one (a dot) and five (a bar). | s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141169606.2/warc/CC-MAIN-20201124000351-20201124030351-00436.warc.gz | CC-MAIN-2020-50 | 6,794 | 66 |
https://www.stockton.edu/sciences-math/faculty-staff/faculty-quint.html | math | Simon R. Quint
Associate Professor of Mathematics
BIOGRAPHYAfter Tufts, I spent four and a half years aboard ships as an officer in the U.S. Navy. Then after quickly filling in a gap of several mathematics courses that I missed as an undergraduate non-mathmematics major, I began a Ph.D. program at Berkeley and finished with a thesis on unitary representations of solvable Lie groups. That is when I started to see connections among the various areas of mathematics department instituted a Pre-Colloquium (before the weekly Colloquium) – highlighting innerconnections for graduate students. At Occidental College, my next position, at my suggestion the mathematics department instituted a capstone course Innerconnections in Mathematics that I taught. While there I started working on a manuscript for a book, which evolved to Viewing Mathematics via Innerconnections. Between Occidental and Stockton, I spent a year at Grinnell College. At Stockton, I have served as a supervisor for several mathematics majors in their senior projects, many of which were extensions of their Fellowship for Distinguished Students projects. All of these projects involved innerconnections among areas in and from undergraduate mathematics, with my manuscript servicing as the major references for each project. In spring 2014, I received a sabbatical for continued work on the manuscript for the innerconnections book.
Ph.D., University of California at Berkeley
B.S., Tufts University
AREAS OF EXPERTISE
Innerconnections in mathematics; representations of Lie groups
Innerconnections in Mathematics
Topics in Mathematics
Topics in Geometry
Foundations of Mathematics
Calculus I, II and III
Since receiving my Ph.D. degree, my main research interest has been mathematical innerconnections:
primarily of Lie groups and Lie algebras with other areas of mathematics and of the
connections involved in two highlights of contemporary mathematics – the 1995 proof
of Fermat's Last Theorem (:= a conjecture) in basic number theory via proof of a conjecture
in algebraic geometry of elliptic curves and in the 2005 proof of the Poincaré Conjecture
in topology of manifolds via proof of a conjecture in differential geometry. Lie theory,
and the Fermat and Poincaré problems, are among topics that focus on innerconnections
in my manuscript for the book Viewing Mathematics via Innerconnections. Innerconnectedness
among its areas is one of the wondrous, powerful, and lovely aspects of mathematics.
But this characteristic aspect of mathematics generally is unknown to undergraduate
mathematics students. One of my goals is that there will be a final area Mathematical
Innerconnections on the Mathematics Subject Classification – which lists the sixty-three
major areas of mathematics – to expose new and significant innerconnections [The phrases
'mathematical innerconnections' replacing the imprecise 'interrelations' and 'interrelated'
have precise technical definitions which show that the connectedness of mathematics
(something that is not apparent at a first glance of the list of the many subareas
of mathematics) results from the way it evolves. Two areas of mathematics are 'innerconnected'
if one of the areas contributes to the evolution of the other in any of the specific
number of ways; the mediator of the contribution is an 'innerconnection'.]
Viewing Mathematics via Innerconnections – A Graduated Text, manuscript for a textbook
in progress. 2003: "Mathematics Subject Classification as a Dynamic Digraph, for Mathematics
Education", Abstracts of Papers Presented to Amer. Math. Soc., Vol. 24, No. 1,
p. 267, 2003.
2002: "Mathematics via Interrelations, for Undergraduate Courses", abstract in FOCUS, newsletter of Math. Assoc. of Amer., Vol. 21,
No. 6, p.10, 2001.
2000 "Interrelations for Undergraduate Mathematics Courses: Capstone and Others", abstract in FOCUS, newsletter of the Mat. Assoc.
of Amer., Vol. 20, No. 1, p.7, 2000. | s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376826892.78/warc/CC-MAIN-20181215152912-20181215174912-00027.warc.gz | CC-MAIN-2018-51 | 3,941 | 39 |
https://www.genealogy.math.ndsu.nodak.edu/id.php?id=116089 | math | Ufik Lyutfi gizi Ismayilova
Ph.D. Institute of Mathematics and Mechanics, Azerbaijan Academy of Sciences 1982
Dissertation: Well-Posedness in "Whole" of the Cauchy Problem for Quasilinear Evolution Equations and Mixed Problems for Partial Quasilinear Equations of Shrodinger and Hyperbolic Types
Mathematics Subject Classification: 47—Operator theory
Advisor: Sasun Yakubovich Yakubov
No students known.
If you have additional information or corrections regarding this mathematician, please use the update form. To submit students of this mathematician, please use the new data form, noting this mathematician's MGP ID of 116089 for the advisor ID. | s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224652235.2/warc/CC-MAIN-20230606045924-20230606075924-00705.warc.gz | CC-MAIN-2023-23 | 650 | 7 |
http://forum.theonyxpath.com/forum/main-category/main-forum/the-new-world-of-darkness/1050247-what-exactly-is-ectoplasm | math | Exactly as the title suggests. I have been trying to figure out in what book ectoplasm is actually described, as two of the mage spells actually utilize it and my players are asking about it. Since I can't find it in that book, or in the core book I figured I'd post it here in case there was an explanation in any of the various books in the CoD?
No announcement yet.
What exactly -is- Ectoplasm? | s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122865.36/warc/CC-MAIN-20170423031202-00313-ip-10-145-167-34.ec2.internal.warc.gz | CC-MAIN-2017-17 | 397 | 3 |
http://www.tamilspider.com/resources/10054-abacus-classes-in-annanagar-kknagar-vedic-maths-training-annanagar-kknagar | math | This resource will be reviewed shortly.
If you think this resource contain inappropriate content, please report to webmaster.
Nowadays abacus and Vedic maths is by everyone in the world. Because abacus teaches the mathematical calculations very easily. Calculations such as addition, subtraction, multiplication, division, squares and cubes can be done in an easy manner. Abacus is an ancient method found before the computer and calculator to perform arithmetic calculations.
When comes to Vedic maths, Vedic maths provides a higher level of arithmetic calculations which boosts the brain power which is provided by Vedic maths training annanagar, Vedic maths training kknagar. On the whole abacus is having 10 levels of educations. Brainwave provides the abacus and Vedic maths training in an efficient way.
For More Details: http://braincarve.co.in/annanagar | s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250606975.49/warc/CC-MAIN-20200122101729-20200122130729-00322.warc.gz | CC-MAIN-2020-05 | 861 | 5 |
https://kidsworksheetfun.com/gcse-angles-in-polygons-worksheet/ | math | Arrow back back to angles in triangles and polygons including tessellation angles in triangles and polygons including tessellation. The corbettmaths practice questions on angles in polygons.
So we get text interior angle cdb 180 y 48 132 y.
Gcse angles in polygons worksheet. Polygons materials required for examination items included with question papers ruler graduated in centimetres and nil millimetres protractor compasses pen hb pencil eraser. A worksheet can there will be any subject. Gcse maths revision biology revision revision notes math notes study notes maths exam angles worksheet maths solutions math formulas.
This shape has 4 sides so its interior angles add up to. We don t have any way of expression two of the interior angles at the moment but we do have their associated exterior angles and we know that interior plus exterior equals 180. These review sheets are great to use in class or as a homework.
Interior angles in a polygon sum to 180 n 2 where n is the number of sides of the polygon. 180 times 4 2 360 degree. Tracing paper may be used.
Topic is a complete. 30 pages drawing hands on clock worksheet. This sheet covers interior and exterior angles in polygons.
More lessons for gcse maths math worksheets examples solutions and videos to help gcse maths students learn how to find the interior and exterior angles of polygons. Worksheet using the formula for the sum of interior and exterior angles. The exterior angle of a regular n sided polygon is 360 n.
Whether you want a homework some cover work or a lovely bit of extra practise this is the place for you. Gcse 9 1 exam question practice trigonometry free 78. Edexcel gcse mathematics linear 1ma0 angles.
Gcse 9 1 exam question practice angles in polygons 4 9 79 customer reviews. A angles in polygons worksheet answers is a few short questionnaires on an actual topic. Worksheet using the formula for the sum of exterior angles.
