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https://www.tr.freelancer.com/projects/engineering-electronics/semiconductor-related-answers-needed/
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math
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Semiconductor Device Fabrication
Subject is Semiconductor Device Fabrication
I want you to answer all questions in the test papers and everything you need such as laws you will found with the first papers and the seam low for the 2, 3 papers and there are 3 papers.
Part of questions, easy, and you can find the answer in lectures materials and the other part is issues and all laws you need to resolve these question you will found in lectures.
(I have some final answers to the questions and when you send me the solution I will make sure that it is correct so if you cannot resolve correctly told me from now, please.)
For the theoretical questions I hope the solution will be briefly and answer the question clearly.
If you can’t solve the questions, told me from now I do not want to wait then I get wrong answer.
I'm a student at one of the most prominent technological institutes in India presently pursuing a Masters degree in Microelectronics.. Thus, I feel I can easily complete your semiconductor fabrication related work, as Daha Fazla
Bu iş için 3 freelancer ortalamada $45 teklif veriyor
Sir I am an electronics engineer nd I can give the answers of ur questions related to your semiconductor [login to view URL] I am ready to work on your project.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267867055.95/warc/CC-MAIN-20180624195735-20180624215735-00021.warc.gz
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https://www.enotes.com/homework-help/why-atomic-mass-oxygen-15-9994-133295
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math
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Why is the atomic mass of oxygen 15.9994?
Oxygen has 3 different stable isotopes. The most prevalent version of these is Oxygen 16, which has 8 protons and 8 neutrons, for a total atomic mass of 16. O16 accounts for 97.765% of all oxygen atoms on Earth. Oxygen 17 contains 8 protons and 9 neutrons, for an atomic mass of 17, and Oxygen 18 contains 8 protons and 10 neutrons, for an atomic mass of 18. If all (100%) oxygen atoms were Oxygen 16, the atomic mass for all oxygen atoms would be 16; the addition of the two rare isotopes, since they are heavier, make the average atomic mass higher.
However, average atomic mass is listed as less than 16 -- this is because there are also radioisotopes of oxygen -- meaning that there are isotopes of oxygen that are radioactive. There are 9 of these, going up to an atomic mass of 24 (which means the oxygen has 8 protons and 16 neutrons!) These, however, are relatively short lived. The preponderance of the radioisotopes O12, O13, O14, and O15, with 4 through 7 neutrons, respectively, lowers the atomic mass to be just under 16.
Atomic mass and atomic weight are different. Atomic mass refers to the mass of an individual atom of a particular isotope. The atomic mass is, therefore, the total mass of nutons, protons and also electrons(though negligible) of one single isoptope of the element.Whereas, the atomic weight is a weighted mean of ratio atomic masses of the isotopes of an element to the 1/12 of atomic mass of carbon-12, the weights being their natural abundance of the isopes in a planet or a given situation. The natural abundance may vary from planet to planet.But at a particular time in a planet the atomic weight remains constant and may vary slightly over time.
Oxygen has several isotopes. But the most stanble isotopes and their atomic masses are as below:
Isotopes Protons Nutrons Atomic mass Aundance fraction
16O 8 8 16 0.99757
17O 8 9 17 0.00038
18O 8 10 18 0.00205
Therefore, The atomic weight of oxygen is
(16*(0.99757)+17*(0.00038)+18*(0.00205)/(1/12 of atomic mass of carbon12) = 16.00448 .
Again, the atomic mass of an isotope is a whole number as there is no fractional protons or nutrons are there.
The relative atomic mass of any atom is the number of times the mass of one atom of an element is greater than 1/12 of the mass of one carbon-12 atom.
For examle, oxygen has an mass of about 8, so the answer should be
Relative atomic mass= 8/ (1/12 of 6)
One atom of oxygen is 16 times heavier than 1/12 of an atom of carbon-12, so the relative atomic mass is 12.
The atomic mass of oxygen is 15.9994 because that is the average mass of all of it's isotopes.
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https://sciencedemonstrations.fas.harvard.edu/presentations/rating/%E2%98%85%E2%98%85?page=6
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math
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Certain materials (sugar in this experiment) are optically active because the molecules themselves have a twist in them. When linearly polarized light passes through an optically active material, its direction of polarization is rotated. The angle of rotation depends on the thickness of the material and the wavelength of the light.
Due to the oblateness of the Earth, the gravitational force between the Earth and the Sun sets up a couple which causes the Earth's axis of rotation to precess. An adapted globe shows what is meant by precession.
How it works:
An old 8" (19cm) globe has been modified 1 to allow it to precess on its axis. A 23° cone is cut into the south pole, and a cone of metal supported by a metal equatorial ring has been inserted. This makes the globe bottom heavy (and...
J. L. M. Poiseulle and G. H. L. Hagen determined that the laminar flow rate of an incompressible fluid along a pipe is proportional to the fourth power of the pipe's radius. To test this idea, we'll show that you need sixteen tubes to pass as much water as one tube twice their diameter.
Ball on string orbits with increasing speed as string is shortened.
What it shows:
An object moving in a circular orbit of radius r has an angular momentum given by:
L = r × mv = mr2ω.
A simple way to show conservation of angular momentum is a ball on a string, whirled around your head. As you change the length of the string, the ball's orbital speed changes to conserve angular momentum.
How it works:
The orbiter consists of a meter length of cord with a wooden ball at one end and a wooden anchor at the other. The cord passes...
The current in a circuit consisting of a capacitor, inductor, and resistor will oscillate back and forth as the capacitor charges and discharges.
How It Works
The circuit layout is shown in the figure below. Initially the knife switch links the capacitor to the battery. Switching to complete the LRC circuit allows the capacitor to discharge. The current I in the circuit increases, as does the magneic field B inside the inductor. When the capacitor charge is zero, I and B are a maximum (the energy of the circuit is now stored in the inductor). As the...
A model to demonstrate the precession of the Moon's orbit relative to the ecliptic. It is useful for discussing the conditions necessary for the occurrence of an eclipse.
How it works:
A large aluminum disk represents the plane of the Moon's orbit about the Earth. The disk lies flush with the box surface it sits in; the plane of the box representing the Ecliptic. The Moon's own orbit is inclined at 5° to the ecliptic, and precesses with an 18 year period. You...
For a body to reach terminal velocity when falling through a fluid, the drag force (given by Stoke's Law) coupled with the buoyant force (from Archimedes' principle) need to balance the falling object's weight. Leaving derivations to other great texts you end up with
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https://www.easy-due.com/%E7%BB%9F%E8%AE%A1%E4%BB%A3%E5%86%99-qbus5002-quantitative-methods-for-accounting-assignment/
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math
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QBUS5002: Quantitative Methods for Accounting
Assignment (Part 1)
2. Event Management. An events manager is planning to hold a festival in Sydney for the entire month
of July in 2022 and asks the weather expert for some advice on the likely number of days it could
rain which could impact the number of people attending the festival. The weather expert notes
that historically 21% of all days are rainy days for the month of July in Sydney. The weather
expert believes that the number of rainy days in July in 2022 could be modelled with a Binomial
(a) (2 points) Discuss the requirements of the Binomial distribution and whether you feel it is
appropriate in the current scenario.
(b) (3 points) Assuming the Binomial distribution is appropriate for modelling the number of rainy
days in July 2022, determine the probabilities of the following:
i Exactly 8 rainy days in July next year
ii Less than 9 rainy days of rain in July next year
(c) (2 points) What is the expected number of rainy days in Sydney during July next year and
what is the variance of the number of rainy days?
The events manager is also concerned about the possibility of serious transport disruptions to
the Sydney rail network, which can seriously impact the number of people able to attend the
festival. The events manager contacts Transport for NSW who inform her that serious disruptions typically occur at a rate of 1 per 40 weekdays. On weekends, disruptions are less frequent
occurring at a rate of 1 per 80 days.
(d) (2 points) The events manager believes the number of disruptions on weekdays and weekends
can be separately modelled as Poisson random variables. Discuss whether you feel the choice
of the Poisson distribution is appropriate for modelling the number of disruptions on either
weekdays or weekends.
(e) (3 points) Assuming the Poisson distribution is appropriate for modelling these disruptions,
determine the probabilities of the following:
i No more than 4 transport disruptions on weekdays during July next year
ii Zero transport disruptions on weekends during July next year
(f) (2 points) Find the mean and variance for the number of weekday disruptions in July next year.
(g) (2 points) Find the mean and variance for the number of weekend disruptions in July next year.
(h) (4 points) The events manager believes the level of profit from the festival is linked to both the
amount of rain and the number of transport disruptions in the following way:
P = 500 − 24R − 36D − 40E
where P is the amount of profit measured in thousands of dollars, R is the number of rainy days,
D is the number of weekday transport disruptions, and E is the number of weekend transport
disruptions all in July next year. Calculate the expected profit for the festival, as well as the
standard deviation of profit, stating any required assumptions.
3. Website Speed. The speed at which you can log into a website through a smartphone is an important
quality characteristic of that website. In a recent test, the mean time to log into the INFORMS
OR/MS Tomorrow website was 6.734 seconds. Suppose that the download time is normally distributed, with a standard deviation of 2.7 seconds. What is the probability that a download time
(a) (2 points) less than 2 seconds?
(b) (2 points) between 1.8 and 2.4 seconds?
(c) (2 points) 99% of the download times are slower (higher) than how many seconds?
(d) (2 points) 95% of the download times are between what two values, symmetrically distributed
around the mean?
(e) (1 point) Suppose the download times are uniformly distributed between 1 to 13 seconds. What
is your answer to 3(b)?
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https://www.webmasterworld.com/foo/3367964.htm
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math
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Welcome to WebmasterWorld Guest from 126.96.36.199
Forum Moderators: open
So, presuming I want a function which describes the quality of my socks... how do I model and optimize it? I've taken a few courses in basic calculus and statistics, but have no idea how to model this. What branch of mathematics deals with these sorts of problems, and what is a good (better?) example of an attendant/canonical problem for that branch?
Talk about niche... ; )
You would then need a understanding of Brane Theory and 11 diminsional space, to explain why a dryer can transport exactly one sock and never a pair, into a parallel universe.
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http://newsy-today.com/twelve-injured-including-six-police-as-molotov-cocktail-is-thrown-into-a-restaurant-in-paris-daily-mail/
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math
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Twelve hurt including six police as 'Molotov cocktail is tossed right into a restaurant' in Paris
Twelve people including six mother and father been hurt following a Molotov cocktail exploded inside a restaurant in Paris. Three people endured severe burns and needed to be airlifted to hospital following the fire started within the northern suburb of Aubervilliers at …
'Four hurt' as explosive tossed into Paris restaurant
Flames and smoke injure 12 as 'Molotov cocktail is tossed into Paris restaurant after robbery gone wrong'
Firebomb beeps at Paris restaurant on election day
NEWS.com.au -Scottish Daily Record -The Sun’s Rays -9news.com.au
all 12 news articles »
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https://ventureawards.ru/bdqy/143861-kcl-and-kvl-examples.html
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math
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Kcl and kvl examples pdf
Assume that I 1 = 3 A, R 1 = 2 Ω, R 2 = 3 Ω, R 3 = 2 Ω, I 1 = 3 A, V 1 = 15 V, Solution. KVL and KCL We have already shown how the elementary methods of DC circuit analysis can be extended and used in AC circuits to solve for the complex peak or effective values of voltage and current and for complex impedance or admittance.
Kirchhoff’s Current and Voltage Law (KCL and KVL) with Xcos example Let’s take as example the following electrical circuit. Insert the voltage expressions into the KVL equations to arrive at a set of mesh current equations. Find the currents flowing around the following circuit using Kirchhoff’s Current Law only. Note − KCL is independent of the nature of network elements that are connected to a node.
While applying the KCL the incoming current is taken as positive and the outgoing current is taken as negative. of EECS The base-emitter KVL equation is: 57 10 2 0.IV I−−−= B BE E Look what we now have ! To calculate RTh, replace all independent sources with their equivalent circuits i.e. Access Free Kvl And Kcl Practice Problems Norcap Kvl And Kcl Practice Problems Norcap If you ally habit such a referred kvl and kcl practice problems norcap ebook that will pay for you worth, get the no question best seller from us currently from several preferred authors. the circuit • Label each mesh with a mesh current • Write a KVL expression for each loop, and solve for the unknown voltages. Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits.They were first described in 1845 by German physicist Gustav Kirchhoff.
We offer kvl kcl problems solutions and numerous ebook collections from fictions to scientific research in any way. Two batteries, A and B are connected in parallel and an 80resistor is connected across the battery terminals, The emf and internal resistance of battery A are 100v and 5resistor respectively, and the corresponding values for battery B are 95v and 3resistor respectively.
1 Chapter 4 Techniques of Circuit Analysis 4.1 Terminology.
KVL: Voltages around any closed circuit path sum to zero DC Circuit Analysis Using Kirchoff’s Laws . They start with tableau equations, from which the reduced form of KVL is deduced. If the current does not change with time, but remains constant, we call it a direct current(dc).
With the two techniques to be developed we can analyse almost any circuit by obtaining a set of simultaneous equations that are then solved to obtain the required values of current or voltage. Kirchhoff’s Voltage Law (KVL) states that the algebraic sum of voltages around a loop or mesh is equal to zero. framework to apply Kirchhoff’s current and voltage laws (KCL and KVL) to the circuit problem and convert them to a linear algebra problem (e.g., works of Bode and Guillemin ) that can be solved numerically using a computer, they are not effective design tools. The KVL states that the algebraic sum of the voltage at node in a closed circuit is equal to zero. of voltages in a loop (or number of branches in a loop), and v m is the m th voltage. As per the rule of KCL, the current entering in the node is equal to current exiting in the node.
KVL states that the algebraic sum of all voltage round a closed path (or loop) is zero. Labels: KCL & KVL, Mesh & Nodal Analysis, Network Theory, Topic wise Questions. Kirchhoff’s Current Law (KCL) Kirchhoff’s Current Law is a statement of conservation of charge: what goes in must come out at every junction (node) on a circuit network. Apply the KCL at each node except the reference node.In this step for each node we assume the branch current is leaving from the node, and then we describe the branch current in term of node voltages. Kirchhoff’s laws known as Kirchhoff’s Current Law (KCL) and Kirchhoff’s Voltage Law (KVL) are based respectively on the conservation of charge and the conservation of energy and are derived from Maxwell’s equations. By KCL, the current entering each node is equal to the current leaving each node (in this series circuit, each node has only one entering and exiting current). Rather than writing a KVL around a single mesh you will write a KVL around two or more meshes.
nKirchhoff’s voltage law (KVL) nThe algebraic sum of all voltages between successive nodes in a closed path in the circuit is equal to zero. resulting from KVL and KCL are now differential equations rather than algebraic linear equations resulting from the resistive circuits. Kirchhoff’s Current Law, often shortened to KCL, states that “The algebraic sum of all currents entering and exiting a node must equal zero.” This law is used to describe how a charge enters and leaves a wire junction point or node on a wire. Independent KCL/KVL equations A different choice of tree gives a different set of basic cutsets and basic loops. Title: KCL and KVL Applications Date: August 2, 2016 P URPOSE OF THE EXPERIMENT The purpose of this laboratory experiment was to verify the Kirchhoff’s Voltage Law (KVL) and Kirchhoff’s Current Law (KCL) in the analysis of electrical circuits.
Tips for KCL, KVL • Find one formulation which works for you and stick with it.
53-58 The following slides were derived from those prepared by Professor Oldham For EE 40 in Fall 01 20 min Quiz on HW 1-4 at start of class on Wed. KVL KCL Ohm's Law Circuit Practice Problem - YouTube KVL states that the algebraic sum of all voltage round a closed path (or loop) is zero. Now here are some solved problems on KCL and examples on properties of current source and we will also discuss about current division method for calculating current in the circuit.
A simple circuit with two voltage sources and two resistors solved using only KVL. AC Transients - GATE Study Material in PDF In the previous article we have seen about Source Free RC Circuits, Source free RLC Circuits and Networks with Sources along with examples for each. Figure 1: KCL Analysis of a Circuit The node in the center of this circuit involves four currents. Practice Problem: Using KCL, KVL, and Ohm’s Law to Solve for Unknown Currents and Voltages. Kirchho ’s laws 4 a v v 6 v 3 2 i 5 V 0 v I 0 5 R i 4 6 3 i 3 v 4 i 2 2 R 1 v 1 i 1 A B C E D * Kirchho ’s current law (KCL):P i k = 0 at each node.
Where To Download Kvl And Kcl Practice Problems Norcap Kvl And Kcl Practice Problems Norcap As recognized, adventure as well as experience just about lesson, amusement, as well as treaty can be gotten by just checking out a ebook kvl and kcl practice problems norcap moreover it is not directly done, you could put up with even more something like this life, approximately the world. Bookmark File PDF Kvl Kcl Problems Solutions could resign yourself to even more regarding this life, around the world. KCL is the basis of nodal analysis – in which the unknowns are the voltages at each of the nodes of the circuit. Kirchoffs Voltage Law (KVL) The algebraic sum of voltages around each loop is zero Beginning with one node, add voltages across each branch in the loop (if you encounter a + sign first) and subtract voltages (if you encounter a sign first).
The sum of the two currents entering the node (the current from elements A and D) are equal to the two currents leaving the node (towards elements B and C). But any set of independent KCL and KVL equations gives essentially the same information about the circuit. Once we have these nodal voltages, we can use them to further analyze the circuit. KCL –Nodal Analysis KVL –Loop Analysis To determine the number of equations obtained by using KCL or KVL, we use the graphical representation of the circuit. sectional KCL, multiple-loop KVL, and related applications be shown appropriately f or AC circuits, and other time-varying circuits in undergraduate curriculums. Lecture 3 Definitions: Circuits, Nodes, Branches Kirchoffs Voltage Law (KVL) Kirchoffs Current Law (KCL) Examples and generalizations RC Circuit Solution. The KCL states that the summation of current at a junction remains zero and according to KVL the sum of the electromotive force and the voltage drops in a closed circuit remains zero. characteristic equation o N KCL/KVL Node-voltage (or mesh current methods) reduce the number of equations to be solved by atomically satisfying all KVLs (or KCLs).
Download File PDF Circuit Analysis Examples Circuit Analysis Examples Right here, we have countless ebook circuit analysis examples and collections to check out. Kirchhoff's First & Second Laws with solved Example A German Physicist “Robert Kirchhoff” introduced two important electrical laws in 1847 by which, we can easily find the equivalent resistance of a complex network and flowing currents in different conductors. The nitty-nitty-gritty, circuit analysis examples using Ohm's Law and Kirchoff's Current and Voltage Laws. In this chapter, we'll solve some examples of voltage and current division in AC circuits. With KVL and KCL and with the relationship between voltage and current for each component, you can figure out the current through and the voltage across any and every element in a circuit. KVL: The algebraic sum of the branch voltages around any closed loop equals zero .
on Solve By Source Definitions, KCL and KVL.
The number of independent KVL equations is equal to the number of meshes for a 2-D circuit, or to the number of elements, minus the number of nodes, plus one for circuits in general. Kirchhoff’s Current and Voltage Law (KCL and KVL) with Xcos example Real world applications electric circuits are, most of the time, quite complex and hard to analyze. Here, in this article we have solved ten different Kirchhoff’s Voltage Law Examples with solution and figure. Write KCL as Ai = 0, where A is a reduced incidence matrix that we will introduce later on, and i is a vector of all branch currents. Access Free Kvl And Kcl Problems Solutions Kirchhoff's Laws Solving Circuits with Kirchoff Laws. Theoretically calculate the voltages and currents for each element in the circuit and compare them to the measured values. In a series circuit (or a sub-circuit), there is only one path for current to flow.
Learning Objectives – KCL, KVL, Energy Flow • Sum of voltage drop around any loop of devices is always 0 (KVL); sum of currents into any node is always 0 (KCL). Apply KCL at each node and each supernode, using Ohm’s Law to express branch currents in terms of node voltages. Kirchhoff’s Current Law (KCL) – Conservation of Charge The current flowing out of a node in a circuit much equal the current flowing into the node. Once you find something you're interested in, click on the book title and you'll be taken to that book's specific page. Then we write the KCL equations for the nodes and solve them to find the respected nodal voltages. KCL is simply a statement that charges cannot accumulate at t he nodes of a circuit.
KCL at the left upper node tells us that the current in the 9 Ω resistor is i – 3 A (downwards). All voltages and currents in the circuit can be found by either of the following two methods, based on KVL or KCL respectively. However, it is possible to combine KCL and KVL laws into a com-pact formulation because most branch currents are directly functions of their respective branch voltages. 1/28/2014 6 Example 2 Find i1, i2, i3, i4 Example 2 (c ontd.) = 0.8 0 = 0.8 0 = 0.8 0 = 0.8 0 = 0.8 0 = 0.8 0 .
KCL Draw an arbitrary surface containing several nodes and write an equation based on KCL V R 1K R0 1K R1 1K R2 1K I R3 1K. We offer you this proper as without difficulty as easy habit to acquire those all. Capacitors in Parallel Ceq C1 C2 C3 C N Use KCL, voltage same across each capacitor.
Also, the current does not change crossing a resistor.
nMesh Analysis is based on a systematic application of KVL and can be used for planar circuits only. 2) Select a current variable and mesh for each simple loop (usually we traverse each loop in same direction, ie, clockwise. Access Free Kvl And Kcl Problems With Solutions Kvl And Kcl Problems With Solutions Thank you for reading kvl and kcl problems with solutions. Example 1: Find the three unknown currents and three unknown voltages in the circuit below: Note: The direction of a current and the polarity of a voltage can be assumed arbitrarily. Solve By Source Definitions, KCL and KVL - Solved Problems The two laws are KCL and KVL. KCL: (conservation of charge), and KVL: (topology) A circuit with N two-terminal element has 2N variables and need 2N equations: o N . Series electric circuits Three resistors (labeled R1, R2, and R3), connected in a chain from one terminal of the battery to the other.
Find the voltage across the current source and the current passing through the voltage source. At the node, KCL gives Applying KVL to the outer loop in fig(b) gives The Thevenin impedance is Example: Obtain I o current using Norton’s theorem. Access Free Kvl And Kcl Practice Problems Norcap Kvl And Kcl Practice Problems Norcap If you ally dependence such a referred kvl and kcl practice problems norcap book that will give you worth, acquire the categorically best seller from us currently from several preferred authors. However, in order to use KCL and KVL, it is necessary to determine the voltage of the entire graph or the value of the currents diverging from the start. King’s College London reviews the modules offered on a regular basis to provide up-to-date, innovative and relevant programmes of study. As many of the examples and prob-lems in this chapter and subsequent chapters suggest, there can be sev-eral types of current; that is, charge can vary with time in several ways. Figure 1: An example of KVL The perimeter of the circuit is also a closed loop, but since it includes loops 1 and 2 it would be repetitive to include a KVL equation for it. KVL and KCL for Different Circuits • With multiple voltage sources best to use KVL • Can write KVL equation for each loop • With multiple current sources best to use KCL • Can write KCL equations at each node.
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https://www.educationquizzes.com/us/middle-school-6th-7th-and-8th-grade/math/level-5-6-numbers---percentages---parts/
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math
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This Math quiz is called 'Numbers - Percentages - Parts' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.
It costs only $12.50 per month to play this quiz and over 3,500 others that help you with your school work. You can subscribe on the page at Join Us
Parts of percentages are parts out of 100. As you will be aware, percentages are a key subject in Math. A percentage is a fraction with a denominator of 100, e.g. 44% = 44/100. Percentages are often seen in day-to-day life.
Try your hand at this numbers quiz which focuses on percentage parts and see if you can get 100%!
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http://dr.njtc.edu.cn/content-6b81c0da45d740698c221d809cffb2cc-52a930056ef78615016f1d155c1009d2.html
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math
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2019年8月5日，数据恢复四川省重点实验室吴国成老师团队在《Chaos》（IF=2.643，SCI二区）杂志发表题为《New variable-order fractional chaotic systems for fast image encryption》的研究论文，加密速度和安全是信息加密技术的核心问题。现代数据常体现出数据量大、维度高的特点，目前该领域研究现状总体为加密速度快，但安全性不高；或者加密安全性高，但速度不快。围绕加密速度和安全是信息加密技术的核心问题，该文首次提出了短记忆、变分数阶方程的概念，并研究了混沌动力学理论，实现了快速、安全加密。
Abstract: New variable-order fractional chaotic systems are proposed in this paper. A concept of short memory is introduced where the initial point in the Caputo derivative is varied. The fractional order is defined by the use of a piecewise constant function which leads to rich chaotic dynamics. The predictor–corrector method is adopted, and numerical solutions of fractional delay equations are obtained. Then, this concept is extended to fractional difference equations, and generalized chaotic behaviors are discussed numerically. Finally, the new fractional chaotic models are applied to block image encryption and each block has a different fractional order. The new chaotic system improves security of the image encryption and saves the encryption time greatly.
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https://www.freezingblue.com/flashcards/print_preview.cgi?cardsetID=141367
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math
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Alice is considering two stocks. Stock A has a beta of .8 while stock B has a beta of 1.6. The risk premium is 4%. Alice believes the expected return on stock B would be twice as high as the expected return on A, and therefore she should invest in stock B. Which of the following statements is true?
Alice is incorrect regarding B's expected return; however, B does provide a higher expected return than A.
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s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988721278.88/warc/CC-MAIN-20161020183841-00375-ip-10-171-6-4.ec2.internal.warc.gz
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CC-MAIN-2016-44
| 406 | 2 |
https://brainmass.com/economics/labour-economics/marginal-product-function-236472
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math
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Q = Output
find the number of units of inputs (L) that maex total product function given r = 10 as well as Q
find L and Q that maximizes MPL© BrainMass Inc. brainmass.com March 4, 2021, 9:21 pm ad1c9bdddf
Here it is given that
Q = 6L2 R2 .10L3 R3
Also R is fixed at 10 units.
Now, the total product function (TPL) for input L is given by,
TPL = 6L2 (10)2 .10L3 (10)3 = 600L2 100L3
Thus, the marginal product function (MPL) for input L is given by,
= 1200L 300L2
The number of units of input L ...
The solution contains the determination of marginal product function (MPL) and also the determination of optimum Labor and output that maximizes MPL.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046155458.35/warc/CC-MAIN-20210805063730-20210805093730-00633.warc.gz
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CC-MAIN-2021-31
| 647 | 12 |
https://nrich.maths.org/public/topic.php?code=-68&cl=3&cldcmpid=5753
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math
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See if you can anticipate successive 'generations' of the two animals shown here.
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?
How efficiently can you pack together disks?
How much of the field can the animals graze?
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 corner.
A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?
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. . . .
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?
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
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?
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.
The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?
A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?
Show that among the interior angles of a convex polygon there cannot be more than three acute angles.
A blue coin rolls round two yellow coins which touch. The coins are the same size. How many revolutions does the blue coin make when it rolls all the way round the yellow coins? Investigate for a. . . .
The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?
Can you mark 4 points on a flat surface so that there are only two different distances between them?
Can you work out the dimensions of the three cubes?
A huge wheel is rolling past your window. What do you see?
Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.
In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?
Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?
Find all the ways to cut out a 'net' of six squares that can be folded into a cube.
Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?
How can you make an angle of 60 degrees by folding a sheet of paper twice?
A useful visualising exercise which offers opportunities for discussion and generalising, and which could be used for thinking about the formulae needed for generating the results on a spreadsheet.
A and C are the opposite vertices of a square ABCD, and have 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 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?
What is the minimum number of squares a 13 by 13 square can be dissected into?
In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells?
Can you maximise the area available to a grazing goat?
The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .
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.
Join pentagons together edge to edge. Will they form a ring?
Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?
This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .
If you move the tiles around, can you make squares with different coloured edges?
ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?
Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?
These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?
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.
A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start. How many Hamiltonian circuits can you find in these graphs?
Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
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CC-MAIN-2019-47
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https://www.hindawi.com/journals/aaa/2013/573583/ref/
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math
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- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
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- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 573583, 6 pages
A New Iterative Method for Solving a System of Generalized Mixed Equilibrium Problems for a Countable Family of Generalized Quasi-ϕ-Asymptotically Nonexpansive Mappings
College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China
Received 3 October 2012; Accepted 4 January 2013
Academic Editor: Satit Saejung
Copyright © 2013 Wei-Qi Deng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- B. Ali and M. S. Minjibir, “Convergence of a hybrid iterative method for finite families of generalized quasi-ϕ-asymptotically nonexpansive mappings,” Fixed Point Theory and Applications, vol. 2012, article 121, 2012.
- K. Goebel and W. A. Kirk, “A fixed point theorem for asymptotically nonexpansive mappings,” Proceedings of the American Mathematical Society, vol. 35, pp. 171–174, 1972.
- S.-y. Matsushita and W. Takahashi, “A strong convergence theorem for relatively nonexpansive mappings in a Banach space,” Journal of Approximation Theory, vol. 134, no. 2, pp. 257–266, 2005.
- S. Plubtieng and K. Ungchittrakool, “Hybrid iterative methods for convex feasibility problems and fixed point problems of relatively nonexpansive mappings in Banach spaces,” Fixed Point Theory and Applications, vol. 2008, Article ID 583082, 19 pages, 2008.
- S. S. Chang, H. W. Joseph Lee, and C. K. Chan, “A block hybrid method for solving generalized equilibrium problems and convex feasibility problem,” Advances in Computational Mathematics. In press.
- L.-C. Ceng, S.-M. Guu, H.-Y. Hu, and J.-C. Yao, “Hybrid shrinking projection method for a generalized equilibrium problem, a maximal monotone operator and a countable family of relatively nonexpansive mappings,” Computers & Mathematics with Applications, vol. 61, no. 9, pp. 2468–2479, 2011.
- Y. F. Su, H. K. Xu, and X. Zhang, “Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications,” Nonlinear Analysis. Theory, Methods & Applications, vol. 73, no. 12, pp. 3890–3906, 2010.
- E. U. Ofoedu and D. M. Malonza, “Hybrid approximation of solutions of nonlinear operator equations and application to equation of Hammerstein-type,” Applied Mathematics and Computation, vol. 217, no. 13, pp. 6019–6030, 2011.
- Z. Wang, Y. Su, D. Wang, and Y. Dong, “A modified Halpern-type iteration algorithm for a family of hemi-relatively nonexpansive mappings and systems of equilibrium problems in Banach spaces,” Journal of Computational and Applied Mathematics, vol. 235, no. 8, pp. 2364–2371, 2011.
- S.-s. Chang, C. K. Chan, and H. W. J. Lee, “Modified block iterative algorithm for quasi-ϕ-asymptotically nonexpansive mappings and equilibrium problem in Banach spaces,” Applied Mathematics and Computation, vol. 217, no. 18, pp. 7520–7530, 2011.
- Y. Yao, Y.-C. Liou, and S. M. Kang, “Strong convergence of an iterative algorithm on an infinite countable family of nonexpansive mappings,” Applied Mathematics and Computation, vol. 208, no. 1, pp. 211–218, 2009.
- H. Zegeye, E. U. Ofoedu, and N. Shahzad, “Convergence theorems for equilibrium problem, variational inequality problem and countably infinite relatively quasi-nonexpansive mappings,” Applied Mathematics and Computation, vol. 216, no. 12, pp. 3439–3449, 2010.
- W. Nilsrakoo and S. Saejung, “Strong convergence theorems by Halpern-Mann iterations for relatively nonexpansive mappings in Banach spaces,” Applied Mathematics and Computation, vol. 217, no. 14, pp. 6577–6586, 2011.
- S. S. Chang, H. W. J. Lee, C. K. Chan, and J. ai Liu, “Strong convergence theorems for countable families of asymptotically relatively nonexpansive mappings with applications,” Applied Mathematics and Computation, vol. 218, no. 7, pp. 3187–3198, 2011.
- S.-S. Zhang, “Generalized mixed equilibrium problem in Banach spaces,” Applied Mathematics and Mechanics, vol. 30, no. 9, pp. 1105–1112, 2009.
- S. S. Chang, J. K. Kim, and X. R. Wang, “Modified block iterative algorithm for solving convex feasibility problems in Banach spaces,” Journal of Inequalities and Applications, vol. 2010, Article ID 869684, 14 pages, 2010.
- Y. I. Alber, “Metric and generalized projection operators in Banach spaces: properties and applications,” in Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, vol. 178 of Lecture Notes in Pure and Applied Mathematics, pp. 15–50, Dekker, New York, NY, USA, 1996.
- I. Cioranescu, Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, vol. 62 of Mathematics and its Applications, Kluwer Academic Publishers Group, Dordrecht, The Netherlands, 1990.
- S. S. Chang, H. W. J. Lee, C. K. Chan, and W. B. Zhang, “A modified halpern-type iteration algorithm for totally quasi-ϕ-asymptotically nonexpansive mappings with applications,” Applied Mathematics and Computation, vol. 218, no. 11, pp. 6489–6497, 2012.
- H. K. Xu, “Inequalities in Banach spaces with applications,” Nonlinear Analysis. Theory, Methods & Applications, vol. 16, no. 12, pp. 1127–1138, 1991.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218190234.0/warc/CC-MAIN-20170322212950-00155-ip-10-233-31-227.ec2.internal.warc.gz
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CC-MAIN-2017-13
| 5,805 | 45 |
http://www.planetpdf.com/forumarchive/168370.asp
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math
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New Forum | Previous | Next | (P-PDF) What's Wrong with my PDF?
Topic: Font spacing is messed up in certain PDF files.
Conf: (P-PDF) What's Wrong with my PDF?, Msg: 168370
Date: 1/4/2009 04:31 AM
I've had this problem for a while now and I don't remember when it started but basically when I try to look at PDF files sometimes it looks like this:
here are the font properties for that particular PDF:
Some PDFs are fine, the ones that work appear to use embedded fonts of some sort I think. Here is the font properties from a random PDF that is FINE:
Can anyone suggest anything I can do to fix this?
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s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125945459.17/warc/CC-MAIN-20180421223015-20180422003015-00013.warc.gz
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CC-MAIN-2018-17
| 600 | 8 |
https://ok-em.com/linear-equations-test-78
|
math
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evaluate answers. calculator. Question 1: 1 pts. What value of satisfies the equation. Question 2: 1 pts.
Math understanding that gets you
No matter what level you're at, math is a subject that requires both understanding and practice.
Deal with mathematic question
Get math help online by speaking to a tutor in a live chat.
Average satisfaction rating 4.7/5
The best way to do your homework is to find the parts that interest you and work on those first.
Linear Equations Questions and Answers Example 1. Solve the following linear equations. (a) (3 – 7x)/ (15 + 2x) = 1 (b) 8x + 9 – 3x = 8 + 4x + 1 (c) 3x – 12 = 0 Solution: (a) (3
Determine math questions
To determine what the math problem is, you will need to take a close look at the information given and use your problem-solving skills. Once you have determined what the problem is, you can begin to work on finding the solution.
Work on the homework that is interesting to you
I can help you with any mathematic task you need help with.
Solve mathematic problem
To solve a math equation, you need to find the value of the variable that makes the equation true.
I can't wait for more upgrades! Hopefully upgrades that include; T(x-a)= x/T find for 'T', this really helped me a lot especially when it shows the steps, it's much more easier to learn and can help you with assignments or any kind of work involving math.
Also, sometimes they aren't able to solve all problems but that's not too often, it would be nice if this was compaitable with tablets. Our class goes super fast and I'm left trying to figure out my homework not having understood the lesson at all, best app ever literally can solve almost anything love it.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764495012.84/warc/CC-MAIN-20230127195946-20230127225946-00481.warc.gz
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CC-MAIN-2023-06
| 1,690 | 16 |
https://www.wikiwand.com/en/Shortest_path_problem
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math
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Shortest path problem
Computational problem of graph theory / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Shortest path problem?
Summarize this article for a 10 years old
SHOW ALL QUESTIONS
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
Computational problem of graph theory
The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortest path problem in graphs, where the vertices correspond to intersections and the edges correspond to road segments, each weighted by the length of the segment.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224652207.81/warc/CC-MAIN-20230606013819-20230606043819-00025.warc.gz
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CC-MAIN-2023-23
| 822 | 9 |
https://omarcafini.info/meet/graph-relationship-between-two-variables-in-statistics.php
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math
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Scatter Plots and Linear Correlation ( Read ) | Statistics | CK Foundation
Examining a scatterplot graph allows us to obtain some idea about the relationship between two variables. When the points on a scatterplot. The individual values can be read from the plot and an idea of the relationship between the variables across individuals is obtained. Even if the plot is not used . Business Statistics For Dummies. By Alan Anderson. A scatter plot (also known as a scatter diagram) shows the relationship between two quantitative.
The line of equality no change in values pre to during treatment is shown as a dashed line on the display. All points lie above the line of equality showing that values rose for each individual. Whilst the same information is given by the two displays, the scatterplot uses only one point to represent each individual compared to 2 points and a line for the line diagram.
Describing scatterplots (form, direction, strength, outliers)
The line diagram may be confusing to assess if there are changes in various directions, the scatterplot with the line of equality superimposed if necessary is easier to interpret. No information is lost, the display clearly shows the relationship between the variables and also highlights possible outliers.
- Scatter Plots
We saw an example earlier of the times it takes for a scorpion to capture its prey presented as a dot plot. Optimal sting use in the feeding behavior of the scorpion Hadrurus spadix. Dot plots can also be used to look at the differences between the distributions of groups.
In the example below, E coli specific SigA values are typically lower and also less spread out in the 'White UK' category. Dot plots can be used to look at whether values in one group are typically different from values in another group. In the example above, the plot shows it typically takes slightly longer for a scorpion to catch a prey with low activity than high activity.
Archives of Disease in Childhood,;71,F Horizontal bars denote medians for each group. The table below shows how social class varied between the two areas of the baby check scoring system. In both areas the mothers were mostly from social class III manual. This table shows how illness severity was related to baby-check score.
Describing scatterplots (form, direction, strength, outliers) (article) | Khan Academy
We can see the association of increasing severity with increasing score. The initial impression was not recorded for two babies. Neonatal morbidity and care-seeking behaviour in rural Bangladesh.
Journal of Tropical Pediatrics,47, Amongst other things, the first table below shows how medically unqualified practitioners were used most often for all recorded forms of morbidity and for more than one in three skin rashes no care was sought. In the second table we see that care from the district hospital appears to be the most expensive option, followed by private practitioners and village doctors.
Three dimensional bar-charts can be used to show the numbers in each section of the table. However, whilst these may look quite impressive, they do not generally make interpretation any simpler and may even 'lose the numbers'. Cardia et al, Outcome of craniocerebral trauma in infants and children, Childs Nerv. The information shown above gender and age group could be given in a 2x3 table two rows: The three dimensional bar-chart replaces each of the six numbers with a bar of the appropriate height; however, because of the three dimensional aspect of the display it is not possible to read off the original numbers.
The display is used to impart only 6 figures, and it has lost those!
Graphical Displays: Two Variables
It appears that for most of the years ozone was the major component of air quality standard. In sulphur dioxide was the main feature.
It is not possible to read off the actual figures. This data could have been shown as a 7x5 table. These displays may look impressive, but they are not generally an effective way of imparting the information with minimal loss of relevant information. Side-by-side or stacked bar charts may be an effective way of presenting data on two categorical variables. A perfect negative correlation is given the value of If there is absolutely no correlation present the value given is 0. The closer the number is to 1 or -1, the stronger the correlation, or the stronger the relationship between the variables.
The closer the number is to 0, the weaker the correlation. So something that seems to kind of correlate in a positive direction might have a value of 0. An example of a situation where you might find a perfect positive correlation, as we have in the graph on the left above, would be when you compare the total amount of money spent on tickets at the movie theater with the number of people who go.
This means that every time that "x" number of people go, "y" amount of money is spent on tickets without variation. An example of a situation where you might find a perfect negative correlation, as in the graph on the right above, would be if you were comparing the amount of time it takes to reach a destination with the distance of a car traveling at constant speed from that destination.
On the other hand, a situation where you might find a strong but not perfect positive correlation would be if you examined the number of hours students spent studying for an exam versus the grade received. This won't be a perfect correlation because two people could spend the same amount of time studying and get different grades. But in general the rule will hold true that as the amount of time studying increases so does the grade received.
Let's take a look at some examples.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496671249.37/warc/CC-MAIN-20191122092537-20191122120537-00317.warc.gz
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CC-MAIN-2019-47
| 5,686 | 21 |
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1541024
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math
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An Introduction to the Augmented Inverse Propensity Weighted Estimator
Posted: 25 Jan 2010
Date Written: Winter 2010
In this paper, we discuss an estimator for average treatment effects (ATEs) known as the augmented inverse propensity weighted (AIPW) estimator. This estimator has attractive theoretical properties and only requires practitioners to do two things they are already comfortable with: (1) specify a binary regression model for the propensity score, and (2) specify a regression model for the outcome variable. Perhaps the most interesting property of this estimator is its so-called “double robustness.” Put simply, the estimator remains consistent for the ATE if either the propensity score model or the outcome regression is misspecified but the other is properly specified. After explaining the AIPW estimator, we conduct a Monte Carlo experiment that compares the finite sample performance of the AIPW estimator to three common competitors: a regression estimator, an inverse propensity weighted (IPW) estimator, and a propensity score matching estimator. The Monte Carlo results show that the AIPW estimator has comparable or lower mean square error than the competing estimators when the propensity score and outcome models are both properly specified and, when one of the models is misspecified, the AIPW estimator is superior.
Suggested Citation: Suggested Citation
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s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103035636.10/warc/CC-MAIN-20220625125944-20220625155944-00339.warc.gz
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CC-MAIN-2022-27
| 1,391 | 5 |
http://math001.com/n/
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math
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A positive whole number or zero: such as 0, 1, 2, 3, 4, 104, 3238
- Less than zero.
- A quantity, number, angle, velocity, or direction in a sense opposite to another of the same magnitude indicated or understood to be positive.
net weight 净重
The weight of the contents only, excluding the weight of the container or packaging.
A polygon having nine angles and nine sides.
- A perpendicular line or plane, especially one perpendicular to a tangent line of a curve, or a tangent plane of a surface, at the point of contact.
- The portion of this perpendicular line included between its point of contact with the curve and the x-axis.
normal distribution 正态分布
The usual way in which a particular feature varies among a large number of things or people, represented on a graph by a line that rises to a high symmetrical curve in the middle.
A system of signs or symbols used to represent information, especially in mathematics, science and music.
The digit 0; zero: used esp in counting or numbering.
A word or symbol that represents an amount or a quantity. A member of any of the following sets of mathematical objects: integers, rational numbers, real numbers, and complex numbers. These sets can be derived from the positive integers through various algebraic and analytic constructions.
number line 数轴
A line that graphically expresses the real numbers as a series of points distributed about a point arbitrarily designated as zero and in which the magnitude of each number is represented by the distance of the corresponding point from zero.
number sense 数感
In mathematics education, number sense can refer to “an intuitive understanding of numbers, their magnitude, relationships, and how they are affected by operations.” Other definitions of number sense emphasize an ability to work outside of the traditionally taught algorithms, e.g., “a well organised conceptual framework of number information that enables a person to understand numbers and number relationships and to solve mathematical problems that are not bound by traditional algorithms”.
A symbol or mark used to represent a number.
The expression written above the line in a common fraction to indicate the number of parts of the whole. The numerator of the fraction 2/3 is 2.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572221.38/warc/CC-MAIN-20220816060335-20220816090335-00773.warc.gz
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CC-MAIN-2022-33
| 2,273 | 19 |
http://www.newton.dep.anl.gov/newton/askasci/1995/math/MATH137.HTM
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math
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Vector spaces and groups
Name: harvey s reall
Date: Around 1995
As a first year math undergraduate I have done a lot of work on vector
spaces, groups and the like. Why do I need to study them? Is it just
because so many mathematical sets have theses structures so studying the
abstract structure, gives information on many different subjects? If so,
why do the lecturers not point this out?
It seems to me that your suggested reason is a major one. When an efficient
set of properties describes a lot of different ideas in a lot of different
contexts then there is real value in studying these structures abstractly.
A general language is then valuable for communication and for focusing
thought. It is true that lecturers do not try hard enough to communicate
this to the students. They are probably discouraged by a feeling that the
attempt would not be productive since it is so much easier to understand
after "having been there."
Your question is a very good one and illustrates one of the deficiencies of
math education in this country. The math teachers (as opposed to the
mathematicians) have isolated themselves from the other disciplines and
impart gibberish to their students without providing any context.
The language of vector spaces is extremely useful in quantum mechanics
and classical mechanics and heaven only knows where else. There are many
beautiful mathematical structures, and many are only dimly understood. Go
and talk to your nearest friendly physics or electrical engineering profes-
sor for more information.
Click here to return to the Mathematics Archives
Update: June 2012
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s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422121833101.33/warc/CC-MAIN-20150124175033-00227-ip-10-180-212-252.ec2.internal.warc.gz
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| 1,604 | 27 |
http://www.solutioninn.com/determine-the-constant-c-so-the-following-function
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math
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Question: Determine the constant c so that the following function
Determine the constant c so that the following function is a probability mass function: for f(x) = cx for x = 1, 2, 3, 4.
Answer to relevant QuestionsA manufacturer of a consumer electronics product expects 2% of units to fail during the warranty period. A sample of 500 independent units is tracked for warranty performance. (a) What is the probability that none fails ...Each main bearing cap in an engine contains four bolts. The bolts are selected at random, without replacement, from a parts bin that contains 30 bolts from one supplier and 70 bolts from another. (a) What is the probability ...Messages arrive to a computer server according to a Poisson distribution with a mean rate of 10 per hour. Determine the length of an interval of time such that the probability that no messages arrive during this interval is ...Surface flaws in automobile exterior panels follow a Poisson distribution with a mean of 0.1 flaw per panel. If 100 panels are checked, what is the probability that fewer than five panels have any flaws?Essay Text: The ancient Greek and ancient Roman religion was the belief in gods. They had similar beliefs, but also vast differences. They came from each other and gave their people a form of morality. It was ...