Instructions use black ink or ball point pen. Ideal for gcse revision this worksheet contains exam type questions that gradually increase in difficulty. The complete range of ks3 gcse skills are covered and there are some problems solving questions at the end.
Videos worksheets 5 a day and much more. An interior and corresponding exterior angle sum to 180. How to find the sum of the exterior angles and interior angles of a polygon.
Worksheet interior angles in polygons. The sum of exterior angles of any polygon is 360. Finding the interior angles of a polygon. | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816977.38/warc/CC-MAIN-20240415111434-20240415141434-00657.warc.gz | CC-MAIN-2024-18 | 2,485 | 12 |
https://www.slideserve.com/karim/metadata-characteristics-as-predictors-for-editor-selectivity-in-a-current-awareness-service | math | Thomas Krichel & Nisa Bakkalbasi 2005-10-31 Metadata characteristics as predictors for editor selectivity in a current awareness service
outline • Background to work that we did • RePEc (Research Papers in Economics) • NEP: New Economics Papers • The research • Theory • Method • Results • Other work done for NEP.
RePEc • Digital library for academic Economics. It collects descriptions of • economics documents (working papers, articles etc) • collections of those documents • economists • collections of economists • Pionneering effort to create a relational dataset describing an academic discipline as a whole. • The data is freely available.
RePEcprinciple • Many archives • Archives offer metadata about digital objects or authors and institutions data. • One database • Many services • Users can access the data through many interfaces. • Providers of archives offer their data to all interfaces at the same time. This provides for an optimal distribution.
it's the incentives, stupid • RePEc applies the ideas of open source to the construction of bibliographic dataset. It provides an open library. • The entire system is constructed in such a way as to be sustainable without monetary exchange between participants.
some history • Thomas Krichel in the early 1990s dreamed about a current awareness service for working paper. It would later have electronic papers. • In 1993 he made the first economics working paper available online. • In 1997 he wrote the key protocols that “govern” RePEc.
US Fed in Print IMF OECD MIT University of Surrey CO PAH Blackwell RePEc is based on 500+ archives • WoPEc • EconWPA • DEGREE • S-WoPEc • NBER • CEPR • Elsevier
to form a 340+k item dataset 161,000 working papers 180,000 journal articles 1,300 software components 1,200 book and chapter listings 8,000 author contact & publication listings 9,100 institutional contact listings more records than arXiv.org
IDEAS RuPEc EDIRC LogEc CitEc RePEc is used in many services • EconPapers • NEP: New Economics Papers • Inomics • RePEc author service • Z39.50 service by the DEGREE partners
NEP: New Economics Papers • This is a set of current awareness reports on new additions to the working paper stock only. Journal articles would be too old. • Founded by Thomas Krichel in 1998. • Supported by the Economics department at WUStL. • Initial software was written by Jose Manuel Barrueco Cruz. • First general editor was John S. Irons.
why NEP • Public aim: Current awareness if well done, can be an important service in its own right. It is sheltered from the competition of general search engines. • Private aim: It is useful to have some, even though limited classification information. This should be useful in performance measures within subject areas.
modus operandi: stage 1 • The general editor uses a computer program who gathers all the new additions to the working paper stock. This is usually done weekly. • S/he filters out new descriptions of old papers • date field • handle heuristics • The result is an issue of the nep-all report.
modus operandi: stage 2 • Editors consider the papers in the nep-all report to filter out papers that belong to the subject. This forms as issue of a subject report nep-???. • nep-all and the subject reports are circulated via email. • A special arrangement makes the data of NEP available to other RePEc services.
some numbers • The are now 60+ NEP lists. • Over 37k subscriptions. • Close to 16k subscribers. • Over 50k papers announced. • Over 100k announcements. • Homepage at http://nep.repec.org All this is a fantastic success!!
problem with the private aim • We would have to have all the papers to be classified not only the working papers. • We would need to have 100% coverage of NEP. • This means every paper in nep-all appears in at least one subject report.
coverage ratio • We call the coverage ratio the number of papers in nep-all that have been announced in at least one subject report. • We can define this ratio • for each nep-all issue • for a subset of nep-all issues • for NEP as a whole
coverage ratio theory & evidence • Over time more and more NEP reports have been added. As this happens, we expect the coverage ratio to increase. • However, the evidence, from research by Barrueco Cruz, Krichel and Trinidad is • The coverage ratio of different nep-all issues varies a great deal. • Overall, it remains at around 70%. • We need some theory as to why.
two theories • Target-size theory • Quality theory • descriptive quality • substantive quality
theory 1: target size theory • When editors compose a report issue, they have a size of the issue in mind. • If the nep-all issue is large, editors will take a narrow interpretation of the report subject. • If the nep-all ratio is small, editors will take a wide interpretation of the report subject.
target size theory & static coverage • There are two things going on • The opening new subject reports improves the coverage ratio. • The expansion of RePEc implies that the size of nep-all, though varying in the short-run, grows in the long run. Target size theory implies that the coverage ratio deteriorates. • The static coverage ratio that we observe is the result of both effects canceling out.
theory 2: quality theory • George W. Bush version of quality theory • Some papers are rubbish. They will not get announced. • The amount of rubbish in RePEc remains constant. • This implies constant coverage. • Reality is slightly more subtle.
two versions of quality theory • Descriptive quality theory: papers that are badly described • misleading titles • no abstract • languages other than English • Substantive quality theory: papers that are well described, but not good • from unknown authors • issued by institutions with unenviable research reputation
practical importance • We do care whether one or the other theory is true. • Target size theory implies that NEP should open more reports to achieve perfect coverage. • Quality theory suggests that opening more report will have little to no impact on coverage. • Since operating more reports is costly, there should be an optimal number of reports.
overall model • We need an overall model that explains subject editors behavior. • We can feed this model with variables that represent theoretical determinants of behavior. • We can then assess the strength of various factors empirically.
method • The dependent variable is announced. It is one if the paper has been announced, 0 otherwise. • Since we are explaining a binary variable, we can use binary logistic regression analysis (BLRA). This is a fairly flexible technique, useful when the probability distributions governing the independent variables are not well known. • That's why BLRA is popular in the life sciences.
independent variables: size • size is the size of the nep-all issue in which the paper appeared. • This is the critical indicator of target size theory. We expect it to have a negative impact on announced.
independent variables: position • position is the position of the paper in the nep-all issue. • The presence of this variable can be justified by the combined assumption of target size and editor myopia. • If editors are myopic, they will be more liberal at the start of nep-all then at the end of nep-all.
independent variables: title • title is the length of a title of the paper, measured by the number of characters. • This variable is motivated by descriptive quality theory. A longer title will say more about the paper than a short title. This makes is less likely that a paper is being overlooked.
independent variables: abstract • abstract is the presence/absence of an abstract to the paper. • This is also motivated by descriptive quality theory. • Note that we do not use the length of the abstract because that would be a highly skewed variable.
independent variables: language • language is an indicator if the language of the metadata is in English or not. • This variable is motivated by descriptive quality theory and the idea that English is the most commonly understood language. • While there are a lot of multilingual editors, customizing this variable would have been rather hard.
independent variables: series • series is the size of the series where a paper appears in. • This variable is motivated by substantive quality theory. • The larger a series is the higher, usually, is its reputation. We can roughly qualify by size and quality • multi-institution series (NBER, CEPR) • large departments • small departments
independent variables: author • author is the prolificacy of the authors of the paper. • It is justified by substantive quality theory. • This is the most difficult variable to measure. We use the number of papers written by the registered author with the highest number. • Since about 50% of the papers have no registered author, a lot of them are excluded. But there should be no bias by the exclusion.
create categorical variables • size_1 [179, 326) • size_2 [326, 835] • title_1 [55, 77) • title_2 [77, 1945] • position_1 [0.357, 0.704) • position _2 [0.704, 1.000] • series_1 [98, 231) • series_2 [231, 3654]
results • P(announced=1| x) =(exp(g(x))/(1+exp(g(x)) • g(x) = 0.2401- 0.2774*size_1 - 0.4657* size_2 + 0.1512*title_1+ 0.2469*title_2 + 0.3874*abstract + 0.0001*author + 0.7667*language -0.1159*series_1 + 0.1958*series_2 • position is not significant. author just makes the cut.