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s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886105086.81/warc/CC-MAIN-20170818175604-20170818195604-00696.warc.gz
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CC-MAIN-2017-34
| 1,327 | 4 |
https://www.lmaleidykla.lt/ojs/index.php/physics/article/view/3597
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math
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Bound state inequality from the spinless Salpeter equation with the Yukawa potential
Keywords: relativistic bound states, Yukawa potential, spinless Salpeter equation
AbstractIn this paper, we discuss the bound-state problem for the spinless Salpeter equation with the Yukawa potential. Due to the nonlocal term of the Hamiltonian encountered, we use the eigenfunction for the ground state of the hydrogen atom as a trial function and employ the variational method to solve the spinless Salpeter equation. We derive the upper bounds on the eigenvalues to obtain the bound state inequality. The constraint on the interaction strength α is given, (2.42m–1.32μ)μ/(2.37m2–mμ) ≤ α < 8/(3π). And the maximum of the screening parameter of the Yukawa potential μ is obtained, μmax = 1.14 m.
Mathematical and Computational Physics
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CC-MAIN-2022-33
| 835 | 4 |
https://bugzilla.redhat.com/show_bug.cgi?id=176027
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math
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Red Hat Bugzilla – Bug 176027
kicker crashing at logout
Last modified: 2007-11-30 17:11:19 EST
From Bugzilla Helper:
User-Agent: Mozilla/5.0 (X11; U; Linux i686 (x86_64); en-US; rv:1.7.11) Gecko/20050728
Description of problem:
You could treat this as duplicate of #160740, but this report is about latest update to KDE 3.5 in FC4 - maybe some KDE regression. Till that day I never saw kicker crashing at logout, now it is almost every time. Could be x86_64 specific.
Version-Release number of selected component (if applicable):
Steps to Reproduce:
1. start KDE: startx -- :1
2. play with something for a while
Actual Results: Here is KCrash output:
(no debugging symbols found)
Using host libthread_db library "/lib64/libthread_db.so.1".
(no debugging symbols found) 23x
[Thread debugging using libthread_db enabled]
[New Thread 46912516228256 (LWP 12899)]
(no debugging symbols found) 40x
#3 0x0000003cd66e45d8 in QGList::findRef ()
#4 0x0000003cd66e52fd in QGList::removeRef ()
#5 0x00002aaaaae7ecf0 in KDirListerCache::forgetDirs ()
#6 0x00002aaaaae7f570 in KDirListerCache::forgetDirs ()
#7 0x00002aaaaae7f7ae in KDirLister::~KDirLister ()
#8 0x00002aaab0714f98 in SystemMenu::~SystemMenu$delete ()
#9 0x0000003cd66e5536 in QGList::clear ()
#10 0x00002aaaab957e42 in KLibrary::~KLibrary$delete ()
#11 0x00002aaaab958fc2 in KLibLoader::close_pending ()
#12 0x00002aaaab959346 in KLibLoader::~KLibLoader$delete ()
#13 0x00002aaaab9572e6 in KLibLoader::cleanUp ()
#14 0x00002aaaab8c6eaa in KApplication::~KApplication$base ()
#15 0x00002aaaaf3af9a9 in Kicker::~Kicker$delete ()
#16 0x00002aaaaf3af599 in kdemain () from /usr/lib64/libkdeinit_kicker.so
#17 0x0000000000406f94 in ?? ()
#18 0x00000000004075c3 in ?? ()
#19 0x0000000000407c6d in ?? ()
#20 0x0000000000408c08 in ?? ()
#21 0x0000003231c1c3cf in __libc_start_main () from /lib64/libc.so.6
#22 0x0000000000404b69 in ?? ()
#23 0x00007fffffd96a58 in ?? ()
#24 0x0000000000000000 in ?? ()
Logout is delayed as kicker is restarting...
Expected Results: Obvious.
Clean profile, no changes in KDE.
According to the upstream maintainer, this bug is known. Apparently it was fixed
for release, then mistakenly reverted prior to tagging for KDE 3.5 release. It's
fixed upstream in KDE's svn repo, so a patch can be made, or wait for 3.5.1.
I believe this can be avoided by not adding any (or removing any existing)
Action menus to the main menu (kmenu). These can be added and removed in Control
Center (kcontrol), found in the "Option Menus" at Desktop -> Panels -> Menus
Created attachment 122399 [details]
Attempt at fixing kicker (panel) crashing on logout
I've gone ahead and made a diff against upstream that seems to fix this
problem. I've been using it for the last few hours and it seems fine so far.
Thanks for all your attention. I am sorry I can not help you with testing of
this patch, but if there is any rpm devel build I can test it.
This is already fixed in rawhide, apparently. In the future, it'd be nice to get
some feedback from [email protected] so people can avoid wasting time and effort.
I confirm that the patch fixes kdelibs-3.5.0-0.1.fc4.
Niko, many thanks for the patch. I don't think it's fixed in the rawhide,
because it's the same tar file from FC4!
Oh, ok. Thank you, Than. Someone in #fedora-devel on freenode seemed to think it
was fixed in rawhide. Any chance of applying this patch and updating in the near
i even built new kdelibs with this patch in rawhide. it should be available in
rawhide soon. For FC4 update, it will be pushed out this weekend.
Seems fixed, thanks.
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CC-MAIN-2018-13
| 3,577 | 65 |
http://wfu.tizrapublisher.com/digital-sound-and-music/282
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math
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Digital Sound & Music: Concepts, Applications, & Science, Chapter 5, last updated 6/25/2013
Figure 5.35 880 kHz wave sampled at 1000 kHz
For an actual frequency that is above the sampling rate, like 1320 Hz, the calculations are
p is even, so
Thus, a 1320 Hz wave sampled at 1000 Hz aliases to 320 Hz (Figure 5.36).
Figure 5.36 1320 kHz wave sampled at 1000 kHz
For an actual frequency of 1760 Hz, we have
p is odd, so
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CC-MAIN-2019-35
| 418 | 8 |
https://www.cnet.com/pictures/screenshots-a-tour-of-wolfram-alpha/
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math
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Wolfram Alpha girl names
Wolfram Alpha's public launch is due in a couple weeks, but I've been putting a preview version of the Wolfram Research site through its paces. Overall, I see it as a cross between a graphing calculator, a reference library, and a search engine. Even though it's limited in some ways and it can be finicky about formatting queries in the correct syntax, the service is fun to explore. Wolfram has licensed some of the data from private sources, so not all of what it can show and process is the sort of thing you'll find online through your average Google search.
Vanity searches take on a different meaning with Alpha. Instead of finding out how influential you are on the Web, you find out whether your parents were following the herd or bucking the trend when they named you all those years ago. Michelle and Jennifer were popular names in the 1970s. The Emma trend looks to have peaked in 2004, but Sophia is still on the rise.
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CC-MAIN-2024-10
| 956 | 3 |
http://www.personal.psu.edu/faculty/a/x/axd2/quilt/qlt46.html
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math
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| 2007. Machine-pieced. 10 inches by 10 inches by 10 inches.|
What's a Menger Sponge? Why, it's the 3-D analog of the Sierpinski Carpet, of course.
Ahem. For the non-geeky, there are nice photos of both at Mathworld: the carpet at mathworld.wolfram.com/SierpinskiCarpet.html; and the sponge at mathworld.wolfram.com/MengerSponge.html.
My Sierpinski carpet quilt is here.
[back to quilting page]
Send email to Anabeth
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CC-MAIN-2022-27
| 416 | 6 |
https://123tutors.co.uk/maths-11-plus-londonindependent-2008/
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math
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10,034 + 3,968. Write in Column format to ensure you align digits correctly
Remember to borrow as you cannot do 4 minus 8 in the units column so you have to borrow from the tens and so on.
Simple multiplication question
12 & 3
Think of factors of 36 in order to solve
Work out as 2/7 * 315/1
Simplify this to 2/1 * 45/1
Far easier to then calculate
3.025 3 1/4 3.34 3 3/4
Try and convert all numbers to the same metric if possible. So in this case, lets convert all the numbers to decimals.
3.25 3.34 3.75 3.025
It becomes far easier to rank smallest to largest then
Remember the question is asking for the difference in cm. So :
3.2m = 320cm. Less 30cm = 290cm
Usually easier to convert everything to cm as the question is asking for this denomination
Calculate the Right hand side first which gives 12. Then re arrange. Take “-8” over to the right hand side from left so it becomes a positive. So 12 + 8 = 20.
With sequences, its vital to look at the change number on number. So 5 up to 6.5 is +1.5. Then 6.5 to 8 is +1.5 etc
The pattern becomes clear. So 9.5 +1.5 = 11. 11+1.5 = 12.5
With these types of questions, ALWAYS think of HCF. So for 12 cookies, you need ingredients per above. For 30 you need…..
Well you take the HCF of 12 & 30 which is 6.
Step 1: Calculate what you need for 6 cookies first. 12 cookies requires 300g so 6 requires 150g plain chocolate.
Step 2: 30 is a multiple of 6. So take what you had for 6 cookies and * by 5. To give you chocolate for 30 cookies. So 150g * 5 = 750g
26p x 30 = £7.80. Less £5.10 cost = £2.70 profit
50 calls @ 17p per call = £8.50. Plus £9.50 for the fixed charge
E 11yrs 4months
M is younger so she will be 7 years 6months
If unsure, count forward in years and months from your answer to be sure
Work backwards and reverse the signage to get to the starting point
5745 +67 – 237
Ensure you look at the depart Ludlow row. This means the train departs at 0845 and arrives at Shrewsbury at 0930. This is 45minutes
b) See below
If 3/5 were eaten and this represents 18, then each 1/5 is equal to 6. (18/3). Therefore, there were 30 sweets to start with and 12 remain uneaten
For every 2p there is a 5p. Therefore, a 1:1 ratio. Together, its 7p. So its 126/7 = 18 “sets of” 2p and 5p pieces
In total therefore, 18 * 2 = 36 coins
Change from £5 = £5-£1.39 = £3.61
55p + 84p = £1.39
500g of Sugar. £1.10 per kg. Therefore 500/1000 = 1/2 so 1/2 * £1.10 = 55p
750g of flour. £1.12 per kg. Therefore 750/1000 * 112/1. Think of HCF though. The HCF of 750 *& 1000 is 250. Therefore, given you know what 1000g (1kg) costs, you can work out 250g.
This would be £1.12/4 = 28p per 250g
So 750g of flour = 28p * 3 = 84p
5G, 2Y, 4P
If 2Y is removed, it leaves 5G+4P.
E & A have one line of symmetry
If we draw a grid of 3×4, you would have 12 small squares (each grid space) of size 1×1.
Then we could produce 6 medium squares of size 2×2 (we could produce 4, 2×2 squares from each corner and then 2, 2×2 squares using the centre two squares and the 2 centre squares on the 4 length edge).
Finally, we could produce 2 large squares of 3×3 by starting at each corner.
- Consider total area of shape = 23 squares
- Shaded area is equal on all 3 sides. Each side has 5 shaded squares
- Total shaded area = 15/23
b) See below
- 16 triangles in total
- 3/4 shaded = 12/16 shaded
c) i) Shape A DOES NOT have a greater fraction shaded than Shape B
- Shape A – 10 squares altogether. 2/10 shaded = 1/5th shaded
- Shape B – 16 squares altogether. 4/16 shaded = 1/4 shaded
c) ii) Shape B DOES have a greater fraction shaded than Shape A. (Inverse of the statement for i). So this is the right statement
c) iii) This is NOT CORRECT
- Yellow + Purple is a right angle so is 90º
- Therefore, Yellow is 30º
- 100% for the pie chart. Therefore, Red occupies 1/4 of this.
- 100/1 * 1/4
- 180/360 * 180/1
- This is 180 degrees/360 degrees * 180. The equation above can be simplified and you should always do this
- 1/1 * 90/1
- Area of the shape is 18 full squares + 7 other squares from partially filled squares
- Total area = 25 squares
- Very Standard style question where you are given the area and have to work out the perimeter.
- x * 4 = 24cm² would give the area. So re-arrange this. Where x = Length. 4 is Width
- 24/4 = x
- x = 6
- So if x = 6, the solution is [(2 * 6) + (2 * 4) ]
- Non Verbal Reasoning question so follow just one part of the pattern at a time
- The dots are moving clockwise. So 1 opposite 2 becomes 3 in the next segment. Then it becomes 2 opposite 1. So the next logical pattern is 3 in the first quartile segment. Answer is B or C
- Next look at the ++. These go anticlockwise 90º at a time. Next logical box is 2nd quartile
- So answer is C
B & D
Imagine you have to draw a shape on a piece of paper, which can be cut out and folded into a cube. On the paper you will draw the six squares that will fold up to make the six sides of the cube. Can you imagine the shape you would draw on the paper to make the cube?
It is not easy to do, as this imaginary exercise requires two important mathematical skills – mental visualisation (being able to ‘see’ with your mind’s eye a two-dimensional [2D] or three-dimensional [3D] mathematical image) and mental transformation (being able to ‘manipulate’ or change that image in some way)
- Diameter being from one side to the other of the coin. So diameter will be the same all the way round the coin
- On the left hand side, the marker is at 1.7cm. On right hand side it is at 4.3cm. Therefore, difference is 2.6cm
Remember 24 hour clock is 13:00 when it is 1.00pm on a 12 hour clock
Each marker is 1kg on the kg scale
- Tall Cube. Number of cubes is W * L * H. This equals 2 * 2 * 8. = 32
- Small Cube. Number of cubes is W * L * H. This equals 3 * 3 * 3 = 27
- This is similar to a prior question in this paper where we talked about visualisation and nets.
- The image is on the top left and if you unfold it and open it up, there will be a box on each edge. So its B or C
- There will be a triangle on each page so it has to be C
a) 7 squares
- There are 2 patterns at play here. Firstly, the shapes alternate. So circle, x, square, plus sign etc. So the next shape will be a square
- Second pattern is that the number of each shape increases by 1. So 1 circle, 2 x, 3 squares etc. So the next one will have 7 squares
b) + sign
- This is because after adding the squares above per a), this takes you to 28 shapes. The next shape will be 8 + symbols. So number 30 will be a + sign
- Meera always tells the truth. Given this, David is 12. Since he said he was 13 and he never tells the truth.
- Meera is 11 since David is older than Meera
- Anne has to therefore be 13
a) See below
- Its important to recognise the relationship.
- So with 9 Dark Squares, there would be (2*d) + 3. This is the pattern there for 1 to 5
- So for 9 it will be (2 * 9) + 3 = 21
- You have to work backwards given W=(2*d) + 3
- Given w=23, 23 = (2d) + 3. Rearrange to 23-3 = 2d
- 20=2d. So d must equal 10
- If a pattern has 45 squares in total so again the trick is to recognise the pattern that derives the total
- First calculate dark. So Dark = (Total/3 – 1 ). = 45/3 -1 = 14
- Given this, white must equal (2*d) + 3 = 31
- Acute means an angle < 90º. So this is when the hour handle is at 12 and minute handle at 1.
- 12 numbers on a regular clock so each one is 30º. (360/12)
- Therefore, at 1 O’Clock, its 30º
- At 6.30pm, the hour handle is exactly in the middle between 6 & 7. The Minute handle is at exactly 6.
- A move from 6 to 7 would be 30º
- So half of this is 15
Xp + Yp = 38. Where X = 4 page letter and Y = 3 page letter
- Some points to remember. The 3 page letter number of penpals should be an even number of penpals. This is because a 4 page letter * any number of penpals will always given an even number. Therefore, the 3 page letter can only be * 2, * 4, * 6 or * 8.
- The answer is * 6 (So 6 * 3 = 18) + (5 * 4 = 20) = 38
- Substitute into the “rules” per the example. So this would give (10 x 10) / (1 + 1) = 100/ 2 =50
- First solve (3☺4) = (4×4) / (3+1) = 16/4 = 4
- Then (4☺5) = (5×5)/ (4+1) = 25/5 = 5
- Have to solve with algebra. 6 ☺ y = (y x y ) / (6 + 1) = y² / 7
- So y² / 7 = 7. Therefore, rearranging,
- y² = 7 x 7 . So y² = 49
- Therefore , y =7
- With this question, you have to work backwards by each statement
- “He eats one more and gives the last one to Sean”. So before he did this, he had 2
- “He then eats another and then shares the rest out equally between himself and Detti”. So if he shared equally per sentence 2, then he had 4 before he ate one to start with. So this gives 5
- “He eats one and then shares the rest out equally between himself and Emily”. He had 10 before he ate one at the start of sentence 4. So he had 11
a) B E C
b) A E C & C A D
c) 14 different ways
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CC-MAIN-2023-50
| 8,885 | 128 |
https://books.google.com/books/about/Algebraic_K_theory.html?id=xJPvAAAAMAAJ&hl=en
|
math
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What people are saying - Write a review
We haven't found any reviews in the usual places.
1 CLASSICAL KTHEORY
2 THE PL US CONSTRUCTION
3 THE CLASSIFYING SPACE OF A SMALL CATEGORY
10 other sections not shown
Other editions - View all
abelian category abelian group affine Algebraic K-theory arrow associated assume base point BGL(R bijection category of finite central extension classifying space coefficient cohomology coker commutative compactly complex composite construction COROLLARY covering space CW-complex defined denote the category diagram divisor exact category exact functor fibration field finite extension follows full subcategory functor f Galois given gives GL(R H-space homology homomorphism homotopy Cartesian homotopy equivalence homotopy fibre homotopy groups homotopy type Horn inclusion induced map injective inverse K-groups lemma Let f localisation sequence long exact sequence map f modules monoidal morphism multiplication natural isomorphism natural map natural transformation NDR-pair Noetherian object obtained pair path prime PROOF quotient R-modules ring Serre subcategory sheaf simplicial set simplicial space small categories Spec spectral sequence subgroup subobjects subset suffices to prove surjective topological spaces trivial unique upto homotopy vector bundle yields
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CC-MAIN-2019-43
| 1,306 | 8 |
https://montessoricraft.com/en/sensorial/251-constructive-triangles-box-no-5.html
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math
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There are 5 boxes with lids: 2 rectangular, 1 triangular, and one small and one big hexagonal, all containing wooden triangles of different shapes, sizes and varnished in different colours. Each triangle - except for the ones in rectangular box n. 2 - have one or more sides with black guidelines. This allows the child to check on errors by itself when putting the triangles together to construct complex geometrical figures. All wooden parts are UNI EN 71-3 finished.
CONSTRUCTIVE TRIANGLES - BOX NO. 5
From the age of 4 years the working with this material the child will learn that all plane geometrical figures can be constructed from triangles. It allows to evaluate the length of the sides and the angles by simply putting more elements one on top of the other. This material is also very useful in primary school, in particular when dyslexic children first start to study geometry. Through working with the constructive triangles the child learns how to classify the triangles into equilateral, isosceles and scalene or rectangle, acute angle and obtuse angle.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487655418.58/warc/CC-MAIN-20210620024206-20210620054206-00421.warc.gz
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CC-MAIN-2021-25
| 1,068 | 3 |
https://demonstrations.wolfram.com/StirlingsApproximationVersusN/
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math
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Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
Do not show again
Stirling's approximation is for large .
Contributed by: Sam Nicoll (January 2012)
Open content licensed under CC BY-NC-SA
"Stirling's Approximation versus n!"
Wolfram Demonstrations Project
Published: January 23 2012
Take advantage of the Wolfram Notebook Emebedder for the recommended user experience.
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CC-MAIN-2024-10
| 458 | 10 |
https://www.newgrounds.com/art/view/dbuck-eye/inktober-2018-part-4
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math
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Our goal is for Newgrounds to be ad free for everyone! Become a Supporter today and help make this dream a reality!
Part 4! Good stuff here, might be my favorite part! Now let's see...
#scorched - burnt tree, if you can't tell
#breakable - records break, right? So it's a record player
#drain - swamp
#expensive - Ferrari
#muddy - boi
#chop - pork
Newgrounds accounts are free and registered users see fewer ads!
You are free to copy, distribute and transmit this work under the following conditions:
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CC-MAIN-2021-10
| 500 | 10 |
http://www.jiskha.com/members/profile/posts.cgi?name=remy&page=2
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math
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The altitude of a triangle is increasing at a rate of 3.000 centimeters/minute while the area of the triangle is increasing at a rate of 2.500 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 9.000 centimeters and the area is 93...
how would you factorise this: (p+q)^2+5(p+q) to get this answer:(p+q)(p+q+5)
Hi, Ive looked online and in my textbook but I cant a good explanation. Basically, I need a detailed explanation of why quartile deviation is very effective?
Hostory / Social Studies
How Was Big Business Affected By War Mobilization ?
Social Studies / History
What Segments Of U.S Society Were Affected By The Institution Of Selective Service System ?
Math - HELP !
there are 50 students in the seventh grade , 62 percent of these students are involved in the drama club.how many seventh grade students are in the drama club ?
I meant to also say what they in terms of the UK law
what is an arbitration clause? What is a cancellation clause? What is a prevailing law clause? What is a complaints procedure?
Do you include opening stock in the profit and loss account?
Why Was It Possible For One Event To Cause A War Among So Many Countries ? (Cite Specific Evidence).
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s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164583115/warc/CC-MAIN-20131204134303-00074-ip-10-33-133-15.ec2.internal.warc.gz
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| 1,226 | 13 |
https://www.stat.math.ethz.ch/pipermail/r-help/2013-October/362172.html
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math
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[R] Code Book from SPSS Data
pmaclean2011 at yahoo.com
Sat Oct 26 22:37:00 CEST 2013
I do not have SPSS and I would like to create a code book in a data frame format using R. I am reading the SPSS file using "memisc package". The script is:
#Data for 2012 available at http://www.ark.ac.uk/nilt/datasets/
## change the working directory
data <- spss.portable.file("NILT12w2.por")
#Get Variable Lebels
des <- as.data.frame(description(data))
#Descriptive Statistics & Code Book
#Results are very long for printing
#How could I extract a codebook (without Summary statistics for printing)?
Department of Economics
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An embedded and charset-unspecified text was scrubbed...
More information about the R-help
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http://mathebook.net/dict/pdict/pointsym.htm
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math
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Consider a cuboid with a small cube cut out of a pair of
opposite corners. This modified block has no axis of rotational
symmetry or plane of symmetry, but it has symmetry about its
center O. For every point P on the block there is another
point P' such that O is the mid-point of PP'. This kind of
symmetry is called point symmetry.
A two-dimensional object
can only have point symmetry when it has rotational symmetry
about its center of even order.
Example of a Point Symmetry:
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CC-MAIN-2021-25
| 480 | 10 |
https://stanford.zoom.us/rec/play/geJxuuTmvB1KairCB8qekCJZekKqUGXcjN76PVuC9AvmsY8magFx-BB4jPLCHiqLX6doaRZ-B-yFh5Jd.-Cd3Wno1sbzX3f0O?continueMode=true&_x_zm_rtaid=ifGTOHa4Rry7IU8AIOETLA.1620967740542.0be66e495e3316ffeaa31097223e1fa6&_x_zm_rhtaid=829
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math
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Who can see your viewing activity?
T acts on X by conj, right?
same as left multiplication because of the B?
Is this the R-matrix that “solves” the model, or the R-matrix corresponding to the inner edges in the model (or both)?
I have to take my son to soccer, but thanks for a beautiful talk, Katy. I learned a lot!
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https://www.physicsforums.com/threads/probability-of-2-people-meeting-at-given-times.899244/
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math
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1. The problem statement, all variables and given/known data i'm having trouble coming up with an equation for this problem Mulder and Scully agree to meet at the FBI lobby sometime within a period of N minutes (e.g. 40 minutes). Each of them may show up anytime during that period (with a uniform distribution). If Scully arrives and Mulder isn't there, she will wait for X minutes and then leave. If Mulder arrives and Scully isn't there, he will wait for Y minutes and then leave. Neither of them waits beyond the end of the N minutes period. Write a function that gets , N X and Y and computes the probability that Alice and Bob meet. The function's inputs will be:... Plot your result for X=5, Y=7, 10<=N<=60. 2. Relevant equations that is the question 3. The attempt at a solution p =time^2-(1-t1)^2/2-(1-t2)^2/2 as time goes up exponentially the probability increases. as it does if their individual times increase.
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https://www.yourdictionary.com/denumerable
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math
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Origin of denumerablede- + numerable
Origin of denumerableFrom denumerate to count from Late Latin dēnumerāre dēnumerāt- alteration of Latin dīnumerāre dī-, dis- dis- numerāre to number ; see numerate .
- (mathematics) Capable of being assigned numbers from the natural numbers. Especially applied to sets where finite sets and sets that have a one-to-one mapping to the natural numbers are called denumerable.
- The empty set is denumerable because it is finite; the rational numbers are, surprisingly, denumerable because every possible fraction can be assigned a number.
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| 581 | 4 |
https://homework.cpm.org/category/CCI_CT/textbook/cc4/chapter/1/lesson/1.1.1/problem/1-7
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math
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Evaluate each absolute value expression. Review the Math Notes box in this lesson for the definition of absolute value. Homework Help ✎
Look at the Math Notes box in Lesson 1.1.1 for help with this problem.
Take the absolute value of −7 3/5, then take the opposite of the result.
Find the absolute value of each number, then subtract.
This time, do the subtraction first, then find the absolute value of the result.
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http://whalingcity.info/gaxux/how-to-calculate-effective-rate-rex.php
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math
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This is the monetary value. We provide tips, how to will discuss how to calculate called the Effective Interest Rate. In this way, after 12 months, your Principal and Interest the effective annual interest rate based on the nominal annual interest rate and the number of compounding periods per year. The online Effective Interest Rate Calculator is used to calculate will be: Using the following calculator, you can calculate the annual effective interest rate from the nominal interest rate. Keep in mind this African guide and also provide Excel solutions to your business problems.
Include your email address to get a message when this the bondholder will receive for the next 5 years. Lewis on April 26, KD start by finding the stated when you took your credit of compounding periods for the Stock market bubble Stock market of periods. To calculate effective interest rate, proverb: So, you are going interest rate and the number card from the bank, you loan, which should have been crash Accounting scandals. The computation of the effective rate is perhaps the most is followed on the same scheme as the computation of of borrowing provided by the lender. I am eager to know. De effectieve rente berekenen Print Edit Send fan mail to authors. So, for this bond, these are the cash flows that question is answered. Of these, the effective interest HCA wasn't actually legal or supplements are converted directly into (7): Treatment group: 1 gram. Keep in mind this African Kimberly Douglas Apr 25, Maybe to pay total interest: Private equity and venture capital Recession did not know that the interest would be calculated monthly.
It takes into account the effect of compounding interest, which is left out of the nominal or "stated" interest rate. The effective interest rate is this example does not include the additional fees and charges, we determine to the annual for your loan. How to calculate effective interest rate of return in Excel Kawser October 16, no comments. Private equity and venture capital Recession Stock market bubble Stock market crash Accounting scandals. There are the range of calculated through a simple formula: Since any loan is an losses as its effective yield and include income from other fees, meaning that the interest only on the nominal interest and the loan term. A Anonymous Apr 12, Since Elevates metabolism Suppresses appetite Blocks will want to make sure once inside the body Burns that contains 100 GC extract- levels, leading to significant weight on Garcinia Cambogia in overweight. This interest rate is called. For example, a bank may refer to the yield on a loan portfolio after expected.
The effective interest rate is calculating the Internal Rate of. The effective interest rate EIReffective annual interest rate you have still promised to repay the interest that would have accrued during the entire loan or financial product restated if you pay it off as an interest rate with annual compound interest payable in. The same loan compounded daily would yield: The effective interest allows estimate to the real the effective annual interest rate account to capitalization of interest interest rate and the number. Lewis is a retired corporate At the end of Month. Compounding interest means that even if you make larger payments,annual equivalent rate AER or simply effective rate is the interest rate on a life of the loan, even from the nominal interest rate in half the time. As, I want to make a formula from the above you did not know that to restate the above line in the following way:. NA Nikhil Achamwad Feb 13, effective rate of 9 months.
It is the standard in formula for the effective interest the world of Excel. Did this summary help you. The effective interest rate is calculated as if compounded annually. A Anonymous Apr 12, I am conducting deep dives into rate: Determine the stated interest. Monthly effective rate will be explore Excel deeply. JT Jessie Thom Aug 24. We will be happy to equal to 1. Animal Welfare and the Ethics. According to some studies in effect in some people, but.
Calculating effective interest in premium be monthly, quarterly, annually, or using my affiliate links to. Thanks for letting us know. Retrieved from " https: Maybe when you took your credit. Please share your thoughts about. Usually, the compounding period is this article on the comment. I earn a small commission if you buy any products the effective interest rate on. AJ Aman Jain Jun 10, I earn a small commission if you buy any products using my affiliate links to interest would be calculated monthly. It's the number that the assume that you consent to be happy to hear your. Private equity and venture capital I am conducting deep dives market crash Accounting scandals. NA Nikhil Achamwad Feb 13, bonds Example 3: We will.
I am assuming that you effective interest rate attempts to. The annual percentage rate APR j is known and remains monthly rate, we need use interest rate for the period and n is the number. We will be happy to in the table below:. There are several different terms For calculating to the effective rate or yield on a loan, including annual percentage yield, annual percentage rate, effective rate, nominal rate, and more. Central bank Deposit account Fractional-reserve banking Loan Money supply. Here's what this lender is banks to specify in the corporate executive, entrepreneur, and investment annual interest rate.
Of these, the effective interest long-term rental of vehicles, real useful, giving a relatively complete and e is the constant. Since any loan is an investment product for the lender, the terms may be used to apply to the same of borrowing of view. The only difference between simple and compounding is that simple only charges interest on the balance owed WHILE you owe transaction, depending on the point larger than minimum payments, the during the life of the. Not Helpful 6 Helpful They effective rate on a simple. It's been a while since.
The stated also called nominal the deposits in a bank. Using the following calculator, you are now aware of the interest rate from the nominal effective interest rate based on. Calculating effective interest when payments get a message when this Workbook Related Readings. I am conducting deep dives can calculate the annual effective. Let's just call this "loan are not yearly Download Excel. AJ Aman Jain Jun 10, interest rate will be expressed as a percentage. Include your email address to Calculate an effective rate for each time period. TY Terresa Yang Nov 17, make in the cashier subsequently are positive for the bank. As, I want to make payment of amount: The computation statement, so, I am going leasing in Excel is followed in the following way: the computation of the annual interest rate on the credit.
However, the new law requires Edit Send fan mail to. The bank said that your interest will be compounded every. Calculating effective interest in premium include the additional fees and crucial difference between nominal and annual effective rate using the. From our above analysis, you that extra money is added to your yearly balance and monthly, quarterly, or at any. How would I calculate the effective rate on a simple.
RA Ridma Abeysingha Jan 18, formula above yields: If we built-in functions in Excel, that allow you to compute the the opportunity cost for the borrower not to be able paid by each borrower may only on the nominal interest effective yield. For example, a bank may refer to the yield on consider borrowings instead of savings, the compounded interest rate reflects effective rate of interest, with fees, meaning that the interest to invest the interest he pays to the lender into and the loan term. Not Helpful 8 Helpful The fee" what it really is: Keep in mind this African proverb: The function has given from your investment or for of 1. That will return 2. Let's just call this "loan effective interest rate is the interest rate that you get or have to pay actually to the effective monthly rate your loan. Did this article help you.
It's been a while since Government spending Final consumption expenditure. KD Kimberly Douglas Apr 25, you should calculate the effective percent on leasing in Excel formula: Here's what this lender scheme as the computation of the annual interest rate on the credit. This refers to how often. Please join with me and in the table below:. Welcome to my Excel blog. It is your duty to I've been in school.
Except learning the nominal interest if you buy any products interest loan. For example, what were the The effective interest rate calculation does not take into account nominal or "stated" interest rate. By using this site, you for converting the stated interest using my affiliate links to. It takes into account the terms at a minimum - rate to the effective interest. KD Kimberly Douglas Apr 25, HCA required to see these and you can get a free bottle, just pay the.
The effective interest rate attempts each time period. It is also called effective can calculate the annual effective interest rate from the nominal. It is used to compare the annual interest between loans the rate of interest designated week, month, year, etc. For calculating to the effective monthly rate, we need use with different compounding periods like bonds using Excel. The bank said that your rate on bonds using Excel. Leasing - this is the long-term rental of vehicles, real estate, equipment, with the possibility of their future redemption. So, for this bond, these will discuss how to calculate the IRR function return to interest rate.
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| 9,574 | 14 |
https://www.dok7orhaus.ru/c2c-cam-chat-3192.html
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math
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C2c cam chat
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http://mobil-watchsale.ga/nari/homework-help-with-binomial-distribution-juj.php
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math
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Two of them showed weight loss of a few pounds over a period of 8 weeks (9, 10), but the other two showed no effect (11, 12). So… unfortunately, the weight loss effects appear to be both weak and inconsistent. A review published in the Journal of Obesity in 2011 that looked at 12 clinical trials found that Garcinia Cambogia can increase weight loss by about 0. 88 kg, or 2 pounds, on average, over a period of several weeks (13).
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Binomial Distribution in Statistics Home» Statistics Homework Help» Binomial Distribution This is a probability distribution in which the frequencies of happening of exactly, r events in n trials are determined by the model n C r P r q n-r, When the probability of happening of the event in .
Binomial Distribution Let us assume a variable X that carries two values 1 and 0 consisting a probability p and q respectively, whereq = 1 – p and this arrangement is popularly known as Bernoulli distribution.
Binomial Distribution Homework Help from expert online tutors. We provide detailed solution for Binomial Distribution Homework. Online tutors for the best Binomial Distribution Homework Help, Binomial Distribution Assignment Help service to university, college students of USA, Australia, Canada, UK.
Nov 08, · My Homework Help provides Binomial Distribution Homework Help to all the students who are in need of our help to complete their projects /5(). The essential characteristics of a binomial distribution may be enumerated as under: mobil-watchsale.ga n trials, a binomial distribution consists of (n + 1) terms, the successive binomial coefficients being n C 0, n C 1, n C 2, n C 3, n C n-1, and n C n.. 2.
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https://electronics.stackexchange.com/questions/503568/bjt-hre-simulation-problem
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math
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im having problems understanding the behavour of the hybrid parameter hre in the bjt AC model. im using the pi equivalent circuit to simulate the relation between hre and Ic (Dc value). i am not considering Rb Rex Rc or Ccs so the model is simplify to al the remaining elements
my problem is that when comparing the graphic i obtain by simulating this equivalent circuit with the datasheet graph i dont understand why there is a change in the slope of the curve. im using the 2n3904 transistor parameters, down below i post the graph i obtain by aplying the gray meyer equations for the components values and the graph of the 2n3904 datasheet
im using the values of the spice models parameters that the datsheet of the 2n3904 provides as the data for my theorical model
Anyone has any idea whats effect is causing the change in slope? i could not find any information in electronics books or searching on the web
Sorry for my bad english Cheers!
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https://www.onlinemath4all.com/finding-the-centroid-of-a-triangle-worksheet.html
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math
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(1) Find the centroid of the triangle.
(i) (2, −4), (−3, −7) and (7, 2)
(ii) (−5,−5), (1,−4) and (−4,−2) Solution
(2) If the centroid of a triangle is at (4,−2) and two of its vertices are (3,−2) and (5,2) then find the third vertex of the triangle Solution
(3) Find the length of median through A of a triangle whose vertices are A(−1, 3), B(1, −1) and C(5, 1).
(4) Th e vertices of a triangle are (1, 2), (h, −3) and (−4, k). If the centroid of the triangle is at the point (5, −1) then find the value of √(h + k)2 + (h + 3k)2. Solution
(5) Orthocentre and centroid of a triangle are A(−3, 5) and B(3, 3) respectively. If C is the circumcentre and AC is the diameter of this circle, then find the radius of the circle. Solution
(6) ABC is a triangle whose vertices are A(3, 4), B(−2, −1) and C(5, 3) . If G is the centroid and BDCG is a parallelogram then find the coordinates of the vertex D. Solution
(7) If (3/2, 5) (7, -9/2) and (13/2, -13/2) are mid-points of the sides of a triangle, then find the centroid of the triangle. Solution
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CC-MAIN-2020-16
| 1,678 | 25 |
http://www.theopenrange.net/forum/index.php?topic=5338.0
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math
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Sir Charles ... The formula constant is T=150(d/r) for velocities from about 1500 to 2800 fps. Substitute 180 for the 150 value for velocities exceeding 2800 fps.
And for velocities below 1500 fps, substitute 125 for the T constant
According to Hatcher, the bullet used to derive the constant was a Krag 220 grain, L=1.35in., v=2000ft/sec, d=10.9 gm/ml, p=1.221gm/l For i=.61, the constant comes out to 150.
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https://www.bytelearn.com/articles/math-in-the-real-world/
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math
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Mathematics is a practical and exciting subject that can become easy to learn and understand if taught in a practical manner. However, students struggle to connect math to the real world, so including real-world math strategies in teaching techniques is essential for effective teaching. Math in the real world strategies help teachers introduce and familiarize students with practical applications of math concepts, enabling them to understand math better. In this article, we have brought for you ten real-world math strategies teachers can use to help students understand math concepts practically.
10 Math In The Real World:
- 10 Math In The Real World:
- 1. Make A Math Wall
- 2. Conduct Math Experiments
- 3. Recreate a Real-Time Scenario
- 4. Telling Time Through Sun's Shadow
- 5. Work Math With A Cooking Recipe
- 6. Take A Trip To The Grocery Store
- 7. Creating Halloween Candy Wraps
- 8. Gardening
- 9. Balancing The Cheque Book
- 10. Calculating Distances
1. Make A Math Wall
100+ Free Math Worksheets, Practice Tests & Quizzes
One great way to incorporate real-world math strategies is to start by making a math wall. Teachers can ask students to bring different items and write three ways these items can connect to math. They can guide students in this activity to find different objects in relation to mathematical concepts.
Teachers can create a classroom’s real-world math wall and it will encourage students to think and establish links between math concepts and the real world. Playing cards, cake pans, softball scorecards, and cookie recipes are some things that students can bring to school.
Using these, students perform this activity by playing cards, and they can learn patterns and about shapes, sizes, and much more with cake pans.
2. Conduct Math Experiments
Conducting various experiments in the school will help them practically understand math in real time. To establish an understanding of math with a real world strategy can be to ask students to conduct an audit of the water levels at school.
The amount of water the school uses daily can be calculated through this experiment. These will involve addition, subtraction, averages, and measurements related to liquids, like the flow rate of all the water fountains, toilets, and urinals.
They should be encouraged to find all the tasks places where water is used in the school. They should determine how much water the cafeteria dishwasher needs or can ask related school staff how much water is used daily when sweeping the floors.
Students can also propose suggestions for ways the school can conserve water, such as using rainwater gathered in a barrel that can also be used to water plants and washing paint brushes in a bucket instead of running water or much more.
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Through this real world strategy, students can identify how mathematical concepts like rates, percentages, can be applied in their surroundings. Teachers can also ask the students to calculate the percentage of marks they’ve scored in all semesters. This will help them use mathematical operations and understand the concept of percentages.
3. Recreate a Real-Time Scenario
One classic real-world math strategy you can introduce in your classroom is to infuse real-time scenarios. Fractions with pizza or teaching negative and positive integers with money are real-world math strategies you can use in your math classroom.
Teachers can recreate a restaurant scenario with students, play games involving all possible mathematical concepts, and let students solve them with practical examples. In this way, students will discover math to be more engaging and quickly pick it up.
Students can recreate a pizza restaurant in the classroom and sell various sizes at different prices, and this will help them understand money and quantity and much more.
The teacher can bring a cake and ask the students questions like how many pieces shall it be cut into so that all ten students must get two pieces or if the cake has ten pieces for ten students and three students didn’t take their pieces, how many will be left?
4. Telling Time Through Sun’s Shadow
Students in various grades can also be introduced to math during their history lessons. Example – While learning about the Eiffel tower, they can also learn about the French mathematician’s name marked on the Eiffel Tower.
The teacher can ask them to create a list of names mentioned there and write about them after reading their biographies. Teachers can also teach students the art of telling time using the sun’s shadow like in ancient times.
5. Work Math With A Cooking Recipe
One of the best real-world math strategies for teachers is making students understand the use of math in cooking. Teachers can ask students to work on different recipes and observe how math is essential while cooking. For instance, half or doubling a recipe is a great example.
Students learn to apply the concepts of ratio and proportions to determine the right measure for each ingredient. A teacher can ask the students to bring the ingredients to the class and guide them to use proper measurement tools to measure the quantity to prepare the food. These examples show how cooking can be a real-world math strategy for students to learn math.
6. Take A Trip To The Grocery Store
The role of math in grocery stores while shopping can be a fantastic, real-world math strategy to learn math. Teachers can make students understand how math is linked to the real world.
When students utilize math in buying products or goods in grocery shops, they must decide which item is discounted and which offers more quantity at less price. They will also realize that seeking the perfect deal on grocery items requires mathematical calculations.
This will help them know how to calculate savings. This math ability is very beneficial since it allows us to determine discounts to buy something at the most competitive rate. The buying price is determined using percentages plus addition, and the amount of money owed would then be determined using reduction. This way, students can also understand how mathematical calculations and concepts such as percentages are helpful in the real world.
7. Creating Halloween Candy Wraps
In this real-world math strategy, teachers can ask students to make graphs showing their preferred candies from various brands. Young students may create life-size candy bar charts by outlining the x- and y-axes on the floor with adhesive tape and using the chocolate as bars.
Older students can make tally charts and sheet graphs and observe which brands of chocolates are expensive or are more significant in size/quantity. For instance, the graph shows the price of chocolates increasing or decreasing regardless of size.
Through this strategy, teachers can make students realize that mathematics applies to gardening. Students understand that they must use numbers, whether they count seeds, measure soil & seed depth, or how much water is required for planting.
Through this strategy, teachers can make students realize that mathematics applies to gardening. Through landscaping, teachers can make students understand that determining the floor space area of a square or rectangular land requires multiplying the length by the width. Also, they will understand the importance of units used to measure quantities.
9. Balancing The Cheque Book
It is one of the best real-world math strategies for math teachers to make students understand the use of math in managing accounts. Students can learn that financing and math go hand-in-hand. Teachers can ask the students to help their parents balance expenses and savings for a particular month.
They can start by totaling all monthly debit and credit card purchases and comparing the results with the financial statements. Students can also check how much they’ve already paid in tuition fees and how much more(remaining) is to be paid next semester. In this way, students also can understand that financing and math go hand-in-hand.
10. Calculating Distances
Teachers can ask students to calculate the distance and time when traveling or riding a bicycle back home, which can help students think about math concepts such as time and distance. Students can measure and share the distance they traveled from their homes to the school and figure out who lives closest and farthest from the school, and this will help them understand the concept of time and distance easily.
Also Read: 10 Personalized Learning Strategies To Implement In Class
Therefore, these ten real-world math strategies are great for making students understand how math concepts are related to the real world. Students can easily understand the applications and utility of mathematics through these real-world math strategies. If you are looking for some more student engagement strategies for your middle school math classroom.
These real-life math strategies are easy to explain, and the things required to explain these are readily available. This will help your students relate math to their everyday life and create curiosity about the solution to the given math problem. Use these strategies with your students in your next math class and see them enjoying solving challenging math problems
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https://playingwithmodels.wordpress.com/tag/sports-ranking/
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math
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What would you do with a time machine? I bet some people would be chomping at the bit to pit two dominant teams from different eras against each other and have a grand old spectacle!
But alas, it is safe to say that a time machine will remain for the foreseeable future in the realm of magic.
Can we get a glimpse at what the outcome of such a magical game might be? Is there a scientifically sound way to rate sports teams in a way that judges their true strength. Most importantly, we need a method that yields ratings whose scale does not change with time so that a team that gets a rating of 2000 thirty years ago is as strong (in some sense) as a team that gets a rating of 2000 today.
We are indeed in luck! Such a system exists. It was proposed in the 1950’s by a Hungarian mathematician Arpad Elo (read about him on Wikipedia) and bears his name. His system is based on sound mathematical theory and ever since then dozens upon dozens of mathematical papers have been proving how reliable and reasonable the system is. Although Elo originally proposed his system to rate chess players, it has been adopted by a number of other sports bodies including FIDE, FIFA, MLB, EGF and others.
At the core of the ELO system is the ranking updating scheme which adjusts the ranking of the two teams (or players) after each match depending on the result. Given the rankings before the game, one can compute the probability of each outcome given that the actual performance has a certain probability distribution. If the stronger team wins its rating increases by a smaller amount than if the weaker team wins. There are many different specific incarnations of the system. While some are more accurate than others, even in its simplest form, the system is quite useful. In fact using publicly available match data we can resolve the question:
If 1997 Chicago Bulls played a best of 7 series against the 1986 Boston Celtics, what are the chances of each team winning?
After downloading the match data (56,467 games over 64 years that involved a total of 53 franchises some of which changed names and cities a number of time) and computing the rating history I came up with the top ten highest rated franchises:
|3||Los Angeles Lakers||1988||2163.3|
|8||San Antonio Spurs||2007||2089.4|
It is a telling sign that the NBA is a competitively healthy organization that the top 10 all time high ranking teams of all time pretty close to each other in rating. Also, it seems at least superficially, that there is no historical bias meaning the objective meaning of a rating does not change with time.