odds ratio • size_1 1.32 [1.22, 1.44] • size_2 0.83 [0.76, 0.90] • title_1 1.16 [1.07, 1.26] • title_2 1.28 [1.18, 1.39] • abstract 1.47 [1.34, 1.62] • language 2.15 [1.85, 2.51] • series_1 1.11 [1.02, 1.20] • series_2 1.37 [1.26, 1.49] • author 1.05 [1.01, 1.09]
scandal! • Substantive quality theory can not be rejected. That means that the editors are selecting for quality as well as for the subject. • The editors have rejected our findings. Almost all protest that there is no quality filtering.
consequences • There has been no program to expand list. • There has to be a concentrated effort to help editors to find subject specific papers. • More effort needs to be made for editors to really find the subject-specific papers. This can be done by • the use of a more efficient interface • the use of automated resource discovery methods.
ernad • editing reports on new academic documents. It is purpose-built software system for current awareness reports. • It has been designed by Thomas Krichel, http://openlib.org/home/krichel/work/altai.html • The system was written by Roman D. Shapiro.
statistical learning • The idea is that a computer may be able to make decision on the current nep-all reports based on the observation of earlier editorial decisions. • ernad now works using support vector machines (SVM), with titles, abstracts, author name, classification values and series as features.
performance criteria • We are not aware of performance criteria for the sorting of papers in a report. • Precision and recall appear useless. • Expected search length and average search don't appear very attractive. • Thus research into precise criteria is required.
SVM performance • If we use average search length, we can do performance evaluations. • It turns out that reports have very different forecastability. Some are almost perfect, others are weak. • Again, this raises a few eyebrows!
what is the value of an editor? • If the forecast is perfect, we don't need the editor. • If the forecast is very weak the editor may be a prankster.
pre-sorting reconceived • We should not think of pre-sorting via SVM as something to replace the editor. • We should not think about it encouraging editors to be lazy. • Instead, we should think it as an invitation to examine some papers more closely than others.
headline vs. bottomline data • The editors really have a three stage process of decision. • They read title, author names. • They read the abstract. • They read the full text • A lot of papers fail at the first hurdle. • SVM can read the abstract and prioritize papers for abstract reading. • Editors are happy with the pre-sorting system.
Thank you for your attention! [email protected]://openlib.org/home/krichel/ | s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487621519.32/warc/CC-MAIN-20210615180356-20210615210356-00177.warc.gz | CC-MAIN-2021-25 | 12,506 | 45 |
https://stars.library.ucf.edu/facultybib1990/1086/ | math | Abbreviated Journal Title
Neutral Electron Flow; Planar Diode; Stability Properties; Field; Instability; Physics; Fluids & Plasmas
The analysis of the planar magnetron Vlasov distribution function [Phys. Fluids 31, 2362 (1988)] is extended to the cylindrical case. In momentum space, the model distribution function is f(w,p(theta)) = Ne(-betaww)e-(OMEGAbetatheta/4p0)(ptheta-p0)2 where w(p(theta)) is the single particle energy (angular momentum), beta(w)(beta(theta)) is the inverse of the thermal energy associated with variations in w(p(theta)), p0 is the angular momentum at the cathode, and OMEGA is the electron cyclotron frequency (= eB0/mc). The problem is shown to be too ''stiff '' numerically to permit a pure numerical solution even using very high accuracy and state-of-the-art numerical schemes. It is shown that one may use a global singular perturbation expansion, similar to, but significantly more complex than the one used in the planar case, to solve the resulting nonlinear ordinary differential equation for the spatial dependence of the distribution function, density, electrostatic potential, and drift velocity.
Physics of Plasmas
Kaup, D. J. and Choudhury, S. Roy, "A Model Cylindrical Magnetron Vlasov Distribution Function" (1994). Faculty Bibliography 1990s. 1086. | s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146907.86/warc/CC-MAIN-20200227221724-20200228011724-00504.warc.gz | CC-MAIN-2020-10 | 1,294 | 5 |
https://mapviewerhelp.goldensoftware.com/projections/Characteristics_of_Projections.htm | math | Some projections are imbued with characteristics that tell us if certain types of measurements (e.g. measurements of distance, area, etc.) are accurate on the projected map. Some of these characteristics include the following:
A projection is said to be equal area when the area of any given part of the map covers the same area on the Earth as any other part of the map of the same size. For example, if a one inch diameter circle on the map covers a 100 mile diameter circle on the Earth's surface, then we know that a one inch diameter circle anywhere else on the map is known to cover another 100 mile diameter circle on the Earth. In order for a projection to be equal area, however, consistency in the shapes, scales, and/or angles across the map must be sacrificed. Equal area projections include Albers Equal Area, Bonne, Eckert IV, Eckert VI, Lambert Azimuthal Equal Area, Mollweide, and Sinusoidal.
A projection is said to be conformal when the local angles for points on the map are represented accurately. This means that the angles between any given point and any nearby points are accurate, but are not necessarily accurate for widely separated points on the map. A side effect is that conformal projections preserve the precise perpendicular intersections between parallels and meridians on the map. When mapping smaller areas, relative shape is preserved. In order for a projection to be conformal, however, consistency in the surface areas, shapes, and/or scales across the map must be sacrificed. Conformal projections include Gauss-Kruger / Gauss Conformal, Hotine Oblique Mercator, Lambert Conformal Conic, Mercator, Oblique Mercator, State Plane Coordinate System Projections, Transverse Mercator, and Universal Transverse Mercator.
A projection is said to be equidistant when the scale between at least one specific origin point on the map with respect to every other point on the map is represented accurately. In order for a projection to be equidistant, however, consistency in the surface areas, shapes, and/or angles across the map must be sacrificed. The Azimuthal Equidistant, Equidistant Cylindrical, Equidistant Conic, and Cassini projections are equidistant.
With a projection of the azimuthal form, the direction of (or angle to) all points on the map are accurate with respect to the center point of the projection. Azimuthal projections include Azimuthal Equidistant, Gnomonic, Lambert Azimuthal Equal Area, Orthographic, and Stereographic.
None of the Above
Some projections try to minimize the effects of all distortions and as a result do not minimize any one distortion in particular. These projections include Polyconic, Robinson and Robinson-Sterling, Unprojected Lat/Long, and Van der Grinten.
In addition to the characteristics described above, some projections have highly specialized characteristics that may be useful in certain applications. For example, on maps made with a Mercator projection, all lines of constant direction (rhumb lines) are known to be straight, thereby making such maps very desirable as navigational charts.
Introduction to Map Projections
Geometric Forms of Projection
Characteristics of Projections
Latitude and Longitude Coordinates
Latitude and Longitude in Decimal Degrees
Using Scaling to Minimize Distortion on Latitude and Longitude Maps | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816587.89/warc/CC-MAIN-20240413083102-20240413113102-00050.warc.gz | CC-MAIN-2024-18 | 3,316 | 14 |
http://onlinelibrary.wiley.com/doi/10.1002/9781118109656.ch5/summary | math | 5. Monte Carlo Solutions of Differential Equations
Published Online: 29 NOV 2011
Copyright © 2011 John Wiley & Sons, Inc. All rights reserved.
Empirical Model Building: Data, Models, and Reality, Second Edition
How to Cite
Thompson, J. R. (2011) Monte Carlo Solutions of Differential Equations, in Empirical Model Building: Data, Models, and Reality, Second Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118109656.ch5
- Published Online: 29 NOV 2011
- Published Print: 24 OCT 2011
Print ISBN: 9780470467039
Online ISBN: 9781118109656
- dirichlet problem;
- Fokker-Planck equation;
- gambler's ruin problem;
- Monte Carlo solution
This chapter provides a distinction between Monte Carlo and simulation. It shows a closed-form solution for the gambler's ruin problem; it would be ridiculous to use a simulation to solve it. It is by means of an analogy of real-world problems to the general equation that simulation becomes useful. The examples provided in the chapter are given to give the reader a feel as to the practical implementation of simulation-based algorithms as alternatives to the usual numerical approximation techniques. A certain amount of practice quickly brings the user to a point where he or she can write simulation algorithms in days to problems that would require the numerical analyst months to approach. The algorithm for solving the Fokker-Planck problem and Dirichlet problem are not simply analogues of the classical differential-equation formulations of these systems. They are, in fact, descriptions of the axioms that typically give rise to these problems.
Controlled Vocabulary Terms | s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701167113.3/warc/CC-MAIN-20160205193927-00069-ip-10-236-182-209.ec2.internal.warc.gz | CC-MAIN-2016-07 | 1,637 | 16 |
https://www.topperlearning.com/doubts-solutions/while-solving-problems-when-do-we-take-positive-g-during-body-39-s-upward-and-downward-motion-what-terms-shoud-we-take-as-positive-and-negative-jaubps44/ | math | In motion solving question of motion under gravity there are two methods to solve those questions
1. First method is sign convention like taking upward direction as positive and downward direction as negative, that whatever tha measurement we take along upward as positive whether it can be velocity or displacement and measurement along downward is taken as negative,. You can also change sign convention according to convenience.
For the given question it was already declared that upward direction is positive so the downward direction will be negative, and you must know acceleration due to gravity always acts toward the centre of the earth (downward ). Since it is acting downward then it will be taken as negative. And its direction is fixed so it will always be negative for the entire motion
2. Other method is taking acceleration direction as direction of reference . So the quantity measured along the direction of acceleration will taken as positive and against will be taken as negative. This method is use to solve horizontal rectilinear motion. Like car is running on road. | s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991801.49/warc/CC-MAIN-20210515100825-20210515130825-00019.warc.gz | CC-MAIN-2021-21 | 1,088 | 4 |
https://www.oaklandsprimary.co.uk/friday-22/ | math | When you are reading, you know someone is speaking when you see these marks " and ". We call them speech marks or quotation marks.
The first " shows where someone starts talking, and the second " shows when they stop talking.
eg "Look out" shouted Kipper.
Can you find where to put the speech marks in these sentences?
You have been given a job by Mrs Wright to use a calculator to work out the answers to these number sentences. Unfortunately your calculator is quite old and some of the buttons don't work. For each question, look at which number key is broken and think of a method to help you work out the answers. Hint: think about your number bonds to 10, and near round numbers, eg 19 is almost 20! | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817002.2/warc/CC-MAIN-20240415142720-20240415172720-00614.warc.gz | CC-MAIN-2024-18 | 705 | 5 |
https://groups.yahoo.com/neo/groups/primenumbers/conversations/topics/17901?l=1 | math | Re: Cubic x^3 + x^2 + x + t prime generators
- --- In [email protected], "Mark Underwood"
>Oops, how did I get this muddled? Too many beers when I wrote the
> Robert, k^n-k^(n-1) has of course factors of k so I assume you did a
> typo somewhere?
response most probably. I meant to say:
k^p-(k-1)^p, where p is prime | s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187825812.89/warc/CC-MAIN-20171023073607-20171023093607-00471.warc.gz | CC-MAIN-2017-43 | 315 | 7 |
https://www.turbosquid.com/3d-models/3d-max-electric-331-tram-cissie/1138386 | math | ##General## This is high-poly model of Metropolitan Electric Tramways No: 331
This was the third and final experimental Feltham tram built by the Union Construction Co. for the M.E.T. in 1929, nicknamed at the time, Cissie. The tram being constructed for pay as you enter with the conductor standing at the door and taking fares on boarding, hence the central doors. 'Cissie' was used solely on the Whetstone - Cricklewood service 40. 'Cissie' was retired from service in 1951 and travelled extensively until being delivered to the National Tramway Museum at Crich in 1961
##Geometry## The model was modeled in 3ds max 2017 Is smootheable and editable (turbosmooth). | s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125945111.79/warc/CC-MAIN-20180421090739-20180421110739-00433.warc.gz | CC-MAIN-2018-17 | 666 | 3 |
https://designoverwrite.com/the-price-elasticity-of-demand-measures-the-extent-to-which-the-quantity-demanded-changes-when/ | math | I am a self-aware person, I have no problems buying things that I think are worth paying more than they cost, and I don’t feel threatened when they are offered to me. By the way, if there are any people that I don’t like doing wrong, don’t know about.
When I first started researching this topic, the first thing I did was look up the price elasticity of demand. The concept is that if you add two goods, one that will increase the quantity demanded and one that will decrease the quantity demanded, you can determine the price elasticity of demand. If the quantity demanded increases, the price elasticity of demand will be low, and vice-versa, if the quantity demanded decreases, the price elasticity of demand will be high.
The concept is pretty straight forward, but I think that most people are understating the importance of the concept. In reality, supply and demand are often highly complex, and to be sure, the price elasticity of demand is one of the most important metrics to keep in mind.
The concept goes back to a concept I learned in high school called “the price elasticity of demand,” which is basically the product of the supply and the demand curves. In economics, supply and demand curves are just a way of measuring how much you can make something if you have enough people making it. Supply curve is the graph that shows how much of a product will exist in the world regardless of how much it costs to produce.
The supply curve for a particular item is the diagram that shows how much of that item there currently is. The demand curve is the graph that shows how much you will have to buy an item in order to get it.
Supply and demand curves are very important, but they’re not the most important aspect of economics; they’re just a way to graph the amount of a product that you can make if you have enough people making it. But when we look at supply and demand curves in the context of the housing market, they become a lot more important.
The supply and demand curves for housing are especially important because of their relationship to prices. The more housing there is, the more money will be available to buy more housing. In general, prices and demand are connected. As a result, the price elasticity of demand (or the “price elasticity of demand” as economists call it) measures the extent to which the quantity demanded changes when the price changes.
As a result of these and other data-driven economic models, there are a few questions about how much price elasticity of demand has to be measured to determine the amount of housing needed to support the demand. If housing costs are measured as a percentage of the cost of housing, then the rate of housing change is expected to be much less than the rate of housing change as a percentage of the cost of housing.
As this is a major concern, you can estimate the price elasticity of demand by using the average number of people who purchased the house. This is where the average price elasticity of demand is really key.
To determine how much housing you need to pay for housing, you can measure how much you need to pay for housing. The housing market is just getting real. The average price elasticity of demand is about as low as people do in the United States, so you should know how much you need for housing. | s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500151.93/warc/CC-MAIN-20230204173912-20230204203912-00508.warc.gz | CC-MAIN-2023-06 | 3,316 | 10 |
http://www.myswitzerland.com/pt/magazine/magazine_composed.cfm?template=2&LIMIT=128&model=page&offset=124&ancestor_node_ids=25268,25269,25140,25276,25292,25277,25280,29819,25273,25274,25275,25279,25282,25261,25287 | math | 2 Nights in Double room, Half-board, 1 x cinema entrance ticket per person per stay, Free outdoor parking, WLAN, Entrance to the sauna landscape, fruit and mineral water as a courtesy in room, bathrobe / bath towel (on loan), Use of the wellness facilities, Visitor/Tourist card, Arrival daily permitted
2 nights’ accommodation in a multi-bed room including breakfast buffet, lunch pack and free admission to the Gutenberg Museum. Costs: adults in dormitory $$CHF 69$$ Accommodation prices for families with children under 6 years of age as well as reduced price family admission on request. Please enquire directly in the youth hostel. 3-course menu for $$CHF 14.50$$ instead of $$CHF 17.50$$ on request
2 nights’ accommodation in a multi-bed room incl. breakfast buffet and voucher for a 2-day summer ski pass. Costs: adults in dormitory $$CHF 191$$ youth 16-19 years $$CHF 174$$ Important: The package is payable in full at the time of booking and is non-refundable. | s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042988860.4/warc/CC-MAIN-20150728002308-00340-ip-10-236-191-2.ec2.internal.warc.gz | CC-MAIN-2015-32 | 973 | 3 |
https://www.mysciencework.com/publication/show/efcc0ff974e424192f75ee3fa19a9249 | math | Abstract The limit cycles of the van der Pol oscillator X ̈ + AX − 2BX 3 +ε(z 3 +z 2X 2 +z 1X 4) X ̇ = 0 , for B > 0, are studied in first-order approximation, using the Jacobian elliptic functions with the method of harmonic balance. The transitory motion, and in consequence the limit cycles and their stability are also studied in an approximate quantitative way with a generalized method of the slowly varying amplitude and phase. The bifurcations of these non-linear oscillators are studied using the methods of differentiable dynamics to obtain the qualitative behaviour. Quantitative values for the radius, frequency and energy of the limit cycles are given. The presence and stability of zero, one, or two limit cycles depend on the parameters z i . The presence of bifurcations depends on z i and A. | s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917121453.27/warc/CC-MAIN-20170423031201-00280-ip-10-145-167-34.ec2.internal.warc.gz | CC-MAIN-2017-17 | 813 | 1 |
http://www.kinvee.com/doce/product.asp?P_ID=1225&page=1&c_id=136 | math | mobile stage truck,mobile stage trailer
Why the industry chooses Kinvee products :
•Expertise: Kinvee has been designing mobile stages for 5 years.