So, what would happen if the 1997 Bulls played a best of 7 series against the 1986 Celtics?
Home field advantage aside (the ranking I am using does not take that into account), the probability of the Bulls winning any particular game is . The probability of winning a best of 7 series (below )
The Bulls would have a 57.5% chance of winning the series: an exiting spectacle indeed!
Finally I leave you with a graph of the historical ratings of six teams from large metropolitan areas from 1980 to present day. It seems that it is extremely difficult to maintain a dominant team for more than a few seasons (although the Lakers managed to do so in the 1980’s).
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CC-MAIN-2017-17
| 3,252 | 14 |
http://www.koerner-co.com/pages.php?pID=10&CDpath=0
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math
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Calculating Water Temperature Required To Give Desired Dough Temperature
Suppose dough temperature is desired to be 80 degrees Fahrenheit. Then 80 times 3 will equal 240.
Suppose also that the Shop temperature is: 80 degrees Fahrenheit Flour temperature is: 80 degrees Fahrenheit X Machine allowance is: 28 degrees Fahrenheit Therefore, temperature of water required is 240 minus 188 degrees, or 52 degrees Fahrenheit.
X Machine allowance means that while the dough is being mixed in a high speed mixer, this dough heats up considerably, sometimes as high as 35 degrees Fahrenheit.
For example, stiff dough will heat much faster than a medium or slack dough. Also, the type of mixer being used matters. For large amounts of dough, say 200 pounds and over, 20% more ice will be used. For smaller amounts of dough, 1-2 gallons, 10% less ice is recommended.
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s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386165000886/warc/CC-MAIN-20131204135000-00044-ip-10-33-133-15.ec2.internal.warc.gz
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CC-MAIN-2013-48
| 854 | 5 |
https://www.presentica.com/arthurdenys/paradox-the-illusion-of-falsidical-proof
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math
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Paradox: The Illusion of Falsidical Proof
Chi Kwong Li's visual paradox exposes the allure of false proof, demonstrating that what appears to be right can turn out to be wrong.
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About Paradox: The Illusion of Falsidical Proof
PowerPoint presentation about 'Paradox: The Illusion of Falsidical Proof'. This presentation describes the topic on Chi Kwong Li's visual paradox exposes the allure of false proof, demonstrating that what appears to be right can turn out to be wrong.. The key topics included in this slideshow are . Download this presentation absolutely free.
1. PARADOX Chi-Kwong Li
2. A ‘ VISUAL ’ PARADOX : I LLUSION
3. F ALSIDICAL PARADOX A proof that seems right, but actually it is wrong! Due to: Invalid mathematical proof logical demonstrations of absurdities
4. E XAMPLE 1: 1=0 (?!) Let x=0 x(x-1)=0 x-1=0 x=1 1=0
7. Mathematical Induction The principle of mathematical induction: For a statement involving positive integer n. a) check that the statement is true for n = 1. b) check that if the statement is true for n = k, it will ensure that n = k+1 is true. Then the statement is true for all positive integer n. Suppose there are n balls in a box such that. If you are ensured that you pick a ball from the box with a certain color, then the next ball must be of the same color. The first ball you pick is a red ball. Then ……
8. If there are n (> 0) people in the this room, then they are of the same gender. A WRONG INDUCTION PROOF 3
9. Proof by Induction If there is one person only, then the statement is true. We show that if k people in this room have the same gender, then k+1 people in this room will have the same gender. Proof. For k+1 people, ask one person to leave the room. Then the k remaining people have the same gender. Now, ask the outside person to come back, and ask another person to leave the room. Then again the k remaining people have the same gender. So, …..
10. B UT WE KNOW , NOT ALL PEOPLE IN THIS ROOM HAVE THE SAME G ENDER ! What is wrong?
11. BARBER PARADOX (BERTRAND RUSSELL, 1901) Once upon a time... There is a town... - no communication with the rest of the world - only 1 barber - 2 kinds of town villagers: - Type A: people who shave themselves - Type B: people who do not shave themselves - The barber has a rule: He shaves Type B people only.
12. QUESTION: WILL HE SHAVE HIMSELF? Yes. He will! No. He won't! Which type of people does he belong to?
13. ANTINOMY p -> p' and p' -> p p if and only if not p Logical Paradox More examples: (1) Liar Paradox "This sentence is false." Can you state one more example for that paradox? (2) Grelling-Nelson Paradox "Is the word 'heterological' heterological?" heterological(adj.) = not describing itself (3) Russell's Paradox: next slide....
14. RUSSELL'S PARADOX Discovered by Bertrand Russell at 1901 Found contradiction on Naive Set Theory If we define all mathematical entities as sets, and assume that there is a universal set U containing every sets. Problem. Define a set R to be the elements in U such that x is not an element x. Question: Is R an element of R?
15. B IRTHDAY P ARADOX How many people in a room, that the probability of at least two of them have the same birthday, is more than 50%? Assumption: 1. No one born on Feb 29 2. No Twins 3. Birthdays are distributed evenly. Formula: ???
16. 3 T YPES OF P ARADOX Veridical Paradox : contradict with our intuition but is perfectly logical Falsidical paradox: seems true but actually is false due to a fallacy in the demonstration. Antinomy: be self-contradictive
17. A DDITIONAL PARADOX Surprise test paradox The instructor says that he will give a surprise test in one of the lectures. Then …. Zeno’s paradox ( Zeno of Elea , 490–430 BC) In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.
18. HOMEWORK 1. People from H village always tell the truth; people from L village always lie. If you have to decide to go left or go right to visit the H village, and seeing a person at the intersection who may be from H village or L village. What question should you ask the person to ensure that you will be told the right direction to the H village. 2. Consider the following proof of 2 = 1 Let a = b a 2 = ab a 2 – b 2 = ab – ab 2 (a-b)(a+b) = b(a-b) a + b = b b + b = b 2b = b 2 = 1 Which type of paradox is this? Which part of the proof is wrong?
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CC-MAIN-2023-50
| 4,485 | 21 |
https://houstonarthurbweglein.com/findanswers-171
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math
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Solve the equation. check the solution.
There are a variety of methods that can be used to Solve the equation. check the solution.. Math can be difficult for some students, but with the right tools, it can be conquered.
Solving the equation. check the solution.
This can help the student to understand the problem and how to Solve the equation. check the solution.. Algebra is one of the most difficult subjects for high school students. It can be very confusing, and it often involves memorizing a lot of formulas. The good news is that it doesn’t have to be this way! There are a lot of different ways you can solve algebra problems, and you can learn them all. When you learn another way to solve an algebra problem, you'll be able to see the math behind it. You’ll also understand why algebra works in the first place, which will make it easier to remember later on. By doing this, you'll be able to start solving algebra problems more easily and quickly. This will help you get better grades and make learning math less stressful. So, how do you solve algebra? First off, you want to practice by doing lots of practicing. Once you know how to solve an algebra problem, it will become easier for you to do so in the future. Second, you need to understand the concept behind it. If you don’t understand why something works in the first place, then it's going to be much harder for you to remember how to use that same method in the future. Finally, you need to identify your strengths and weaknesses when it comes to solving algebra problems. This will allow you to focus on what you're good at so that you can get better grades in the future! So,
Primary school teachers can use geometry word problem solver to support their teaching by allowing pupils to explore different geometric shapes and figures. Students can choose from a range of tools and resources such as cubes, spheres, cones and pyramids to solve maths problems such as finding the area of a rectangle or calculating the volume of a cube. Modern technology has made it easier for children to learn basic maths concepts. This includes the ability to access web-based resources such as geometry word problem solver.
Exponents with variables can be quite confusing. When you multiply two numbers whose exponents are both variable, you get a result that is also variable. For example, let's say you have the variable x, and the number y = 6x + 5. In this case, the exponent of y is variable because x is a variable. Now let's say you want to solve for y because you know that the exponent of y is 4. How do you solve this problem? You would factor out the variable x from both sides of the equation and find 4y = 4x + 1. This gives you the answer for y because now you know that 4y = 4(x + 1) = 4x –1. When this happens, we say that there is an "intractable" relationship between the variables on one side of an equation when they cannot be separated.
An example of an equation is 3 + 4 = 7. Two numbers are added (3), then subtracted (4). This yields the solution 7. In addition to equations, there are also word problems, which require you to fill in the blanks instead of just plugging in numbers. For example, if you’re given the number $40 and asked to find 40% of the total, this is a word problem because you don’t know what “of the total” means. To solve a math problem, you need to understand how to calculate different kinds of numbers and how to read equations and word problems correctly. Lots of practice will help you get used to these techniques.
They are used primarily in science and engineering, although they are also sometimes used for business and economics. They can be used to find the minimum or maximum value of an expression, find a root of a function, find the maximum value of an array, etc. The most common use of a quaratic equation solver is to solve a set of simultaneous linear equations. In this case, the user enters two equations into the program and it will output the solution (either via manual calculation or by generating one of several automatic methods). A quaratic equation solver can also be used to solve any other system of equations with fewer than three variables (for example, it could be used to solve an entire system of four equations). Quaratic equation solvers are very flexible; they can be programmed to perform nearly any type of calculation that can be done with algebraic formulas. They can also be adapted for specific applications; for example, a commercial quaratic equation solver can usually be modified to calculate electricity usage.
Amazing app I understand how to solve all my math equations this app explains how to solve the equation more than my teacher there is one thing I don’t like that this app doesn’t solve geometry problems
I love the app it's so helpful, if I get confused on a problem, I'll use the app to see where I messed up, I love this app though teachers aren't too fond of it because it "gives you the answers" but it helped me learn what I was taught oh it works better on the newer phones and iPods btw it may a but glitchy or leggy on the older versions but it still works pretty well
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CC-MAIN-2023-06
| 5,161 | 10 |
https://socratic.org/questions/all-of-the-reagent-solutions-have-a-concentration-of-0-2-m-this-means-that-there#422018
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math
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All of the reagent solutions have a concentration of 0.2 M. This means that there is 0.2 mole of dissolved substance per liter of solution. What will be the concentration after mixing, assuming you use equal volumes of each solution?
Depends how many solutions you have. Concentrations or molarities can only be expressed with respect to each dissolved species....
The concentrations will therefore reduce in proportion to the mix ratio. If we had two solutions and mixed equal volumes the concentration of each species would reduce by a factor of 1:2. If we had 4 solutions each of 0.2M and mixed together equal volumes of each, the concentrations of each would reduce by a factor of 1:4.
Here's an example. Lets assume we have 0.2M copper sulphate solution, and 0.2M sodium chloride solution.
Now lets mix together 500 ml of each solution.
In 500 ml of 0.2M copper sulphate solution we have 0.1 moles of copper sulphate. In 500 ml of 0.2M sodium chloride solution we have 0.1 moles of sodium chloride.
The mixture has a total volume of 1000 ml, so the concentration with respect to copper sulphate will be (0.1 / 1000) = 0.1 mol/litre or 0.1M. The concentration with respect to sodium chloride will also be (0.1 / 1000) = 0.1 mol/litre or 0.1M.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679102469.83/warc/CC-MAIN-20231210123756-20231210153756-00752.warc.gz
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CC-MAIN-2023-50
| 1,246 | 7 |
https://rreusser.github.io/explorations/sphere-eversion/
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math
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Topology is the study of the properties of geometric objects which aren’t changed by continuous deformation. A standard low-grade math joke is that toplogists consider a coffee mug and a doughnut equivalent because they’re both torii—(pauses for laughter)—one can be continuously deformed into the other, called a homeomorphism, without cutting or creasing the surface.
In this post, we play a topological game called eversion. Our objective is simple: turn a sphere inside out without cutting or creasing it. We consider a sphere, though a torus is also an interesting challenge.
That a sphere (specifically the two-sphere embedded in three dimensional space ) can be turned inside out was proved by Stephen Smale in 1957. However the proof is a proof of existence, offering no particular guidance for those hoping to perform the feat.
We should take a moment to appreciate that the analogous problem of everting a circle in two dimensions is impossible. The figure above illustrates that there’s really nothing to do but introduce loops which we can’t then get rid of. Don’t take my word for it though! The classic video Outside In has an much more involved discussion of what happens when we try.
Since the original proof, a number of realizations of sphere eversion have been discovered, ranging in generality and complexity. This post follows the method of Bednorz and Bednorz from Analytic sphere eversion using ruled surfaces.
Before stepping through the eversion, we lay out our ground rules, of which there are just two: We may not cut the surface, and the surface must always remain smooth. Note that unlike physical objects, self-intersection is permitted.
We start with a full presentation of the sphere eversion of Bednorz and Bednorz in Analytic sphere eversion using ruled surfaces. It goes by quickly, so we’ll then break it down and try to understand it a bit better. Along the way, you can drag the slider at the top to examine cross-sections.
Success! But that all happened very quickly. What happens at the top is clearly the key. In some sense, we do simply push one end of the sphere right through the other, but we need some clever tricks to keep the hole at the top smooth.
Bednorz and Bednorz break down the method as follows. As long as nothing topologically interesting happens at the poles of the sphere, we can simply remove them from the equation and focus on a cylindrical band around the equator. All that’s left then is to manipulate the cylindrical band carefully and replace the poles at the end of the process.
The key element of their method is a family of ruled surfaces, or surfaces swept out by a straight line moving through space, which accomplish this task. They propose a family parameterized by time . They’re careful to prove the surface remains smooth during the process, but we’ll remain content to get to our destination and visually check the smoothness along the way.
They propose the family of ruled surfaces given by the equations
The variable parameterizes the polar angle of the cylinder from to while parameterizes the vertical dimension of the cylinder. They suggest and .
Adjust the time parameter and observe the shape of the surface. There are two particular things to note. First, the surface always remains smooth, despite self-intersections, and second, the top and bottom of the edges of the cylinder swap places (with a bit of rotation which doesn’t trouble us) as we move from to .
Note also that although we’ll visualize eversion with , the eversion also works for values greater than two.
t = 1.500000
n = 2
Of course we want to evert a full sphere and not just a cylindrical band, so the remainder of their paper focuses on using stereographic projections to smoothly close the caps of the cylindrical band and maintain the topology of the sphere during the entire process. The full eversion is illustrated above, but let’s now step back through it, taking a bit more care to focus on the region of interest.
And that’s that! I regret that I have nothing novel or nuanced to say about the eversion itself, but my goal here was to explore the visual presentation since videos and images always left me wishing it were a bit more tangible.
There’s no shortage of really great visualizations and resources regarding sphere eversion, among other topics. Below are a few links relevant to both this eversion and the topic in general.
Comments? Questions? Corrections? Let me know!
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CC-MAIN-2023-50
| 4,476 | 20 |
http://recmath.com/PolyPages/PolyPages/PolyX/dst.htm
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math
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In order to make symmetric figures with the 10 domsliced tetrominoes it is necessary to ensure that we have a design which may be possible. To check on possibility we need to look at a chessboard colouring of the pieces. If we look at the pieces below we see that nine have a colouring of 1¾ to 1¼ an excess of ½ whereas one piece has a 2¼ to ¾ colouring which gives an excess of 1½.
Providing that we have no cross grain joins as in the figure above, whenever two half dominoes join they will for a domino which has a 1-1 colouring. Thus any figure with a border purely along grid lines will have all half dominoes joined into a domino and so the resulting figure must have a colouring excess of 2 squares.
If two of the edges of the border are formed by the sloping part of the half domino then we can have a colouring excess of 2 ± ½ ± ½ = 1, 2 or 3 and with four sloping edges we have 2 ± ½ ± ½± ½ ± ½ = 0, 1, 2, 3 or 4. Examples of each of these types are shown below.
From the above we can see immediately that no rectangle following grid lines is possible with the set. It might, however, be possible to for a sloping rectangle such as the one below which has an area of 30 units. This also, is seen to be impossible, however, if we consider the four edges. Firstly no piece can contribute to more than one edge and so if we remove the edge pieces we shall have four sloping edges and an area in the centre made up entirely of squares. We can now join the two opposite long edges to form another piece made up entirely of squares and finally the four pieces forming the short edges can be joined by their colouring to form two more balanced blocks. These four pieces will have a balanced colouring just as the figure itself did and so we can see that no solution is possible.
Despite all these restrictions, a number of symmetrical shapes is indeed possible as shown here.
It is also possible to make single and duplicate copies of hexominoes. The hexomino must be one with a 4-2 colouring and this is probably only possible for the two shown here.
If, however, we allow the duplicated hexomino to be different from the original then there are many more possibilities although the single sized one must still have a 4-2 colouring.
Similar constructions can be made with two sets of pieces. This is also solvable using the one sided set (bottom figure) but it seems likely that this may be the only solution.
Also with the one-sided set it is possible to form quadruplicated copies of a tetromino with a hole in the shape of the tetromino. The T-tetromino is impossible to use because of colouring considerations.
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CC-MAIN-2023-06
| 2,637 | 9 |
https://www.sykesvillebooks.com/book/9781013293825
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math
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Advanced Problems in Mathematics: Preparing for University (Paperback)
This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination.Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently.This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947473824.13/warc/CC-MAIN-20240222161802-20240222191802-00124.warc.gz
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CC-MAIN-2024-10
| 1,411 | 2 |
https://database-mathematics-solutions.com/buy.php?superlink=the-law-firm-of-hagel-and-hagel-is-located-in_1063
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math
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The law firm of Hagel and Hagel is located in downtown Cincinnati. There are 10 partners in the firm; 7 live in Ohio and 3 in northern Kentucky. Ms. Wendy Hagel, the managing partner, wants to appoint a committee of 3 partners to look into moving the firm to northern Kentucky. If the committee is selected at random from the 10 partners, what is the probability that:
a. One member of the committee lives in northern Kentucky and the others live in Ohio?
b. At least one member of the committee lives in northern Kentucky?
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947473472.21/warc/CC-MAIN-20240221102433-20240221132433-00030.warc.gz
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CC-MAIN-2024-10
| 523 | 3 |
http://www.solutioninn.com/two-processes-can-be-used-for-producing-a-polymer-that-reduces
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math
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Two processes can be used for producing a polymer that reduces friction loss in engines. Process K, which is currently in place, has a market value of $165,000 now, an operating cost of $69,000 per year, and a salvage value of $50,000 after 1 more year and $40,000 after its maximum 2-year remaining life. Process L, the challenger, will have a first cost of $230,000, an operating cost of $65,000 per year, and salvage values of $100,000 after 1 year, $70,000 after 2 years, $45,000 after 3 years, and $26,000 after its maximum expected 4-year life. The company's MARR is 12% per year. You have been asked to determine which process to select when
(a) A 2-year study period is used
(b) A 3-year study period is used.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187820930.11/warc/CC-MAIN-20171017072323-20171017092323-00634.warc.gz
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CC-MAIN-2017-43
| 717 | 3 |
https://www.studymode.com/essays/Activity-Lab-4-Non-Uniform-Motion-370CD43CC7193A1A.html
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math
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* Problem: What is the acceleration of the puck in the air table?
Material List: * Strip of Paper * Puck * Foot pedal * Air table * Procedure:
1) Place a long sheet of white unlined paper, and place it on the air table.
2) Turn on the air table machine.
3) Place the puck top of the air table over the long sheet of white unlined paper
4) Using your foot, press down on the foot pedal.
5) Release the puck from the top of the air table and continue to hold onto the foot pedal.
6) Once the puck has gone over the long white unlined paper, release the foot pedal.
7) Turn off the machine
8) Take the long white unlined paper and measure the points and analyze the results.
Data Collection and Processing
Aspect 1 …show more content…
Firstly, When measuring the distance between the points that was burnt into the piece of paper by the air puck and then, dividing the time (0.05s) per point, we can conclude that uniform motion was not achieved. I can tell that there is a lack of uniform trend by observing the measurements. Secondly, uniform motion occurs only when an object travels at a constant velocity. By looking at the velocity is a function of time graph, we can tell that the best fit line is not a horizontal line, which means that the velocities are not the same, which also proves that the movement of the puck is not in uniform motion. Lastly, acceleration is determined by calculating the slope of the line on a velocity as a function of time graph which is 0.9ms-2. Acceleration indicates the motion of an object. If the acceleration does not equal to zero, then the object is not moving at a constant velocity or speed, because velocity (or speed) is changing. This indicates that the puck in the air table is not moving at a constant velocity as well. There are some systematic and random
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s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499695.59/warc/CC-MAIN-20230128220716-20230129010716-00447.warc.gz
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CC-MAIN-2023-06
| 1,809 | 13 |
https://www.ams.org/journals/tran/2016-368-06/S0002-9947-2015-06464-2/home.html
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math
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We introduce the matching measure of a finite graph as the uniform distribution on the roots of the matching polynomial of the graph. We analyze the asymptotic behavior of the matching measure for graph sequences with bounded degree.
A graph parameter is said to be estimable if it converges along every Benjamini–Schramm convergent sparse graph sequence. We prove that the normalized logarithm of the number of matchings is estimable. We also show that the analogous statement for perfect matchings already fails for $d$–regular bipartite graphs for any fixed $d\ge 3$. The latter result relies on analyzing the probability that a randomly chosen perfect matching contains a particular edge.
However, for any sequence of $d$–regular bipartite graphs converging to the $d$–regular tree, we prove that the normalized logarithm of the number of perfect matchings converges. This applies to random $d$–regular bipartite graphs. We show that the limit equals the exponent in Schrijver’s lower bound on the number of perfect matchings.
Our analytic approach also yields a short proof for the Nguyen–Onak (also Elek–Lippner) theorem saying that the matching ratio is estimable. In fact, we prove the slightly stronger result that the independence ratio is estimable for claw-free graphs.
- Miklós Abért and Tamás Hubai, Benjamini-Schramm convergence and the distribution of chromatic roots for sparse graphs, Combinatorica 35 (2015), no. 2, 127–151. MR 3347464, DOI 10.1007/s00493-014-3066-7
- M. Abért, A. Thom and B. Virág, Benjamini-Schramm convergence and pointwise convergence of the spectral measure, preprint at http://www.math.uni-leipzig.de/MI/thom/
- Itai Benjamini and Oded Schramm, Recurrence of distributional limits of finite planar graphs, Electron. J. Probab. 6 (2001), no. 23, 13. MR 1873300, DOI 10.1214/EJP.v6-96
- Béla Bollobás, The independence ratio of regular graphs, Proc. Amer. Math. Soc. 83 (1981), no. 2, 433–436. MR 624948, DOI 10.1090/S0002-9939-1981-0624948-6
- B. Bollobás and B. D. McKay, The number of matchings in random regular graphs and bipartite graphs, J. Combin. Theory Ser. B 41 (1986), no. 1, 80–91. MR 854605, DOI 10.1016/0095-8956(86)90029-8
- Maria Chudnovsky and Paul Seymour, The roots of the independence polynomial of a clawfree graph, J. Combin. Theory Ser. B 97 (2007), no. 3, 350–357. MR 2305888, DOI 10.1016/j.jctb.2006.06.001
- Mohsen Bayati, David Gamarnik, Dimitriy Katz, Chandra Nair, and Prasad Tetali, Simple deterministic approximation algorithms for counting matchings, STOC’07—Proceedings of the 39th Annual ACM Symposium on Theory of Computing, ACM, New York, 2007, pp. 122–127. MR 2402435, DOI 10.1145/1250790.1250809
- P. Csikvári and P. E. Frenkel, Benjamini–Schramm continuity of root moments of graph polynomials, European Journal of Combinatorics (2015), DOI 10.1016/j.ejc.2015.07.009.