•Reliability in engineering: Highest wind resistance, with or without windwalls.
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https://www.physicsforums.com/threads/solution-of-the-nonlinear-2nd-order-differential-equation.250182/ | math | 1. The problem statement, all variables and given/known data I'd like to solve the following non-homogeneous second order differential equation and may I ask smart scholars out there to help me with this? y"(1-1.5(y')^2)=Cx^n, (^ denotes "to the power of") where C and n are constants, and the boundary conditions are: y=0 at x=0, y'=0 at x=L/2 (L is between 100 and 200). Thanks. 2. Relevant equations 3. The attempt at a solution Indtroducing v=y', the equation becomes v'(1.0-1.5v^2)=Cx^n Integration of the above equation provides (v-0.5v^3)=nCx^(N+1)-const. Employing v=0 at x=L/2, const=nC(L/2)^(n+1), and the equation becomes v-0.5v^3=nCx^(n+1)+nC(L/2)^(n+1) I can't go any further. | s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376826306.47/warc/CC-MAIN-20181214184754-20181214210754-00596.warc.gz | CC-MAIN-2018-51 | 689 | 1 |
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https://plus.maths.org/content/comment/reply/node/6379/comment_node_article | math | A kale leaf is crinkled up around its edge.
Picture a curved line. That's not so hard – I'm sure you're already imagining a smoothly curving line drawn on a blank white page, perhaps a circle, or a sine curve wiggling up and down across the page.
Now picture a curved surface. Again, not so hard. You might think first of a something simple like a cylinder or a sphere. Or perhaps something a bit more complicated, like a frilly kale leaf (a good illustration of a hyperbolic surface), a dimpled ball or a flag rippling in the wind.
In a previous article, Kissing the curve, we saw that understanding curvature of one-dimensional lines and two-dimensional surfaces is all a matter of osculating (kissing) circles of the curves in a flat plane. (For surfaces we consider the curves formed by intersecting the surface with planes perpendicular to the tangent planes.)
The osculating circle of this curve at the point P. The curvature at this point is 1/r where r is the radius of the osculating circle.
Mathematicians and physicists are interested in the curvature of higher-dimensional objects. And we are affected by such curvature every day: the gravity we feel is the result of the curvature of the four-dimensional spacetime of our Universe. But how do you describe curvature of something that has more than two dimensions?
It's easy for us to picture a one-dimensional curve drawn on a flat plane. And we can easily picture a two-dimensional surface in three-dimensional space. But for most of us picturing anything in higher dimensions is impossible. Where our brains and imagination fail, we can use maths to paint the picture for us.
We need to generalise the idea of a surface or a line to higher dimensions. Most of the lines we come across, whether they are curved or straight, look locally like a straight line (this is the basis for calculus). A surface, whether curved like a ball, rippling like a flag or flat as a table-top, viewed close up looks like a flat plane. (CGI in movies uses this concept in order to approximate a complicated surface with lots of tiny flat pieces – you can read more in It's all in the detail.) Both lines and surfaces are examples of manifolds – mathematical objects that viewed up close look like ordinary flat space (where points are located using perpendicular coordinate axes), which is known as Euclidean space.
This image is actually made up of millions and millions of shaded triangles.
The tangents to a curve (which you can think of as a one-dimensional manifold) are straight lines. Surfaces (two-dimensional manifolds) also have tangent planes. In fact, the tangent space of an n-dimensional manifold at any point is a Euclidean space of dimension n, . And just as we understood curvature for lines and surfaces, the curvature of a manifold is the amount it differs from its flat tangent space.
In order to understand curvature in this way, the tangent space has to vary smoothly across the surface. If a line or surface has a sharp kink, there is no way to define curvature at this point as the tangent line (or planes) abruptly change from one side of this point to the other, and isn't defined at the kinky point. So in order to consider curvature of manifolds, we consider manifolds that too have smoothly varying tangent spaces across the manifolds. These are called Riemannian manifolds, after the mathematician Bernard Riemann who extended this notion of curvature to many dimensions. (Actually, the precise definition of a Riemannian manifold is that the inner product – the operation that defines distances and angles – for the tangent spaces varies smoothly across the manifold.
The sphere has positive curvature, the saddle has negative curvature and the flat plane has zero curvature. A circle drawn on the sphere would have a smaller area than one drawn on the flat plane. While a circle drawn on the saddle would have a greater area than one drawn on the flat plan. (Image courtesy NASA.)
We saw in the last article that there is a notion of curvature, called Gaussian curvature, that is intrinsic: it can be detected by a 2D resident living on the surface; you don't need an outside perspective to see it. The resident would be able to detect the positive, negative or flat curvature of the surface by summing the interior angles of triangles: positive curvature corresponds to the interior angles adding to more than 180° (such as on the surface of the Earth), a negative curvature to the interior angles adding to less (a surface similar to that of a crinkly kale leaf) and flat (0) curvature to the angles adding exactly 180°.
Similarly, you can understand the curvature of higher-dimensional Riemannian manifolds intrinsically, without caring how the manifold is embedded in any larger space. The simplest measure of curvature on Riemannian manifolds is scalar curvature, , defined for each point in the manifold. This describes how a small ball in the manifold centred on , differs in volume from an equivalent ball in Euclidean space.
To understand this let's go back to something we can picture more easily – a ball of radius on a surface is made up of all the points that lie within a distance of , as measured within the surface, from the centre point : a filled circle. Since you have to measure the distances within the surface, it might not be the same distance you would measure between these two points in the Euclidean space that contains the surface. This is why the circle in the surface is not necessarily the same as the equivalent circle in Euclidean space (ie, a filled circle with centre and radius , where the distances are measured in Euclidean space).
The torus has regions with different curvature: on the outside of the torus curvature is positive (blue), on the inside it's negative (red), and at the top and bottom circles it's zero (grey). (Image from Mark L. Irons.)
At a point with positive curvature the ball on the manifold will be smaller than the equivalent ball of radius in Euclidean space: a circle cut from a flat piece of paper will have to be folded or crumpled to cover the equivalent circle on the surface of a sphere. If the surface has negative curvature at a point , the volume of the ball will be larger than for Euclidean space: to create crocheted versions of hyperbolic surfaces , more and more stitches are needed as the radius increases. (You can read more in Chaotic crochet and Knitting by numbers.)
Our examples of a sphere and hyperbolic surfaces have constant scalar curvature over the whole surface. But you don't have to look far to find a surface with varying curvature: a torus has equal amounts of positive and negative curvature over the whole surface, as shown in the image on the right.
The scalar curvature assigns a single real number to each point – it defines a scalar field across the manifold. And the scalar curvature is enough to completely describe the curvature of a two dimensional manifold (ie. a surface). However in more than two dimensions we need something a little more complicated.
The Ricci curvature describes how conical regions in the manifold differ in volume from the equivalent conical regions in Euclidean space.
Instead of considering how the volume of a whole ball within the manifold differs from one in Euclidean space, we consider the volume of just a sliver of the ball – an angular sector or cone centred around some direction from the centre of the ball. The Ricci curvature, , describes how the sliver of a ball at point in direction in the manifold differs in volume from the equivalent angular sector in Euclidean space. For any point on the manifold, we can define the value of the Ricci curvature in any direction from that point: for any direction we can look at the difference between the volumes of a sliver in the manifold, and a sliver in Euclidean space, in that direction. Unlike the simpler scalar curvature which defines a scalar field across the manifold, the Ricci curvature is a tensor field, that is it is defined for all directions from each point on the manifold. (You can read more about tensors in Feeling tense about tensors?)