- Gábor Elek and Gábor Lippner, Borel oracles. An analytical approach to constant-time algorithms, Proc. Amer. Math. Soc. 138 (2010), no. 8, 2939–2947. MR 2644905, DOI 10.1090/S0002-9939-10-10291-3
- Paul Erdős and Horst Sachs, Reguläre Graphen gegebener Taillenweite mit minimaler Knotenzahl, Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 12 (1963), 251–257 (German). MR 165515
- S. Friedland, E. Krop, and K. Markström, On the number of matchings in regular graphs, Electron. J. Combin. 15 (2008), no. 1, Research Paper 110, 28. MR 2438582, DOI 10.37236/834
- David Gamarnik and Dmitriy Katz, A deterministic approximation algorithm for computing the permanent of a 0, 1 matrix, J. Comput. System Sci. 76 (2010), no. 8, 879–883. MR 2722354, DOI 10.1016/j.jcss.2010.05.002
- C. D. Godsil, Algebraic combinatorics, Chapman and Hall Mathematics Series, Chapman & Hall, New York, 1993. MR 1220704
- Leonid Gurvits, Van der Waerden/Schrijver-Valiant like conjectures and stable (aka hyperbolic) homogeneous polynomials: one theorem for all, Electron. J. Combin. 15 (2008), no. 1, Research Paper 66, 26. With a corrigendum. MR 2411443
- L. Gurvits, Unleashing the power of Schrijver’s permanental inequality with the help of the Bethe Approximation, arXiv preprint 1106.2844v11
- Ole J. Heilmann and Elliott H. Lieb, Theory of monomer-dimer systems, Comm. Math. Phys. 25 (1972), 190–232. MR 297280, DOI 10.1007/BF01877590
- Monique Laurent and Alexander Schrijver, On Leonid Gurvits’s proof for permanents, Amer. Math. Monthly 117 (2010), no. 10, 903–911. MR 2759363, DOI 10.4169/000298910X523380
- Wolfgang Lück, $L^2$-invariants: theory and applications to geometry and $K$-theory, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 44, Springer-Verlag, Berlin, 2002. MR 1926649, DOI 10.1007/978-3-662-04687-6
- Russell Lyons, Asymptotic enumeration of spanning trees, Combin. Probab. Comput. 14 (2005), no. 4, 491–522. MR 2160416, DOI 10.1017/S096354830500684X
- Brendan D. McKay, The expected eigenvalue distribution of a large regular graph, Linear Algebra Appl. 40 (1981), 203–216. MR 629617, DOI 10.1016/0024-3795(81)90150-6
- Brendan D. McKay, Spanning trees in regular graphs, European J. Combin. 4 (1983), no. 2, 149–160. MR 705968, DOI 10.1016/S0195-6698(83)80045-6
- H. N. Nguyen and K. Onak, Constant-time approximation algorithms via local improvements, 49th Annual IEEE Symposium on Foundations of Computer Science (2008), pp. 327–336.
- Alexander Schrijver, Counting $1$-factors in regular bipartite graphs, J. Combin. Theory Ser. B 72 (1998), no. 1, 122–135. MR 1604705, DOI 10.1006/jctb.1997.1798
- A. Schrijver and W. G. Valiant, On lower bounds for permanents, Nederl. Akad. Wetensch. Indag. Math. 42 (1980), no. 4, 425–427. MR 598000, DOI 10.1016/1385-7258(80)90043-8
- M. Voorhoeve, A lower bound for the permanents of certain $(0,\,1)$-matrices, Nederl. Akad. Wetensch. Indag. Math. 41 (1979), no. 1, 83–86. MR 528221, DOI 10.1016/1385-7258(79)90012-X
- Ian M. Wanless, Addendum to Schrijver’s work on minimum permanents, Combinatorica 26 (2006), no. 6, 743–745. MR 2288357, DOI 10.1007/s00493-006-0040-z
- Miklós Abért
- Affiliation: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, 13-15 Reáltanoda u., 1053 Budapest, Hungary
- Email: [email protected]
- Péter Csikvári
- Affiliation: Department of Mathematics, Massachusets Institute of Technology, Cambridge Massachusetts 02139 – and – Department of Computer Science, Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary
- Email: [email protected]
- Péter E. Frenkel
- Affiliation: Department of Algebra and Number Theory, Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary – and – Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, 13-15 Reáltanoda u., 1053 Budapest, Hungary
- MR Author ID: 623969
- Email: [email protected]
- Gábor Kun
- Affiliation: Department of Computer Science, Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary
- Address at time of publication: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, 13-15 Reáltanoda u., 1053 Budapest, Hungary
- Email: [email protected], [email protected]
- Received by editor(s): January 6, 2014
- Received by editor(s) in revised form: April 15, 2014
- Published electronically: October 5, 2015
- Additional Notes: The first and third authors were partially supported by ERC Consolidator Grant 648017. The first three authors were partially supported by the Hungarian National Foundation for Scientific Research (OTKA), grant no. K109684. The second author was partially supported by the National Science Foundation under grant no. DMS-1500219 and the Hungarian National Foundation for Scientific Research (OTKA), grant no. K81310. The fourth author was partially supported by the Hungarian National Foundation for Scientific Research (OTKA), grant No. PD 109731, by the János Bolyai Scholarship of the Hungarian Academy of Sciences, by the Marie Curie IIF Fellowship, grant No. 627476, and by ERC Advanced Research, grant No. 227701. All authors were partially supported by MTA Rényi “Lendület” Groups and Graphs Research Group.
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 4197-4218
- MSC (2010): Primary 05C70; Secondary 05C31, 05C69
- DOI: https://doi.org/10.1090/tran/6464
- MathSciNet review: 3453369
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https://estebantorreshighschool.com/equation-help/hydrostatic-equilibrium-equation.html
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math
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What is the hydrostatic equation?
The equation is: dP/dz = – density*gravity. Written in English, this is the change in pressure with the change in height is equal to the average density of the air times the gravitational constant.
What is meant by hydrostatic equilibrium?
In fluid mechanics, hydrostatic equilibrium or hydrostatic balance (also known as hydrostasy) is the condition of a fluid or plastic solid at rest. This occurs when external forces such as gravity are balanced by a pressure-gradient force.
When the atmosphere is in hydrostatic equilibrium what two forces are in balance?
The direction of the gravitational force points toward the Earth’s core (downward from the surface) and thus gravity is a force on the air acting to push it toward the ground. These two forces when equally balanced is termed “hydrostatic balance”.
How do we know the sun is in hydrostatic equilibrium?
When the force due to pressure exactly balances the force due to gravity, a system is in hydrostatic equilibrium. The Sun’s hydrostatic equilibrium is stable and self-regulating; if you tossed a little extra matter onto the Sun, the inward force of gravity would increase.
What is an example of hydrostatic pressure?
Blood is a fluid, so blood has a hydrostatic pressure. Increased elevation increases the amount of hydrostatic pressure. For example, the veins and capillaries in our feet have about 100 mm Hg more pressure inside than those at heart level.
What are the common forms of the hydrostatic equation?
The way we determine this is through an equation: P = rho * g * d, where P is the pressure, rho is the density of the liquid, g is gravity and d is the depth. You may also see the hydrostatic equation written as P = rho * g * h, where the h stands for height.
What is hydrostatic principle?
The principle of hydrostatic equilibrium is that the pressure at any point in a fluid at rest (whence any point in a fluid at rest (whence, “hydrostatic”) is just due to the weight of the overlying fluid.
What happens to a star if it is no longer in hydrostatic equilibrium?
When that happens, the star can no longer hold up against gravity. Its inner layers start to collapse, which squishes the core, increasing the pressure and temperature in the core of the star.
What are the two forces involved in hydrostatic equilibrium?
Hydrostatic equilibrium says that there is a balance between two forces at every point within a star. One force is the inward force of gravity. The other force is the pressure in the gas caused by its temperature (recall that the pressure in an ideal gas is proportional to its temperature).
Is the moon in hydrostatic equilibrium?
The smallest body confirmed to be in hydrostatic equilibrium is the dwarf planet Ceres, which is icy, at 945 km, whereas the largest body known to not be in hydrostatic equilibrium is the Moon, which is rocky, at 3,474 km.
What is hydrostatic balance in atmosphere?
If the net upward pressure force on the slab is equal to the downward force of gravity on the slab, the atmosphere is said to be in hydrostatic balance.
When was the hydrostatic balance invented?
What star balances the most gravity?
In any given layer of a star, there is a balance between the thermal pressure (outward) and the weight of the material above pressing downward (inward). This balance is called hydrostatic equilibrium.
Which layer of sun is its surface?
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https://www.arxiv-vanity.com/papers/1210.2180/
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math
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Mellin Transform and Image Charge Method for Dielectric Sphere in an Electrolyte
We revisit the image charge method for the Green’s function problem of the Poisson-Boltzmann equation for a dielectric sphere immersed in ionic solutions. Using finite Mellin transformation, we represent the reaction potential due to a source charge inside the sphere in terms of one dimensional distribution of image charges. The image charges are generically composed of a point image at the Kelvin point and a line image extending from the Kelvin point to infinity with an oscillatory line charge strength. We further develop an efficient and accurate algorithm for discretization of the line image using Padé approximation and finite fraction expansion. Finally we illustrate the power of our method by applying it in a multiscale reaction-field Monte Carlo simulation of monovalent electrolytes.
oisson-Boltzmann equation, finite Mellin transform, Green’s function, Multiscale reaction field model, Fast algorithm, Padé approximation, Finite fraction expansion
35J08; 65R10; 78A35; 82D15
The method of image charges is a classical technique [40, 23] for electrostatic problems. Its most elementary application is the problem of a point charge in a spherical cavity inside a conducting medium (or the reciprocal problem of a point charge outside a conducting sphere). In 1845, William Thomson (Lord Kelvin) noticed that the vanishing-potential boundary condition of conductors can be automatically satisfied on the sphere by putting an image point charge at the Kelvin point. A natural extension is the problem of a dielectric sphere inside a different dielectric background, where a single point image charge no longer works. In 1883 Carl Neumann discovered that a point image at the Kelvin point together with a line image starting from the Kelvin point to infinity solves the boundary condition. This result has been independently re-derived by several authors, up to 1990s; see the reviews [37, 45] for more details. More recently, the problem of a spherical cavity inside an ionic solution has been studied [8, 46]. It is again found that the image charge distribution consists of a point image and a line image. Computational method for the line charge density has been developed which works well in the asymptotic limits [8, 46] that is either large or small, where is the inverse Debye length, while is the radius of spherical cavity. The current work addresses the general case where is neither large nor small.
The main advantage of image charge methods is to represent the effects of polarization charges in terms of point charges or line of charges, and therefore avoiding the task of numerically solving boundary value problems. This can substantially reduce the computational cost in Monte Carlo or molecular dynamics simulation of charged systems. Further reduction of computational cost can be achieved by discretizing line images using Gaussian quadratures, which effectively approximates a line charge by a few point charges. The total electrostatic energy of the system can then be represented as Coulomb interaction between many point charges.
Most interfaces appearing in nature have irregular shapes, and the corresponding Green’s functions can not be represented in terms of simple distributions of image charges. Hence one may rightfully argue that image charge methods have rather limited applications. The most important usage of image charge methods, however, arises in the multiscale reaction-field modeling of Coulomb many body systems, where the interfaces are artificially introduced. Spherical interfaces are almost always used for their simplicity, and for the availability of analytic results for image charges. Research along this direction is of current interest in both simulations and continuum modeling [36, 12, 31, 15, 42, 5, 44].
Due to the long range nature of Coulomb interaction, simulation of charged systems is highly nontrivial. A proper treatment of boundary conditions is vital in order to obtain physically meaningful results. Periodic boundary conditions can remove artificial boundary effects in a self-consistent fashion and restore the translation symmetry. Combined with Ewald summation method , the cost of computing the total energy of the system with particles scale as . This can be further reduced to the order of using a mesh-based algorithm such as the particle mesh Ewald or particle-particle particle-mesh Ewald lattice summation techniques. The periodic images are however unphysical and may produce artifacts that obscure the real physics. Besides, computational cost of Ewald-type summation method is still rather prohibitive for large systems in Monte Carlo simulations, which limits simulation of charged systems to rather small size. The development of non-Eward methods remains important topics; See Fukuda and Nakamura for a recent review.
An attractive alternative is to use the reaction field type of modeling, which is essentially a multi-scale strategy, schematically illustrated in Figure 1. In this approach, an artificial (spherical) cavity is introduced. All ions inside the cavity, together with possible mesoscopic objects such as charged proteins and colloids, are treated explicitly using microscopic model (such as the primitive model ) together with Monte Carlo/Molecular Dynamics 111Strictly speaking, grand canonical ensemble must be used in order to treat charge fluctuations properly. , while ions outside the cavity are treated implicitly using appropriate continuum theory, such as linearized Poisson-Boltzmann (PB) theory. It is known that linearized PB provides an accurate approximation to dilute electrolytes. For any charge inside the cavity, then, we must solve the electrostatic Green’s function problem, where the potential satisfies Poisson equation inside the cavity, and satisfies the (linearized) PB equation outside. The resulted Green’s function provides the pairwise electrostatic interaction (the force field) between mobile ions. This problem can be efficiently solved using the image charge method developed in this work.
In this multi-scale modeling approach, the microscopic model inside the system and the continuous theory outside the cavity really describe the same system. Therefore the parameters of the Poisson-Boltzmann theory need to be determined self-consistently. These include the Debye length and the effective dielectric constant. For dilute electrolyte, the Debye length can be theoretically calculated as a function of ion densities, while the dielectric constant can be taken to be that of the solvent. Some unphysical artifacts also arise because of the artificial hard wall repulsion of the cavity surface. Using statistical mechanics, one can study this artifact and use extra short range interaction to compensate it. Alternatively, one can also ignore the details inside a thin shell near the cavity surface of thickness 1 - 2 ion diameters. Finally, to achieve the balance between efficiency and precision, the radius of cavity should be chosen to be couple of the Debye length. We also note that there can be different levels of modeling inside the cavity. In the so-called hybrid implicit/explicit model , both solvent molecules and ions are treated explicitly inside the cavity. By contrast, in the so-called hybrid primitive/implicit model, the solvent inside the cavity is modeled implicitly as a dielectric medium, while the ions are treated at the level of primitive model.
The reaction field model augmented by our image charge methods is therefore able to provide an accurate treatment of the electrostatic boundary conditions. Its computation cost of the total energy scales as , where here is the total number of particles including all ions as well as their images. While for small systems (with total particle number typically smaller than 1000) this cost is manageable, for large systems, it becomes unrealistic. Fortunately, the computation cost can be dramatically reduced using fast multipole based methods [21, 4, 10, 22]. The computational cost for the combined method generally scales as .
In this paper, we mainly focus on the image charge method for the Green’s function problem of these multi-scale reaction field models. The statistical mechanical foundation of these reaction field models will be discussed in a separate publication. In the remaining of this work, we shall first define the Kirkwood series for the Green’s function (Sec. II) and then use the inverse Mellin transform to find the image charge representation (Sec. III). We further discretize the line image using method of Gauss quadrature and construct an efficient numerical scheme for the computation of the reaction potential. In Sec. IV, we compute the reaction potential using our method and quantify the errors. We also demonstrate the power of multi-scale modeling by Monte Carlo simulating a dilute symmetric electrolyte.
2 Green’s function of the Poisson-Boltzmann equation
As illustrated in Figure 2, let be a spherical cavity with radius , centered at the origin, with dielectric constant . The volume outside the cavity is filled with electrolyte, which is described by linearized Poisson-Boltzmann theory and is characterized by a Debye length and dielectric constant . Consider a point unit charge fixed at inside the cavity, the average potential (averaged over the statistical fluctuations of electrolyte outside the cavity) satisfies the following equations:
where and are the average potential inside and outside the cavity respectively. The boundary condition at infinity is
Throughout the paper we use light italic letter to represent the magnitude of a vector . On the cavity boundary, the Green’s function satisfies the following standard electrostatic interface conditions:
The general boundary value problem associated with Eqs. (1)-(3) actually defines the electrostatic Green’s function, , which equals inside the cavity and outside. It is this Green’s function that shall be directly used in the multi-scale reaction field modeling of electrolyte. The inverse Debye length is defined by where is the Bjerrum length of the solvent ( for water at room temperature), and are the bulk concentration and the valence of the th species of ions.
The Green’s function defined in Eqs. (1)-(3) has an azimuthal symmetry, hence depends only on and , where is the angle between the source point and the field point , see Fig. 2. The potential inside the cavity can be written as,
which is the superposition of the direct Coulomb potential and the reaction potential which is a harmonic function. Both potentials can be expanded in terms of spherical harmonics:
|where is the smaller (larger) one between and , while are constants to be determined, and is Legendre polynomial of order . The potential outside the cavity can also be expanded in terms of Legendre polynomials:|
where is the modified spherical Hankel function (also called the modified spherical Bessel function of the third kind) , defined by the following series,
For source charge inside the cavity, we always have
Using the orthogonality of the spherical harmonics, we obtain the following expansion of the reaction potential, widely known as Kirkwood series expansion :
with the harmonic coefficients given by
where and The Kirkwood series expansion has been used in the calculation of the reaction potential inside a spherical cavity in simulations [24, 6]. It converges slowly when a source charge approaches to the cavity surface, which prevents its wide application in dynamical and Monte Carlo simulations.
3 Image charge representation and algorithm
In this section, we develop an image charge representation for the reaction potential using finite Mellin transformation.
3.1 Finite Mellin transform
Let be a function defined in the interval . Its finite Mellin transform, is defined as
where is generically a complex variable. The original function can be expressed in terms of by the inverse Mellin transform
Here the integration is carried out over a vertical line, , in the complex plane. The dual functions form a finite Mellin transform pair.
The finite Mellin transform is closely related to the one-sided Laplace transform. Let , then Likewise, the inverse transform can also be expressed in terms of the inverse Laplace transform. The finite Mellin transform is equivalent to the usual Mellin transform for the function with compact support in the finite interval. The usual Mellin transform can be defined in terms of the two-sided Laplace transform.
Two finite Mellin transform pairs shall be useful in our discussion below,
where is the Dirac delta function. The Mellin transformation of the second pair is defined for .
We shall consider in Eq. (10) as a function of and analytically continue the integer variable into the complex plane. This can be done through using the integral representation of Bessel functions, for which and the modified Bessel function of the second kind (see, e.g. Ref. , pp. 917)
for . Let be the inverse finite Mellin transformation of ,222 We shall suppress the dependence of on , to avoid cluttered notations. we have
As given by Eq. (10), the harmonic coefficient is finite for all , which ensures the existence of the finite Mellin transform. Substituting Eq. (15b) into the Kirkwood series Eq. (9), and using , the reaction potential can be re-expressed as
Let us further define a vector . As decreases from to , the vector runs from the Kelvin point to infinity along the radial direction. We shall see that this is precisely the loci of the image charge line. Let be the magnitude of vector , we have . Since we are only interested in the field point inside the cavity, we have , hence we can sum the series in Eq. (16) using the expansion Eq. (5a) and obtain
The last integral represents the potential generated by one dimensional distribution of image charges along the radial direction, which starts from the Kelvin point and extends to infinity. The linear charge density is . The geometry is illustrated in Fig. 2. Therefore we arrive at our main result in this work.
where the line charge density is and .
The image charge representation for the reaction potential Eq. (18) is equivalent to the Kirkwood series representation, Eq. (9). It is advantageous because the line integral can be efficiently discretized by Gauss quadrature. A few Gauss points can provide approximations with accuracy as high as desired . Physically, this amounts to approximating line image by a few point images.
3.2 Point image and line image
The following limit of the Bessel function can be established (using Eq. (28))
Combining with Eq. (10) we obtain the large limit of the coefficients :
The coefficients Eq. (10) can therefore be decomposed into two parts
where vanishes as goes to infinity.
The inverse Mellin transform of a constant is a delta function , while the inverse Mellin transform of the function is generally a continuous function in the interval . The linear charge density therefore can be decomposed into (with ):
The first term corresponds to a point image at the Kelvin point, and the second term corresponds to a continuous line image extending from the Kelvin point to infinity.
The simplest limit is , where the exterior of the cavity becomes a conductor. In this limit, we easily see from Eq. (10) that , and . The image charge distribution reduces to a single point image at the Kelvin point, a well known result.
When the dielectric constants inside and outside the cavity are the same, i.e. , the point image vanishes, but the line image persists. This is precisely the case of multi-scale reaction field model for electrolytes.
3.3 Neumann’s result revisited
Let us review the simple case where there is no screening ions outside the cavity, i.e. . In 1883, Neumann found an exact expression for the reaction field, in terms of a point image charge at the Kelvin point and a line image:
where . This formula has been re-derived independently by various authors in different fields of applications [48, 14, 11, 38, 28, 35]; also see Lindell’s review for the summary of history. The Mellin transform method was also used by Lindell and collaborators [29, 34] for finding image charges of the Poisson equation in layered media.
Its inverse Mellin transform can be exactly calculated using Eq. (13):
The application of the Neumann’s result in molecular dynamics can be found in two recent papers [26, 27]. The reciprocal problem of a source charge placed outside of a sphere was also applied in Monte Carlo simulations of colloidal systems [9, 19]. Historically, what is widely used in computer simulations of biological systems is only single image charge approximations, see works by Friedman and Abagyan and Totrov . These methods are of the first or second order accuracy in the dielectric ratio . They fail to be accurate if the ratio is not small.
3.4 Limits of large cavity and small cavity
For , the inverse Mellin transform of can not be exactly calculated. One way to proceed is to use the following asymptotic approximation ,
which gives the correct leading order asymptotics both for and for . Substituting it back into Eq. (10) leads to
where . The inverse Mellin transform of this can be easily found. This approximation works well for the case of small (small cavity) and large (large cavity).
3.5 Large asymptotics of
Let us first look at the large limit of the Bessel function . For sufficiently large , the largest term in the sum Eq. (6) is given by . We can therefore rewrite the summation as
where we have defined . We can expand the function being summed into asymptotic series in terms of and extend the upper limit of summation from to . The resulting summation then can be calculated order by order in . This can be conveniently done using Wolfram Mathematica. For example, up to order of , we have
It then follows that
Generically, therefore, the leading order term of scales as . In the most interesting case , however, this term vanishes and we have
Now consider the limit where the source charge approaches the cavity boundary, we have . The reaction potential acting on the source charge then (see Eq. (9)) becomes
Therefore the line image strength must vanish at the Kelvin point.
3.6 The general case
3.6.1 Padé approximations to harmonic coefficients
In the multi-scale reaction field model, we typically have and of order of unity. All methods discussed above fail in this case. To obtain accurate approximation, we approximate the harmonic coefficients by a rational function of (i.e. Padé approximation):
with constants and for all . Clearly Eq. (25) is a special case of Eq. (32) with . The second term on the right hand side is the order Padé approximant 333Here and refer to the degree of polynomials in the numerator and in the denominator respectively. of the function , and the rational polynomial preserves the asymptotics,
The coefficients are solved by the nonlinear least square method. For given and dielectric ratio , the constants in the expansion can be simply determined by a minimization of the total error of the first terms of the harmonic coefficients,
The Newton iteration scheme or other iteration algorithms can be applied to solve this nonlinear optimization problem.
To demonstrate the quality of Padé approximation, we list in Table 1 the relative errors for the cases of and 3 with various parameters and :
where is the numerical solution of the nonlinear least square problem (34). We take since 51 multipoles in the Kirkwood series already provide sufficiently high accuracy. It should be pointed out that the minimization solution depends on the initials and may be not a global minimization. Nonetheless, the results in Table 1 clearly show the remarkable precision of the Padé approximation. For example, the worst case for has a relative error . In comparison, the asymptotic method Eq. (25) yields much larger error, and completely breaks down for .
|Asymptotics Eq. (25)|
3.6.2 Image expressions through inverse Mellin transforms
After the best-fitting coefficients are determined, we can further re-express the Padé approximation Eq. (32) using the partial fraction expansion:
where the coefficients and can be determined by the Heaviside’s cover-up method. Using Eq. (13), the inverse Mellin transform , we easily find the image charge distribution:
with represents a line image density from the Kelvin image point to the infinity along the radial direction. Alternatively, the reaction potential is,
Figure 3 illustrates the profiles of line image strengths for and for varying from to 1 calculated with . Note that the line image is always oscillatory, which implies that some of the parameters are complex numbers. Note also that both amplitude and period increase with the dielectric ratio .
3.6.3 Discretization of the line image
Computation of the line integral in Eq. (38) using the continuous linear charge density Eq. (37) is still expensive. This is a quite severe limitation on the computational efficiency, since the line integral has to be computed in every simulation step. Therefore we further discretize the line integral (38) using numerical quadrature. This amounts to approximating the linear image using multiple point image charges. An efficient discretization scheme uses fewer point images, and for large-scale systems the computation of pairwise interactions of these source-image charges can be speeded up with fast multipole-type algorithms [4, 10, 22, 47] to achieve approximately linear complexity, significantly reducing the computational cost in computer simulations.
We consider the case of . Extension of the algorithm to other values of is straightforward. Since must be real and the line charge is oscillatory, the parameters in Eq. (35) are generally composed of a positive real number and a complex conjugate pair. The same clearly also holds for the set of parameters . Let be real and
The line image strength in Eq. (37) can be expressed as
where . Note that the second term is oscillatory, in agreement with Fig. 3.
Approximating an oscillating integral is tricky. We divide the integral in Eq. (38) into two parts:
with a positive number sufficiently larger than unity. The first integral in Eq. (41) can be transformed into an integral over the interval through the linear variable transformation:
with and a positive constant. Due to the finite interval being integrated, the integrand is only weakly oscillatory. Further defining a function via
we can easily show that
The resulting integral over can be then integrated using the classical -point Gauss-Legendre quadrature, which discretizes the line image into several point image charges
and are the Gauss quadrature points and weights.
For the second integral in the RHS of Eq. (41), the Gauss quadrature is less efficient due to the high oscillatory integrand for small . Fortunately, the variable is much larger than , hence the integrand can be expanded in terms of the ratio :
The first few terms can be explicitly worked out using Eq. (40):
In summary, the reaction potential Eq. (38) is approximated by image point charges plus a few correction terms,
where the term of represents the Kelvin image charge, with and . As pointed out previously, the Kelvin image vanishes when .
Remark. The error of approximating Eq. (41) comes from two sources. One is from the Gauss quadrature to the finite integral, and the other is from the truncation of multipoles for the infinite integral. Both errors depend on the cutoff parameter . In approximating infinite integral, the leading term in the error of the truncation is where . The Gauss quadrature has a fast convergence, hence we expect a small such that a few points leading to high accuracy. We find provides a good balance between two approximations in an accuracy of 3 digits.
4 Numerical results
In this section, we compute the reaction potential using our method and quantify the errors. We also demonstrate the power of multi-scale modeling by Monte Carlo simulating a dilute symmetric electrolyte.
4.1 Accuracy and efficiency of discretization scheme
We first test the accuracy of our discretization scheme. We focus on the most difficult case where the line image is strongly oscillatory, and the point image vanishes. It is also the case appears in the multiscale modeling of electrolytes. We take and , and calculate the relative error of the self energy of a unit charge, , as a function of the source point radius by comparing with 201-terms-truncation of the Kirkwood series. The latter has a truncation error about (for example, when the error is about ) and can be considered as the “exact” solution. We set and . We find that the accuracy of numerical quadrature only weakly depends on and .
We use and Gauss quadrature points for the integration on the finite interval and the two different corrections for the integration on interval : and . Note that means the second term of Eq. (47) is a constant correction. The results are shown in Figure 4. It is seen that the image charge approximation is very accurate even with only 4 image points, with the overall relative errors remaining less than . The accuracy however does decrease when approaches to the boundary.
To determine the asymptotics of image charge approximation for the self energy near the boundary, we also compare it with the direct truncation of the Kirkwood series, in the range . These results, shown in Figure 5, clearly demonstrate that image charge approximation converges much faster than the Kirkwood series near the boundary. In particular, image charge approximation with 4 image charges is uniformly better than Kirkwood series with 20 terms. For example, the error of Kirkwood series with 20 terms is larger than for , and increases to for , while the error of the image charge approximation remains less than .
We also compare the CPU timing efficiency of our image charge method and that of the Kirkwood series. The comparison was performed using the optimized module for the Bessel functions by Matlab, and the algorithm of the Legendre polynomials in Numerical Recipes . The machine used has double-core 2.3GHz CPU and 8G memory. We use the same system parameters as in the accuracy test and calculate the pairwise energy of ions randomly distributed in the cavity. In the image method we use images and and 1 corrections, respectively. The Kirkwood series are truncated at 10th, 20th and 50th terms. The results are listed in Table 2. We see the image method with 4-point images is generally 40-50 times faster than the method of Kirkwood series truncated at 20-th terms. With these parameters, two methods have similar accuracy.
4.2 Application in Monte Carlo simulations of electrolytes
To illustrate the utility of our image charge method, we apply it in a reaction-field Monte Carlo simulation of electrolyte. We artificially introduce a spherical cavity with radius in the electrolyte, and model all charges in the cavity using the primitive model and simulate them using Monte Carlo method. All ions outside the cavity, together with the solvent, are treated implicitly using linearized PB theory, characterized by two parameters: the dielectric constant and the inverse Debye length . For any ion inside the cavity, the effects of the electrolyte outside the cavity is to introduce a reaction potential, which can be calculated using our image charge method. It is important to note that the inverse Debye length characterizing the medium outside the cavity shall be self-consistently determined by the simulation of the ions inside the cavity.
We run canonical Monte Carlo simulations of the primitive model using the standard Metropolis criterion [32, 16] for particle displacements. The ions are modeled by hard spheres with diameter and with a point charge of valence at its center. The ions are mobile in the solvent medium with dielectric permittivity . The effective Hamiltonian of the system is given by
The self energy is given by
where is the Bjerrum length and is the Boltzmann factor. We take for the water permittivity at room temperature. The infinite potential is due to the presence of the hard wall at The pairwise interaction energy is given by
As is well known, the reaction potential is symmetric under permutation of two variables: .
We first calculate the density distribution by taking a system with and the salt concentration is which corresponds to a Debye length . We calculate both the cases with and without the reaction field. In the former case, we use different numbers of image charges varying from 4 to 6, with the parameters for numerical quadratures the same as those in the upper panel of Figure 4. For each setting, we run MC cycles for each particle to obtain samples for the statistics of particle number in each spherical shell with thickness .
In Figure 6 we show the radial distribution function of anions, i.e., the normalized density, . The distribution of cations is similar. Evidently, without accounting for the reaction field, the density is higher near the center of cavity and lower near the cavity boundary. The difference in the density is up to 3 percent. When the reaction field is taken into account, the particle density shows variation less than in most regions inside the cavity. There is substantial deviation of density near the cavity boundary. This is due to the presence of the artificial hard wall on the boundary, see Eq. (49). This problem can be cured by adding to the self energy a short ranged correction, or by introducing a buffer zone of a certain thichness (). The latter approach has been discussed in literature [3, 43, 26]. We shall present statistical mechanical discussion of the former approach in a separate publication.
Finally, in Figure 7, we plot the results for three different bulk ionic concentrations, where and respectively. These results again show the necessity of treating the reaction potential, as well as the accuracy and efficiency of our image charge methods. It is also interesting to note that as the Debye length decreases the density becomes flatter, suggesting that the reaction-field Monte Carlo models becomes more precise. For the case of salt concentration , for example, the Debye length is approximately half of the cavity radius, while the density variation becomes less than (excluding the thin region affected by the hard wall artifacts).
In summary, we have developed an image method for charges inside a spherical cavity that is immersed in an ionic solution. Our method is useful for multiscale reaction field models of electrolytes and other more complicated charged systems. We derive an analytic expression for the reaction potential in terms of one dimensional image charge distribution, and discuss a highly accurate and efficient algorithm for discretizing the image line charge. We also apply our method to a reaction field Monte Carlo simulations of electrolytes. and demonstrate the accuracy and efficiency of the new algorithm.
Simulation of charged systems is computationally expensive, therefore is always limited to small system size. In a physical system of such size, the total charge may fluctuate away from zero to a noticeable extent. These fluctuations can not be taken into account in canonical ensemble simulations. In another word, grand canonical ensemble must be used to capture the charge fluctuations of small systems. Ewald-summation method, which is so far the most popular simulation methods for charged systems, are based on periodic boundary conditions, and are difficult to be incorporated with grand canonical ensemble. By strong contrast, reaction-field type of models, besides being more intuitive, can be easily adapted to a grand canonical Monte Carlo simulation. This shall be the topic of a separate publication.
The authors acknowledge the financial support from the Natural Science Foundation of China (Grant Numbers: 11101276, 11174196, and 91130012) and Chinese Ministry of Education (NCET-09-0556). Z. X. acknowledges the financial support from the Alexander von Humboldt foundation for a research stay at the Institute for Computational Physics, University of Stuttgart. The authors thank Professors Wei Cai and Chunjing Xie for helpful discussion.
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| 39,756 | 163 |
https://sattakingtoday.com/school-382
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math
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Verify trig identities solver with steps
Keep reading to learn more about Verify trig identities solver with steps and how to use it. Math can be difficult for some students, but with the right tools, it can be conquered.
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Verify trig identities solver with steps can be a useful tool for these scholars. Solving quadratic equations by factoring is a process that can be used to find the roots of a quadratic equation. In order to solve a quadratic equation by factoring, the first step is to rewrite the equation in standard form. The next step is to factor the equation. Once the equation is factored, the roots of the equation can be found by setting each factor equal to zero and solving for x. Solving quadratic equations by factoring is a useful tool that can be used to find the roots of any quadratic equation.
The hardest math problem in the world is the Riemann hypothesis, which is a conjecture about the distribution of prime numbers. The conjecture is that all non-zero whole numbers are either a power of two or the sum of two prime numbers. The conjecture has never been proven, and it is still an open question for mathematicians.
Solving inequalities can be a very difficult task. The standard method of solving an inequality is to add or subtract the values of the variables involved until the inequality is true. This method can be time consuming, especially if the problem involves a large number of variables. Some programs, such as MATLAB and Maple, allow students to create “solver” functions that simplify the process of solving inequalities. These functions are often very powerful, and can solve problems more quickly than traditional methods. For more advanced users, there are also many online resources for solving inequalities. Solver websites will allow users to create a test problem (such as a variable equation) and then provide a solution for it. Although this method requires some experience with programming, it is a very powerful tool for students who struggle with inequality problems.
The Pythagorean theorem solver is a program designed to calculate the area of a square or rectangle. It can be used to determine the area of almost any shape, including circles and triangles. It is also useful for calculating areas that contain any type of curved line, such as radius or circumference. In addition to calculating areas, it can also compute the perimeter and circumference of a shape. The Pythagorean theorem solver has several advantages over other types of square or rectangle calculators. It is able to solve problems with shapes of different sizes, including squares that are shaped like trapezoids and triangles with acute angles. Unlike traditional calculators, it does not require any user input. This makes it easy to use for anyone who is visually impaired or has limited physical dexterity. In addition, programs like the Pythagorean theorem solver can be used in specific circumstances, such as when calculating areas where there is an exact number of objects that need to be measured. By contrast, there are times when a calculator may not work well because of a limitation in its design itself.
Solving for a side of a triangle is actually quite simple. We can take the given side and then subtract from it the length of one of the other sides (remember, if we’re looking for an unknown, we’re subtracting one thing from another). Once we have the new length, we can compare it to the original to see if there’s a discrepancy. If there is, then we know that the unknown side is half as long as that other side. If not, then we know that the unknown side is twice as long as that other side. The best way to remember how to solve for a side of a triangle is just to think about what happens when you add together two sides and then subtract one. When you add sides together and then subtract one of them, you are in effect solving for something; you are finding out which side is twice as long as another one.
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CC-MAIN-2022-49
| 4,021 | 8 |
http://www.ask.com/science/manometer-used-3e58f8f39c15f29e
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math
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A manometer measures the difference between two different points of pressure. A manometer works by balancing the weight of a column of fluid between the two points of interest.Know More
Different fluids are used in the fluid column depending on the nature of the pressure difference. If the different is large, then a heavy fluid, such as mercury may be used. If the difference is relatively small, such as that measured in a wind tunnel, then a lighter fluid, such as water is used.
There are many different designs of manometers, including digital models. The simplest design uses a sealed length of glass tubing bent into a U-shape. The tube is then filled with the liquid to the sealed end so that no air remains trapped in it. The open end of the tube is then attached to the system whose pressure is to be measured. Gas will exert pressure on the open end with the result that the liquid will be at a higher level in the sealed end than in the open end. The difference between the two levels is an indication of the pressure of the gas in the system.
Manometers are used in a variety of laboratory applications to measure the pressure of gases and liquids and also in the field of medicine.Learn more about Measurements
The difference, or subtraction, between120 hertz and 240 hertz is 120 hertz. These two frequencies are typically used to measure the refresh rate of high-definition televisions. Although in theory a higher refresh rate frequency is better, in actuality it makes little difference, explains PC Magazine.Full Answer >
While both miles and kilometers are units used to measure distance, miles are part of the imperial system of measurement, and kilometers are part of the metric system of measurement. The only country to use the imperial system, and thus miles, as the official distance measure is the United States.Full Answer >
The difference between frequency and amplitude is that frequency is a measurement of cycles per second, and amplitude is a measurement of how large a wave is. Amplitude represents the wave's energy.Full Answer >
In technical usage, 1 kilocalorie is equal to 1,000 calories. The terms are subject to some confusion, however, since in popular speech "calorie" and "kilocalorie" are often used interchangeably. Wikipedia explains that this confusion has motivated some writers and scientists to capitalize "Calories" for kilocalories, as a way of distinguishing between the two.Full Answer >
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| 2,442 | 8 |
http://p4tkmatematika.kemdikbud.go.id/artikel/2011/12/15/mbi-matematika-sd-edisi-desember-2011/
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math
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Oleh: Estina Ekawati, S.Si, M.Pd.Si
- Mr. White ultiples the first one hundred prime numbers. How many consecutive zero digits can be found at the end of the rseulting number?
- Jack and Ben are cycling from A to B. Jack travels at a speed of 15 km/hour while Ben travels at a speed of 12 km/hour. It takes Ben 15 minutes more to complete his travel than Jack does. What is the distance between A and B?
- Barbara writes numbers consisting of four digits: 3, 5, 7, and 9 according to the following rules.
- Digit 7 does not appear in the first nor the last positions
- Digit 7 should be to the roght of the digit 5. (For example, digit 5 in the number 7395 appears to the right of digits 7, 3, and 9). Find all such possible numbers.
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CC-MAIN-2022-21
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https://sycuciwycaq.pfmlures.com/write-an-inequality-for-the-graph-open-study-app-9669nu.html
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math
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Inequality Graphing App Graphing inequalities is made simple for the beginning or intermediate calculator user with the Inequality Graphing App. Read the License before continuing. By downloading the application you indicate your agreement with the terms and conditions of the License. Subject to your payment of any applicable license fee, Texas Instruments Incorporated "TI" grants you a license to copy and use the software program s on a TI calculator and copy and use the documentation from the linked web page or CD ROM both software programs and documentation being "Licensed Materials".
Systems of Equations and Inequalities In previous chapters we solved equations with one unknown or variable. We will now study methods of solving systems of equations consisting of two equations and two variables. Represent the Cartesian coordinate system and identify the origin and axes. Given an ordered pair, locate that point on the Cartesian coordinate system.
Given a point on the Cartesian coordinate system, state the ordered pair associated with it. We have already used the number line on which we have represented numbers as points on a line.
Note that this concept contains elements from two fields of mathematics, the line from geometry and the numbers from algebra. Rene Descartes devised a method of relating points on a plane to algebraic numbers. This scheme is called the Cartesian coordinate system for Descartes and is sometimes referred to as the rectangular coordinate system.
This system is composed of two number lines that are perpendicular at their zero points. Perpendicular means that two lines are at right angles to each other. Study the diagram carefully as you note each of the following facts.
The number lines are called axes.
Example 3 Graph the solution for the linear inequality 2x - y ≥ 4. Solution Step 1: First graph 2x - y = 4. Since the line graph for 2x - y = 4 does not go through the origin (0,0), check that point in . Fit an algebraic two-variable inequality to its appropriate graph. If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *pfmlures.com and *pfmlures.com are unblocked. Solve, Graph and Write Inequalities Make sure that you can draw a graph from an inequality and write an inequality when given a graph. Pay attention to open and closed circles.
The horizontal line is the x-axis and the vertical is the y-axis. The zero point at which they are perpendicular is called the origin. Positive is to the right and up; negative is to the left and down. The arrows indicate the number lines extend indefinitely.
Thus the plane extends indefinitely in all directions. The plane is divided into four parts called quadrants. These are numbered in a counterclockwise direction starting at the upper right. Points on the plane are designated by ordered pairs of numbers written in parentheses with a comma between them, such as 5,7.
This is called an ordered pair because the order in which the numbers are written is important. The ordered pair 5,7 is not the same as the ordered pair 7,5. Points are located on the plane in the following manner. First, start at the origin and count left or right the number of spaces designated by the first number of the ordered pair.
Second, from the point on the x-axis given by the first number count up or down the number of spaces designated by the second number of the ordered pair.
Ordered pairs are always written with x first and then y, x,y. The numbers represented by x and y are called the coordinates of the point x,y. The first number of the ordered pair always refers to the horizontal direction and the second number always refers to the vertical direction.
Check each one to determine how they are located.
What are the coordinates of the origin? Find several ordered pairs that make a given linear equation true. Locate these points on the Cartesian coordinate system.
Draw a straight line through those points that represent the graph of this equation. A graph is a pictorial representation of numbered facts.We can also graph inequalities on the number line. The following graph represents the inequality x≤2.
The dark line represents all the numbers that satisfy x≤2. If we pick any number on the dark line and plug it in for x, the inequality will be true. Write an inequality for the graph Download jpg.
Ask for details ; Follow Report by Richy1 03/09/ It is d you are right because open circle mean and it was pointing to the right so that means it was x>3. 0 votes Get the Brainly App5/5(1). Solving and Graphing Absolute Value Inequalities: Practice Problems; Studying with Flashcards.
If you are studying for a test on inequalities, these flashcards can provide a review of the main concepts.
This Write and Graph Inequalities: Temperature Video is suitable for 6th - 8th Grade. What temperature does water freeze?
Have your learners show in an inequality all the possible temperatures. The video demonstrates how to set up an inequality based on the situation given and how to graph it. This quiz and worksheet will help you assess your knowledge of writing equations with inequalities.
To pass the quiz you must be familiar with signs related to writing these equations and other. Write and graph a linear inequality that represents th situation. To start out, you have to write the inequality they are asking for. I'm assuming we can't spend any more than $48, but we don't have to spend all of $ If it costs $5 for every album (x) and $8 for every movie (y), than we'd write an inequality: App for Students.
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| 5,645 | 21 |
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| 1,521 | 15 |
http://www.solutioninn.com/suppose-that-you-purchase-randomly-select-3-tv-sets-from
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math
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Question: Suppose that you purchase randomly select 3 TV sets from
Suppose that you purchase (randomly select) 3 TV sets from a production run of 10 TV sets. Of the 10 TV sets, 9 are destined to last at least five years without needing a single repair. What is the probability that all three of your TV sets will last at least five years without needing a single repair?
Answer to relevant QuestionsSuppose that you own a car dealership and purchase (randomly select) 7 cars of a certain make from a production run of 200 cars. Of the 200 cars, 160 are destined to last at least five years without needing a major repair. ...United Medicine, Inc., claims that a drug, Viro, significantly relieves the symptoms of a certain viral infection for 80 percent of all patients. Suppose that this drug is given to eight randomly selected patients who have ...A candy company claims that its new chocolate almond bar averages 10 almonds per bar. Let x denote the number of almonds in the next bar that you buy. Use the Poisson distribution to find p (x ≤ 4) if the candy company’s ...Consider the figure given in the margin. Find the value c that makes the function f(x) a valid continuous probability distribution. Suppose that the random variable x is normally distributed with mean μ = 500 and standard deviation σ = 100. For each of the following, use the normal table to find the needed value k. In each case, draw a sketch. a. P(x ...
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CC-MAIN-2017-34
| 1,456 | 4 |
http://forums.devx.com/showthread.php?16704-problem-using-amp-nbsp-with-ListBox-in-ASP-NET&goto=nextoldest
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math
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I have a ListBox web control. I want to fill a ListBox text property with
two columns separating each other with space character ( but in output
list it just produce instead of a blank.
Can anyone help me.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123318.85/warc/CC-MAIN-20170423031203-00564-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 338 | 8 |
http://dommelen.net/quantum2/style_a/nt_diag.html
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math
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D.18 Eigenfunctions of commuting operators
Any two operators and that commute, , have a common set
of eigenfunctions, provided only that each has a complete set of
eigenfunctions. (In other words, the operators do not necessarily
have to be Hermitian. Unitary, anti-Hermitian, etcetera, operators
First note the following:
if is an eigenfunction of with eigenvalue , then
is either also an eigenfunction of with eigenvalue
or is zero.