The Ricci curvature comes into play when you are considering manifolds of three or more dimensions. For a two-dimensional manifold the Ricci curvature gives you the same information as the scalar curvature – the Ricci tensor has the same value in all directions for any point: . But in three or more dimensional manifolds it is possible for a point to have positive Ricci curvature in one direction and negative Ricci curvature in another.
Moving on up
In four and higher dimensions we need a more complex description of curvature. We're now in territory we can't visualise anymore and we need maths to describe these objects and properties. But we can get a sense of one description of curvature in these higher dimensions by viewing it as an extension of the definition of Gaussian curvature we used to understand the curvature of surfaces.
Consider a plane in the tangent space of the higher-dimensional manifold at some point . Then for any direction in the tangent plane from , there is a unique geodesic curve within the manifold emanating from in the direction. (A geodesic curve is a generalisation of straight lines on a flat plane or great circles on the globe of the world – a unique curve that give the shortest distance between two points in a manifold.) Then, even if our manifold has four or more dimensions, we can sweep out a two-dimensional surface within the manifold, made up of all the geodesic curves within the manifold emanating from as we move through all the directions in the tangent plane.
We can calculate the Gaussian curvature for this surface for any tangent plane at a point . This is called the sectional curvature for the tangent plane . Giving the sectional curvatures for all planes tangent to the manifold at a point describes the curvature of a manifold at completely. The sectional curvatures for all tangent planes at every point in a manifold describe a tensor field.
Equivalently, you can completely describe the curvature of a manifold using the Riemannian curvature tensor. Rather than focussing on the Gaussian curvature of surfaces defined by tangent planes, Riemannian curvature describes how curvature twists tangent vectors as they move around a manifold. (A vector represents a magnitude – its length – and direction.)
Think of a triangle drawn on a flat piece of paper. Imagine attaching a small vector to one of the corners (lying on the paper – as it's a tangent vector to this surface) and move it around the triangle, preserving the angle it makes with each side as it goes (this is called parallel transporting a vector along each line). The vector will have the same orientation when it returns to its starting point, it will be pointing in the same direction.
The angle of the tangent vector attached to the sphere changes direction as it is parallel transported along lines of latitude and longitude.
Now consider a sphere, and to make it easier to keep track of things consider it with the same lines of latitude and longitude we use as coordinates on Earth. Start at the point on the equator of longitude and latitude (point A on the image on the right) and consider a tangent vector to the surface at that point, pointing directly north. Then travel directly north, along the line of longitude, dragging the tangent vector with you, keeping it at the same angle to the line of longitude. At the North Pole (point N in the image) your tangent vector is now pointing in the direction of the line of longitude at , perpendicular to the line of longitude east.
Now travel down the line of longitude east, dragging the tangent vector and keeping it perpendicular to the direction of travel. When you arrive back at the equator, at the point longitude, latitude of east (point B), the tangent vector will now be pointing east along the equator.
Travel back along the equator to your starting spot at latitude, longitude (point A), dragging the tangent vector with you and keeping it parallel withthe equator. When you return to your starting point your tangent vector is now pointing due east. The vector has twisted through an angle of 90 degrees east (indicated by in the image).
If you'd dragged it the other way around the triangle – dragging it east along the equator to longitue east (point B), then up that line of longitude to the North Pole (N) and down the line of longitude to your starting position (A) – it would have instead turned through an angle of 90 degrees west. The orientation of your travel affects the direction of the twist of the vector. (You can play with a demonstration of this idea here.)
The Riemann curvature tensor is based on the idea of parallel transport and how tangent vectors are twisted as they move in this way around loops on a manifold. The actual definition is more complicated, and as mentioned above, is equivalent to giving the sectional curvature of a manifold.
For two-dimensional surfaces, these three types of curvature – scalar, Ricci and Riemann – are all equivalent. But as the dimension of our manifold increases, these measures of curvature begin to differentiate. For three-dimensional manifolds Ricci and Riemann curvature are equivalent, but they give greater information than the scalar curvature. And for manifolds of dimensions four or higher, only the Riemann curvature (or equivalently the sectional curvature) completely describes the curvature of the manifold. Understanding curvature in these higher dimensions provided some of the greatest scientific and mathematical achievements – Einstein's theory of general relativity, and Perelman's proof of the Poincaré's Conjecture. (You can find out how in this more technical article – Smooth manifolds.)
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Rachel Thomas is Editor of Plus. Rachel would like to thank Graeme Segal for all his help and patience in explaining mathematical curvature. | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817106.73/warc/CC-MAIN-20240416191221-20240416221221-00797.warc.gz | CC-MAIN-2024-18 | 13,992 | 37 |
http://learninghubtz.co.tz/form4-necta-qns-ans.php?sub=Y2hlbWlzdHJ5&yr=MjAxNg%3D%3D | math | (b) John measured the volume of gas produced when 5 g of two chemicals X and Y were added separately to hydrogen peroxide under identical conditions. His results for this experiment are represented on the graph below.
John claimed that Y is a better catalyst than X. His partner Steven did not agree.
Why does Steven think that John’s conclusion is wrong?
After the experiment, Steven recovered 5 g of X and 1 g 1 of Y from the two experiments. He claimed that John was wrong. Does Steven’s claim true? Give a reason.
(b) 25cm 3 samples of water A, B, C and D were tested with soap solution. The volume of soap solution required to produce a lather that lasted for a minute was recorded. Fresh samples of each were boiled and tested again with soap solution. The results are shown in Table 1.
Volume of soap solution required (cm 3 ) before boiling
Volume of soap solution required (cm 3 ) after boiling
Which sample probably contains temporary hardness of water only?
Which sample probably contains both permanent and temporary hardness of water? Give a reason for your answer.
13. 0.48g of a metal, M was placed in a test tube and hot copper (II) sulphate solution was added to it and stirred until the reaction stopped. The metal (M) displaced copper from copper (II) sulphate solution. Copper was filtered, washed with water, dried at 1000 C and the mass found to be 1.27g. Given that, the balanced chemical reaction that occurred is M (s) + CuSO 4(aq) MSO 4(aq) + Cu (s)
The number of moles of copper that were formed and the number of moles of M that were used in the reaction.
The relative atomic mass of M and hence identify metal M.
(b) State the appearance of the metal formed (Cu).
(c) With ionic equations, explain why the reaction can be considered to involve both oxidation and reduction. | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100016.39/warc/CC-MAIN-20231128214805-20231129004805-00583.warc.gz | CC-MAIN-2023-50 | 1,806 | 14 |
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https://studyres.com/doc/168217/chapter-8-second | math | * Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project
Chapter 8 Second-Order Circuit SJTU 1 What is second-order circuit? A second-order circuit is characterized by a secondorder differential equation. It consists of resistors and the equivalent of two energy storage elements. Typical examples of second-order circuits: a) series RLC circuit, b) parallel RLC circuit, c) RL circuit, d) RC circuit SJTU 2 1. The Series RLC Circuit 2. The Parallel RLC Circuit 3. Second-Order Circuit Complete Response SJTU 3 1. The Series RLC Circuit FORMULATING SERIES RLC CIRCUIT EQUATIONS Eq.(7-33) SJTU 4 The initial conditions To solve second-order equation, there must be two initial values. SJTU 5 ZERO-INPUT RESPONSE OF THE SERIES RLC CIRCUIT With VT=0(zero-input) Eq.(7-33) becomes Eq.(3-37) try a solution of the form then characteristic equation Eq.(7-39) SJTU 6 In general, a quadratic characteristic equation has two roots: Eq.(7-40) three distinct possibilities: Case A: If , there are two real, unequal roots Case B: If , there are two real, equal roots Case C: If roots , there are two complex conjugate SJTU 7 A source-free series RLC circuit Special case: Vc(0)=V0, IL(0)=0 V0 V(t) tM I(t) SJTU 8 t > tM tM>t>0 What happens when R=0? SJTU 9 Second Order Circuit with no Forcing Function vc(0) = Vo , iL(0) = Io. I. OVER DAMPED: R=2 , L= 1/3 H, C=1.5F, Vo=1V, Io=2A iL(t) = -0.7 e -0.354t +2.7 e -5.646t A vc(t) = 1.318 e -0.354t -0.318 e -5.646t V SJTU 10 SJTU 11 SJTU 12 II. CRITICALLY DAMPED: R=0.943 , L= 1/3 H, C=1.5F, Vo=1V, Io=2A iL(t) = 2e -1.414t -5.83t e -1.414t A vc(t) = e -1.414t+ 2.75 t e -1.414t V SJTU 13 SJTU 14 SJTU 15 III. UNDER DAMPED: R=0.5 , L= 1/3 H, C=1.5F, Vo=1V, Io=2A iL(t) =4.25 e -0.75t cos(1.2t + 1.081) A vc(t) = 2 e -0.75t cos(1.2t - 1.047) V SJTU 16 SJTU 17 SJTU 18 IV. UNDAMPED: R=0 , L= 1/3 H, C=1.5F, Vo=1V, Io=2A iL(t) =2.915 cos(1.414t + 0.815) A vc(t) =1.374 cos(1.414t - 0.756) V SJTU 19 SJTU 20 SJTU 21 EXAMPLE 7-14 A series RLC circuit has C=0.25uF and L=1H. Find the roots of the characteristic equation for RT=8.5kohm, 4kohm and 1kohm * SOLUTION: For RT=8.5kohm, the characteristic equation is whose roots are These roots illustrate case A. The quantity under the radical is positive, and there are two real, unequal roots at S1=-500 and S2=-8000. SJTU 22 * For RT=4kohm, the characteristic equation is whose roots are This is an example of case B. The quantity under the radical is zero, and there are two real, equal roots at S1=S2=-2000. * For RT=1kohm the characteristic equation is whose roots are The quantity under the radical is negative, illustrating case C. In case C the two roots are complex conjugates. SJTU 23 In case A the two roots are real and unequal and the zero-input response is the sum of two exponentials of the form Eq.(7-48a) In case B the two roots are real and equal and the zero-input response is the sum of an exponential and a damped ramp. VC (t ) K1e t K 2tet Eq.(7-48b) In case C the two roots are complex conjugates and the zero-input response is the sum of a damped cosine and a damped sine. t VC (t ) e ( K1Cosdt K 2 Sindt ) SJTU Eq.(7-48c) 24 EXAMPLE 7-15 The circuit of Figure 7-31 has C=0.25uF and L=1H. The switch has been open for a long time and is closed at t=0. Find the capacitor voltage for t 0 for (a) R=8.5k ohm, (b) R=4k ohm, and (c) R=1k ohm. The initial conditions are Io=0 and Vo=15V. SOLUTION: Fig. 7-31 •(a) In Example 7-14 the value R=8.5kohm yields case A with roots S1=-500 and S2=-8000. The corresponding zero-input solution takes the form in Eq.(7-48a). SJTU 25 The initial conditions yield two equations in the constants K1 and K2: Solving these equations yields K1=16 and K2 =-1, so that the zero-input response is SJTU 26 •(b) In Example 7-14 the value R=4kohm yields case B with roots S1=S2=-2000. The corresponding zero-input response takes the form in Eq.(7-48b): The initial conditions yield two equations in the constants K1 and K2: Solving these equations yields K1=15 and K2= 2000 x 15, so the zero-input response is SJTU 27 •c) In Example 7-14 the value R=1k ohm yields case C with roots . The corresponding zero-input response takes the form in Eq.(7-48c): VC (t ) e t ( K1Cosdt K 2 Sindt ) The initial conditions yield two equations in the constants K1 and K2: Solving these equations yields K1=15 and K2=( ) , so the zero-input response is SJTU 28 Fig. 7-32 SJTU 29 In general, a quadratic characteristic equation has two roots: Eq.(7-40) three distinct possibilities: Case A: If roots Case B: If roots Case C: If roots , there are two real, unequal Overdamped situation , there are two real, equal Ciritically damped situation , there are two complex conjugate Underdamped situation SJTU 30 2. The Parallel RLC Circuit FORMULATING PARALLEL RLC CIRCUIT EQUATIONS Eq. 7-55 SJTU 31 Equation(7-55) is second-order linear differential equation of the same form as the series RLC circuit equation in Eq.(733). In fact, if we interchange the following quantities: we change one equation into the other. The two circuits are duals, which means that the results developed for the series case apply to the parallel circuit with the preceding duality interchanges. The initial conditions iL(0)=Io and SJTU 32 set iN=0 in Eq.(7-55) and obtain a homogeneous equation in the inductor current: A trial solution of the form IL=Kest leads to the characteristic equation Eq. 7-56 SJTU 33 There are three distinct cases: Case A: If (GNL)2-4LC>0, there are two unequal real roots and the zero-input response is the overdamped form Case B: (GNL)2-4LC=0, there are two real equal roots and the zero-input response is the critically damped form Case C:(GNL)2-4LC<0, there are two complex, conjugate roots and the zero-input response is the underdamped form s1 , s2 j t iL (t ) e ( K1Cos t K 2 Sin t ) t 0 SJTU 34 EXAMPLE 7-16 In a parallel RLC circuit RT=1/GN=500ohm, C=1uF, L=0.2H. The initial conditions are Io=50 mA and Vo=0. Find the zeroinput response of inductor current, resistor current, and capacitor voltage SOLUTION: From Eq.(7-56) the circuit characteristic equation is The roots of the characteristic equation are SJTU 35 Evaluating this expression at t=0 yields SJTU 36 SJTU 37 EXAMPLE 7-17 The switch in Figure 7-34 has been open for a long time and is closed at t=0 (a) Find the initial conditions at t=0 (b) Find the inductor current for t0 (c) Find the capacitor voltage and current through the switch for t 0 SOLUTION: (a) For t<0 the circuit is in the dc steady state Fig. 7-34 SJTU 38 (b) For t 0 the circuit is a zero-input parallel RLC circuit with initial conditions found in (a). The circuit characteristic equation is The roots of this equation are The circuit is overdamped (case A), The general form of the inductor current zero-input response is using the initial conditions SJTU 39 The initial capacitor voltage establishes an initial condition on the derivative of the inductor current since The derivative of the inductor response at t=0 is The initial conditions on inductor current and capacitor voltage produce two equations in the unknown constants K1 and K2: SJTU 40 Solving these equations yields K1=30.3 mA and K2=-0.309 ma The zero-input response of the inductor current is (c) Given the inductor current in (b), the capacitor voltage is For t 0 the current isw(t) is the current through the 50 ohm resistor plus the current through the 250 ohm resistor SJTU 41 3. Second-order Circuit Complete Response The general second-order linear differential equation with a step function input has the form Eq. 7-60 The complete response can be found by partitioning y(t) into forced and natural components: Eq. 7-61 yN(t) --- general solution of the homogeneous equation (input set to zero), yF(t) is a particular solution of the equation ∴ yF=A/ao SJTU 42 Combining the forced and natural responses Eq. 7-67 EXAMPLE 7-18 The series RLC circuit in Figure 7-35 is driven by a step function and is in the zero state at t=0. Find the capacitor voltage for t 0. SOLUTION: Fig. 7-35 SJTU 43 By inspection, the forced response is vCF=10V. In standard format the homogeneous equation is the natural response is underdamped (case C) SJTU 44 The constants K1 and K2 are determined by the initial conditions. These equations yield K1= -10 and K2= -2.58. The complete response of the capacitor voltage step response is SJTU 45 General second-order circuit Steps: 1. Set a second-order differential equation 2. Find the natural response yN(t) from the homogeneous equation (input set to zero) 3. Find a particular solution yF(t) of the equation 4. Determine K1 and K2 by the initial conditions 5. Yield the required response SJTU 46 Summary •Circuits containing linear resistors and the equivalent of two energy storage elements are described by second-order differential equations in which the dependent variable is one of the state variables. The initial conditions are the values of the two state variables at t=0. •The zero-input response of a second-order circuit takes different forms depending on the roots of the characteristic equation. Unequal real roots produce the overdamped response, equal real roots produce the critically damped response, and complex conjugate roots produce underdamped responses. •Computer-aided circuit analysis programs can generate numerical solutions for circuit transient responses. Some knowledge of analytical methods and an estimate of the general form of the expected response are necessary to use these SJTU 47 analysis tools. | s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153897.89/warc/CC-MAIN-20210729203133-20210729233133-00439.warc.gz | CC-MAIN-2021-31 | 9,571 | 2 |
http://sepaperszkx.emprendiendo.me/an-analysis-of-douglass-mcgregors-theory-x-and-theory-y.html | math | He referred to these two perceptions as theory x and theory y douglas mcgregor then arrived at the conclusion that the failure mode and effects analysis (fmea). Douglas mcgregor (1906 -1964) was a famous management professor in the field of personal development and motivational theory he is best known for his development of the theory x and theory y , a leadership theory on two different leadership styles. Mcgregor theory x & y introductıon theory x and theory y are theories of human motivation created and developed by douglas mcgregor at the mit sloan school of. Definition: the theory x and theory y are the theories of motivation given by douglas mcgregor in 1960's these theories are based on the premise that management has to assemble all the factors of p. Mcgregor developed two theories of human behaviour at work: theory and x and theory y he did not imply that workers would be one type or the other rather, he saw the two theories as two extremes - with a whole spectrum of possible behaviours in between the management implications for theory x.
Douglas mcgregor - comparison of theory x versus theory y (in english) douglas mcgregor - theory x and theory y inc diagrams (in english). Theory x and theory y were first introduced in the early work of douglas mcgregor mcgregor's work made a significant impact on managerial thought it appeared at a time when the behavioral sciences were playing an increasing role in how managers thought about their work it was a period. Feedback from a theory x and theory y perspective the latter sparked a popular theory by a professor at mit named douglas mcgregor mcgregor observed that mangers. Douglas mcgregor - a lasting impression mcgregor's theory x and theory y were the foundation of the human side of enterprise theory x is based on a.
The first being theory y mangers and theory x managers (waddell, jones, george 2010, p49) in this essay i will elaborate more on the douglas mcgregor's theory x and y as well as how the theory has added value in the methods of the management that manager's today use to reach organizational goals. Theory x and theory y please read about douglas mcgregor's theory x and y the exercise sure to use analysis, com theory x / theory y douglas mcgregor. Theory x and theory y framework proposed by mcgregor in his classic book the human side of enterprise (1960) consists of two alternative set of assumptions theory x percieves employees to be lazy, irresponsible and untrustworthy, while according to theory y employees are approached as one of the. Theory x and theory y was created and developed by douglas mcgregor at the mit sloan school of management in the 1960s it describes two very different attitudes towards workforce motivation mcgregor felt that companies followed either one of these approaches. Tion, essays of douglas mcgregor, edited by w g bennis and e h schein (cambridge, mcgregor's six assumptions of theory y and his ideas of.
View and download theory x and theory y essays examples douglas mcgregor's theory x and theory y textual analysis shows that latin business culture focuses. In his book the human side of enterprise (1960), douglas mcgregor studied behavior patterns of individuals in the workplace, and formulated the x and y theory. Key difference - theory x vs theory y theory x and theory y were introduced in 1960 by douglas mcgregor, an american social psychologist in his book 'the human side of enterprise' this is one of the most famous motivational theo. Episode 109: douglas mcgregor's theory x & theory y alanis business academy developed in 1960 by douglas mcgregor, theory x & theory y presents two contrasting views of human behavior in the. Douglas mcgregor was an american social psychologist best known for theory x and theory y opposing assumptions about human behaviour behind every management decision or action building on abraham maslow's hierarchy of needs , mcgregor set out two opposing assumptions about human nature and motivation.
Douglas mcgregor's theory x and theory y biography of douglas mcgregor douglas mcgregor was born on 1906 in detroit, america in 1895, it was here that his grandfather, thomas mcgregor started his business and given its name as, mcgregor institute. Theory x and theory y are theories of human work motivation and management they were created by douglas mcgregor while he was working at the mit sloan school of management in the 1950s, and developed further in the 1960s. Motivation - douglas mcgregor's x and y theory background d ouglas mcgregor, an american social psychologist, developed his theory x and theory y of human motivation at the mit sloan school of management in the 1960s. Douglas mcgregor's theory x and theory y in his 1960 management book, the human side of enterprise, douglas mcgregor made his mark on the history of organizational management and motivational psychology when he proposed the two theories by which managers perceive employee motivation.
A theory x manager knows only the autocratic mode, but a theory y manager can chose to be autocratic, paternalistic, consultative or participatory mcgregor' theories are useful for analysis as well as for the selection of an adequate intervention. The concept of theory x and theory y was developed by social psychologist douglas mcgregor it describes two contrasting sets of assumptions that managers make about their people: theory x - people dislike work, have little ambition, and are unwilling to take responsibility. The limitations of theory x and theory y (douglas mcgregor) definition of theory x and theory y: theory x and theory y was an idea started by douglas mcgregor in the year 1960. Managers generally have one of two perspectives regarding their employees many years ago a professor named douglas mcgregor dubbed these perspectives theory x and theory y theory x assumes that.
Douglas mcgregor devised his concept of theory x and theory y in the usa in the 1950's using a survey of managers, which he then proposed in his book, 'the human side of enterprise' in the 1960's. Theory x and y analysis in management download theory x and y analysis in management this course work is going to focus on the work of douglas mcgregor (1908. - douglas mcgregor's theory x and theory y biography of douglas mcgregor douglas mcgregor was born on 1906 in detroit, america in 1895, it was here that his. | s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583511203.16/warc/CC-MAIN-20181017153433-20181017174933-00449.warc.gz | CC-MAIN-2018-43 | 6,372 | 7 |
https://swmath.org/software/15811 | math | LSDE - A program package for the simulation, graphical display, optimal filtering and maximum likelihood estimation of Linear Stochastic Differential Equations. Continuous time models with sampled data possess several advantages over conventional time series and panel models (special issue 62:1, 2008, of Statistica Neerlandica). For example, data with unequal time intervals can be treated efficiently, since the dynamic model parameters of the system model are not affected by the measurement process. In the linear case, the nonlinear parameter restrictions of the sampled model can be implemented with specialized Kalman filter software (e.g. LSDE) or with structural equations models (SEM) allowing such nonlinear parameter restrictions. In the nonlinear case, most filtering algorithms are formulated in discrete time, but mixed continuous-discrete approaches are also scattered in the literature. The Mathematica program SDE is a collection of algorithms with consequent focus on the mixed continuous-discrete case: continuous time updates combined with discrete time measurement updates. Included are the classical methods of extended Kalman filtering and higher order nonlinear filters, but also new developments such as the unscented Kalman filter (UKF) and the Gauss-Hermite filter (GHF) using approximations of the filter density. We also use the Edgeworth-Hermite expansion of probability densities to obtain generalized Gauss filters (GGHF) utilizing higher order moments such as skewness and kurtosis.
Keywords for this software
References in zbMATH (referenced in 7 articles )
Showing results 1 to 7 of 7.
- Singer, Hermann: SEM modeling with singular moment matrices. II: ML-estimation of sampled stochastic differential equations (2012)
- Singer, Hermann: Continuous-discrete state-space modeling of panel data with nonlinear filter algorithms (2011)
- Singer, Hermann: SEM modeling with singular moment matrices. I: ML-estimation of time series (2010)
- Delsing, Marc J. M. H.; Oud, Johan H. L.: Analyzing reciprocal relationships by means of the continuous-time autoregressive latent trajectory model (2008)
- Oud, Johan H. L.; Singer, Hermann: Continuous time modeling of panel data: SEM versus filter techniques (2008)
- Oud, Johan H. L.; Jansen, Robert A. R. G.: Continuous time state space modeling of panel data by means of sem (2000)
- Singer, Hermann: Continuous panel models with time dependent parameters (1998) | s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103624904.34/warc/CC-MAIN-20220629054527-20220629084527-00617.warc.gz | CC-MAIN-2022-27 | 2,441 | 11 |
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