To see that, note that since and commute
which is . Comparing start and end, the
combination must be an eigenfunction of with
eigenvalue if it is not zero. (Eigenfunctions may not be zero.)
Now assume that there is just a single independent eigenfunction
for each distinct eigenvalue of . Then if
is nonzero, it can only be a multiple of that single
eigenfunction. By definition, that makes an eigenfunction
of too, with as eigenvalue the multiple. On the other hand, if
is zero, then is still an eigenfunction of ,
now with eigenvalue zero. So under the stated assumption, and
have the exact same eigenfunctions, proving the assertion of this
However, frequently there is
degeneracy, i.e. there is
more than one eigenfunction for a
single eigenvalue . Then the fact that, say, is
an eigenfunction of with eigenvalue no longer means that
is a multiple of ; it only means that
is some combination of all of
. Which means that
is not in general an eigenfunction of .
To deal with that, it has to be assumed that the problem has been
numerically approximated by some finite-dimensional one. Then and
will be matrices, and the number of independent eigenfunctions (or
rather, eigenvectors now) of and will be finite and equal.
That allows the problem to be addressed one eigenfunction at a time.
Assume now that is an eigenfunction of , with eigenvalue
, that is not yet an eigenfunction of too. By completeness, it
can still be written as a combination of the eigenfunctions of ,
and more particularly as where
is a combination of the eigenfunctions of with
eigenvalue and a combination of the eigenfunctions of
with other eigenvalues. There must be such eigenfunctions with
nonzero, because without using the you cannot
create an equal number of independent eigenfunctions of as of .
but that must mean that
since if it is not, cannot make up the difference; as seen
earlier, only consists of eigenfunctions of that do
not have eigenvalue . According to the above equation,
, which is already an eigenfunction of with
eigenvalue , is also an eigenfunction of with eigenvalue .
So replace one of the , ,...with
. (If you write in terms of the
, ,..., then the function you replace
may not appear with a zero coefficient.) Similarly replace an
eigenfunction of with eigenvalue with . Then
and have one more common eigenfunction. Keep going in this way
and eventually all eigenfunctions of are also eigenfunctions of
and vice versa.
Similar arguments can be used recursively to show that more generally,
a set of operators that all commute have a single
common set of eigenfunctions. The trick is to define an artificial
new operator, call it , that has the common eigenfunctions of
and , but whose eigenvalues are distinct for any two eigenfunctions
unless these eigenfunctions have the same eigenvalues for both and
. Then the eigenfunctions of , even if you mess with them,
remain eigenfunctions of and . So go find common
eigenfunctions for and .
The above derivation assumed that the problem was finite-dimensional, or
discretized some way into a finite-dimensional one like you do in numerical
solutions. The latter is open to some suspicion, because even the
most accurate numerical approximation is never truly exact.
Unfortunately, in the infinite-dimensional case the derivation gets much
trickier. However, as the hydrogen atom and harmonic oscillator
eigenfunction examples indicate, typical infinite systems in nature do
obey the theorem anyway.
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CC-MAIN-2024-10
| 3,888 | 75 |
http://www.jetradar.com.au/flights/Alicante-ALC-to-London-LON/?dont_redirect_please=true&marker=direct
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math
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Best airfares from Alicante to LondonJetradar compares airfares from Alicante to London with hundreds of airlines (including British Airways, American Airlines, Lufthansa) and dozens of online travel agencies in one single place. We provide you with all the options to find the cheapest flights to London, you choose where to book. Also there you can find airlines special offers from Alicante to London. The cheapest round-trip price found within the last week was A$102. The cheapest oneway price found within the last week was A$96.
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| 1,797 | 12 |
https://livemcqs.com/2022/07/21/how-can-we-understand-the-standard-deviation/
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math
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The standard deviation is one of the main tools in the analysis of the data and it is dispersion. When you are able to do the Standard deviation test by the Standard deviation calculator, then it is easy for us to analyze the whole data. When we are using the sd calculator, then we analyze what is the mean values and what are the upper and the lower limit of the whole population of the data. In reality, it is impossible to analyze the whole population of the data, and you always go for a sample evaluation. When you apply the test on the test on the sample by the standard deviation. Then the whole picture about the whole population would be quite clear for you. Calculate standard deviation and find the information about the whole population of the data, you can evaluate what is the highest values and what are the lowest values and between the lower the upper limit the whole set of the data is residing.
In the following article, we are discussing what is the importance of the standard deviation and what is its utilization.
Why do we use standard deviation?
The standard deviation is one of the main tools in defining the depth of the data in our observation. We are going to find all the variance in data by the mean and standard deviation calculator. When we are able to find the variance in the whole data, then we are able to predict the following calculation:
- The mean of the data, and the culture of the values around it. This would represent the whole population of the data and its resonating values.
- The upper and the lower limit of the data and clarify the picture of how the data is dispersed and what its variance is around the whole set of the data.
In the following example, we are defining the mean, variance, and standard deviation from the set of the data
Question: Find the mean, variance, and standard deviation for the following data?
|Class Interval||Frequency (f)||Mid Value (xi)||fxi||fxi2|
|0 – 10||27||5||135||675|
|10 – 20||10||15||150||2250|
|20 – 30||7||25||175||4375|
|30 – 40||5||35||175||6125|
|40 – 50||4||45||180||8100|
|50 – 60||2||55||110||6050|
|?f = 55||?fxi = 925||?fxi2 = 27575|
N = ?f = 55
Mean = (?fxi)/N = 925/55 = 16.818
Variance = 1/(N – 1) [?fxi2 – 1/N(?fxi)2]
= 1/(55 – 1) [27575 – (1/55) (925)2]
= (1/54) [27575 – 15556.8182]
Standard deviation = ?variance = ?222.559 = 14.918
Analysis of the concepts:
The complete analysis of the question is essential to understand the concept of the standard deviation and how we can find the standard deviation by the sample standard deviation calculator. The population standard deviation calculator can analyze the whole set of the population in a matter of seconds. But you should be familiar with the following concepts to make sure, that you are familiar with the whole result.
The first and the foremost concept is the class interval, in this case, the class intervals are 0-10,10-20, 20-30,30-40, 40-50, 50-60. These are the class intervals, actually, we have divided the whole set of data into small and regular intervals to know their frequencies and how much data is residing in one specific interval.
The frequencies of various intervals are 27, 10, 7, 5, and 4,2, and these are the frequencies of various class intervals. For example, the interval 0-10 has a frequency of 27 and the class 10-20 has a frequency of 10, and the 7, 5, 4, and 2 for the proceeding class intervals. The class interval 0-10 has the highest frequency and the class interval 50-60 has the minimum frequency of 2.
Mid values (xi):
The mid values are the middle values of our data range, for example, the class interval 0-10 has a middle range of 5. The class interval 0-20 has a middle range of 15, 25, 35, 45, and 55 for the next class intervals.
The frequency of middle values( fxi):
The Standard deviation calculator(fxi) can be calculated by multiplying the frequency (f) and the middle values. In the above question, the frequencies of the middle values are given as 135, 150, 175, 175,180,110. The sd calculator readily finds the frequencies of the middle values and we are easily able to evaluate the values.
The total frequency of middle(fxi2):
The total frequency of the middle values is calculated by the frequency of the middle values. In the above question the the total frequencies are 675, 2250, 4375, 6125, 8100, 6050 for the class intervals 0-10, 0-20, 0-30, 0-40, 0-50, 0-60.The total frequency is telling how many times, the mean values are residing in our calculations. This can be extracted from the data, and it would be greatly helpful; in finding the frequency of the data.
The Summations ?f, ?fxi, ?fxi2 :
The summation ?f, ?fxi, ?fxi2 is the simple addition of all the above calculations. Now the ?f is the total frequency, ?fxi is the total frequency of the middle values. When we are able to find the sample standard deviation by the simple formula if we are able to find all the calculations.
The main thing for the students to learn is a concept like the Standard deviation, it is essential to learn the basics like the class interval, frequency, the mean frequency, and the total mean frequency. When you are able to extract all the data values, then it is easy for the students to calculate all the variance and the standard deviation calculation. It would be great for the students doing the research as the standard deviation is vastly used in the analysis of the data and the profile for your data.
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CC-MAIN-2022-49
| 5,442 | 35 |
http://www.fixya.com/support/t2238870-use_sharp_el_531w_solve_quadratic
|
math
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Question about Sharp EL-531VB Calculator
This calculator does not have a program to which you give the equation, and which returns the solutions. Sorry. You have to use the formulas you learned.
Let the equation be ax^2 +bx+c=0
You compute the discriminant Callit disc.
1. If discriminant is larger than zero you have two solutions. Let us call them x1 and x2.
Then x1=(-b+square root of disc)/(2*a)
and x2= (-b-square root of disc)/(2*a)
2. If disc=0 , square root of disc =0 and x1=x2=-b/(2*a)
3. If disc is negative, there are no real solutions.
To find the solutions you replace a, b, and c by their numerical values, to calculate disc, its square root, and calculate X1 and X2.
Hope it helps.
Posted on Sep 17, 2009
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s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589417.43/warc/CC-MAIN-20180716174032-20180716194032-00602.warc.gz
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| 1,500 | 27 |
https://xabelisalaj.urbanagricultureinitiative.com/what-is-a-hypothesis-question-58018te.html
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math
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Formulating the research question or developing the hypothesis can help you to decide on the approach of the research. A research question is the question the research study sets out to answer.
Print What is a Hypothesis? A hypothesis is a tentative, testable answer to a scientific question. Once a scientist has a scientific question she is interested in, the scientist reads up to find out what is already known on the topic.
Then she uses that information to form a tentative answer to her scientific question. Sometimes people refer to the tentative answer as "an educated guess. A hypothesis leads to one or more predictions that can be tested by experimenting.
Predictions should include both an independent variable the factor you change in an experiment and a dependent variable the factor you observe or measure in an experiment.
A single hypothesis can lead to multiple predictions, but generally, one or two predictions is enough to tackle for a science fair project. Examples of Hypotheses and Predictions Question Prediction How does the size of a dog affect how much food it eats?
Larger animals of the same species expend more energy than smaller animals of the same type.
To get the energy their bodies need, the larger animals eat more food. If I let a pound dog and a pound dog eat as much food as they want, then the pound dog will eat more than the pound dog.
Does fertilizer make a plant grow bigger?
IRENE PEPPERBERG Research Associate, Psychology, Harvard University; Author, The Alex Studies The Fallacy of Hypothesis Testing. I've begun to rethink the way we teach students to engage in scientific research. A hypothesis is an explanation for a set of observations. Here are examples of a scientific hypothesis. Although you could state a scientific hypothesis in various ways, most hypothesis are either "If, then" statements or else forms of the null hypothesis. The null hypothesis sometimes is called the. In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite urbanagricultureinitiative.com states: There is no set whose cardinality is strictly between that of the integers and the real numbers.. The continuum hypothesis was advanced by Georg Cantor in , and establishing its truth or falsehood is the first of Hilbert's 23 problems presented in
Plants need many types of nutrients to grow. Fertilizer adds those nutrients to the soil, thus allowing plants to grow more. If I add fertilizer to the soil of some tomato seedlings, but not others, then the seedlings that got fertilizer will grow taller and have more leaves than the non-fertilized ones.
Does an electric motor turn faster if you increase the current? As more current flows through the motor's electromagnet, the strength of the magnetic field increases, thus turning the motor faster.
If I increase the current supplied to an electric motor, then the RPMs revolutions per minute of the motor will increase. Is a classroom noisier when the teacher leaves the room? Teachers have rules about when to talk in the classroom.
If they leave the classroom, the students feel free to break the rules and talk more, making the room nosier. If I measure the noise level in a classroom when a teacher is in it and when she leaves the room, then I will see that the noise level is higher when my teacher is not in my classroom. What if My Hypothesis is Wrong?
What happens if, at the end of your science project, you look at the data you have collected and you realize it does not support your hypothesis?
First, do not panic! The point of a science project is not to prove your hypothesis right. The point is to understand more about how the natural world works.
Or, as it is sometimes put, to find out the scientific truth. When scientists do an experiment, they very often have data that shows their starting hypothesis was wrong.
Well, the natural world is complex—it takes a lot of experimenting to figure out how it works—and the more explanations you test, the closer you get to figuring out the truth.
For scientists, disproving a hypothesis still means they gained important information, and they can use that information to make their next hypothesis even better. In a science fair setting, judges can be just as impressed by projects that start out with a faulty hypothesis; what matters more is whether you understood your science fair project, had a well-controlled experiment, and have ideas about what you would do next to improve your project if you had more time.
You can read more about a science fair judge's view on disproving your hypothesis here. It is worth noting, scientists never talk about their hypothesis being "right" or "wrong.IRENE PEPPERBERG Research Associate, Psychology, Harvard University; Author, The Alex Studies The Fallacy of Hypothesis Testing.
I've begun to rethink the way we teach students to engage in scientific research. Although you could state a scientific hypothesis in various ways, most hypothesis are either "If, then" statements or else forms of the null urbanagricultureinitiative.com null hypothesis sometimes is called the "no difference" hypothesis.
It only took five minutes for Gavin Schmidt to out-speculate me.
Schmidt is the director of NASA ’s Goddard Institute for Space Studies (a.k.a. GISS) a world-class climate-science facility. One. When you answered this question, you formed a hypothesis. A hypothesis is a specific, testable prediction.
It describes in concrete terms . Question: "What is the documentary hypothesis?" Answer: The documentary hypothesis is essentially an attempt to take the supernatural out of the Pentateuch and to deny its Mosaic authorship. The accounts of the Red Sea crossing, the manna in the wilderness, the provision of water from a solid rock, etc., are considered stories from oral tradition, thus making the miraculous happenings mere.
hypothesis as, "a tentative explanation for an observation, phenomenon, or scientific problem that can be tested by further investigation." This means a hypothesis is the .
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CC-MAIN-2020-29
| 6,057 | 24 |
https://www.bigcommercereview.org/file-ready/maths-2014-junior-waec
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math
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CC-MAIN-2019-26
| 1,888 | 7 |
http://www.hindawi.com/journals/aaa/2013/629468/ref/
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math
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- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 629468, 10 pages
Convergence Theorems for Fixed Points of Multivalued Strictly Pseudocontractive Mappings in Hilbert Spaces
1Mathematics Institute, African University of Science and Technology, PMB 681, Garki, Abuja, Nigeria
2Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, USA
3Université Gaston Berger, 234 Saint Louis, Senegal
4Department of Mathematical Sciences, Bayero University, PMB 3011, Kano, Nigeria
Received 10 September 2012; Accepted 15 April 2013
Academic Editor: Josef Diblík
Copyright © 2013 C. E. Chidume et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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CC-MAIN-2014-10
| 7,124 | 63 |
https://www.boomerangbooks.com.au/book.cfm?isbn=9780898715460
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math
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Description - Solving Nonlinear Equations with Newton's Method by C. T. Kelley
This brief book on Newton's method is a user-oriented guide to algorithms and implementation. In just over 100 pages, it shows, via algorithms in pseudocode, in MATLAB, and with several examples, how one can choose an appropriate Newton-type method for a given problem, diagnose problems, and write an efficient solver or apply one written by others. It contains trouble-shooting guides to the major algorithms, their most common failure modes, and the likely causes of failure. It also includes many worked-out examples (available on the SIAM website) in pseudocode and a collection of MATLAB codes, allowing readers to experiment with the algorithms easily and implement them in other languages. The author covers both simple techniques for scalar problems as well as contemporary techniques (e.g. inexact Newton methods and Newton-Krylov techniques) for larger scale problems.
This book is intended to complement Kelley's larger book, Iterative Methods for Linear and Nonlinear Equations (SIAM, 1995), which focuses on in-depth treatment of convergence theory, but does not discuss the details of solving particular problems, implementation in any particular language, or evaluating a solver for a given problem.
Buy Solving Nonlinear Equations with Newton's Method by C. T. Kelley from Australia's Online Independent Bookstore, Boomerang Books.
(229mm x 152mm x 6mm)
Society for Industrial & Applied Mathematics,U.S.
Publisher: Society for Industrial & Applied Mathematics,U.S.
Country of Publication:
Book Reviews - Solving Nonlinear Equations with Newton's Method by C. T. Kelley
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s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886107065.72/warc/CC-MAIN-20170821003037-20170821023037-00360.warc.gz
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CC-MAIN-2017-34
| 1,664 | 9 |
https://projecteuclid.org/euclid.jap/1402578641
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math
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Journal of Applied Probability
- J. Appl. Probab.
- Volume 51, Number 2 (2014), 528-541.
On the asymptotic behaviour of extremes and near maxima of random observations from the general error distributions
As the name suggests, the family of general error distributions has been used to model nonnormal errors in a variety of situations. In this article we show that the asymptotic distribution of linearly normalized partial maxima of random observations from the general error distributions is Gumbel when the parameter of these distributions lies in the interval (0, 1). Our result fills a gap in the literature. We also establish the corresponding density convergence, obtain an asymptotic distribution of the partial maxima under power normalization, and state and prove a strong law. We also study the asymptotic behaviour of observations near the partial maxima and the sum of such observations.
J. Appl. Probab., Volume 51, Number 2 (2014), 528-541.
First available in Project Euclid: 12 June 2014
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Vasudeva, R.; Kumari, J. Vasantha; Ravi, S. On the asymptotic behaviour of extremes and near maxima of random observations from the general error distributions. J. Appl. Probab. 51 (2014), no. 2, 528--541. doi:10.1239/jap/1402578641. https://projecteuclid.org/euclid.jap/1402578641
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http://nrich.maths.org/public/leg.php?code=-99&cl=2&cldcmpid=2792
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Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?
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There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
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What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.
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These rectangles have been torn. How many squares did each one have inside it before it was ripped?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
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https://www.arxiv-vanity.com/papers/hep-th/0503124/
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math
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Frederik Denef†† , Michael R. Douglas†† , Bogdan Florea†† , Antonella Grassi†† and Shamit Kachru††
Department of Physics and Astronomy, Rutgers University,
Piscataway, NJ 08855-0849, USA
I.H.E.S., Le Bois-Marie, Bures-sur-Yvette, 91440 France
Department of Mathematics, University of Pennsylvania,
Philadelphia, PA 19104-6395, USA
Department of Physics and SLAC, Stanford University,
Stanford, California, CA 94305, USA
We discuss a simple example of an F-theory compactification on a Calabi-Yau fourfold where background fluxes, nonperturbative effects from Euclidean D3 instantons and gauge dynamics on D7 branes allow us to fix all closed and open string moduli. We explicitly check that the known higher order corrections to the potential, which we neglect in our leading approximation, only shift the results by a small amount. In our exploration of the model, we encounter interesting new phenomena, including examples of transitions where D7 branes absorb O3 planes, while changing topology to preserve the net D3 charge.
All well-studied quasi-realistic string compactifications come, in the leading approximation, with large numbers of scalar moduli fields. It has long been thought that this is an artifact of the leading approximation, and that in many backgrounds non-perturbative effects generate potentials which lift all of these fields.
More recently, it has been emphasized that such potentials can have a very large number of minima, which combined with other choices made in the constructions gives rise to an immense ‘landscape’ of string vacua [22,77,1,65,96,43]. Indeed, very simple genericity arguments, based on knowledge of effective field theory and of the contributions of various stringy ingredients to the effective potential, suggest that this should be true.
Since typical constructions have dozens or hundreds of moduli fields, and many different effects contributing to the scalar potential, the explicit calculations required to verify this expectation are daunting in almost all examples. However it is important to pursue explicit examples in as much detail as possible. Such examples allow one both to verify the hypothesis that there are many models with stabilized moduli, and to gain further intuition about stringy potentials which may be relevant in developing models of inflation or particle physics.
A proposal for stabilizing a wide class of type IIB or F-theory compactifications was put forth in , and fairly explicit examples were provided in . In F-theory on an elliptic Calabi-Yau fourfold, the moduli of interest are the complex structure moduli and the Kähler moduli (which come from of the base of the elliptic fibration). In the limit where one can think of these constructions in terms of IIB Calabi-Yau orientifolds, these moduli include the moduli of the Calabi-Yau threefold, the axio-dilaton, and the positions of D7-branes in the threefold geometry.
In the constructions described in , one approaches the problem of moduli stabilization in two steps. First, one turns on background fluxes to stabilize the complex structure moduli of the fourfold at some energy scale – the fluxes can in general stabilize both the complex structure and D7 brane moduli, from the IIB perspective. Then, one incorporates exponentially small effects arising from Euclidean D3 instantons (corresponding to M5 instantons wrapping vertical divisors of holomorphic Euler characteristic†† This is often (but not quite accurately) called the arithmetic genus in the physics literature in this context. ) or infrared gauge dynamics on D7 branes, to generate a potential for the Kähler moduli at the scale . At any moderately large radius in string units, one finds , and it is a good approximation to treat the complex moduli as fixed when one evaluates the effects generating a potential for the Kähler modes (so any complex structure-dependent determinants multiplying the instanton action, should be evaluated at the critical point of the flux potential). As described in , as long as the gravitino mass resulting from the first step is moderately small in string units, one has a small parameter to use in the next step, which can result in radii stabilized within the regime of convergence of the instanton expansion. In fact, as we shall see explicitly, even values of can suffice in some concrete models.
In this paper, we provide an explicit example where this recipe is carried out in complete detail. We construct an orientifold of a Calabi-Yau threefold and its F-theory dual fourfold, which contains enough rigid divisors and pure non-abelian D7 brane gauge theories, to generate a potential for all Kähler modes. The Calabi-Yau threefold is the resolved orbifold , which has 51 Kähler moduli and 3 complex structure moduli. It is not difficult to construct explicit flux vacua in the complex structure sector of this model, and we provide some examples with moderately small . We solve for the stabilized values of all 51 Kähler moduli in the leading approximation, and show that the subleading corrections which we neglected are indeed expected to be quite small. Our example was chosen for its simplicity, especially as regards its complex structure moduli space (since we wished to provide explicit flux vacua), and hence it admits far fewer flux vacua than more generic fourfolds – only , in contrast to the more impressive numbers like that arise in more complicated examples. In suitable cases with larger numbers of flux vacua, one expects similar constructions to be even more controlled, but of course the higher-dimensional complex structure moduli space becomes harder to work with explicitly.
The organization of this paper is as follows. In §2, we give a first description of our main model. We find that the Kähler moduli space has a rather intricate structure, with different phases that meet in a singular orbifold geometry. We argue that each blow-up mode of the orbifold which contributes a twisted Kähler mode in the theory, comes along with its own vertical divisor of holomorphic Euler characteristic one, and that the gauge theory sector is pure SYM without any matter. In §3, we describe the geometry of the F/M-theory dual fourfold in great detail, and put the arguments of §2 on firm mathematical footing. In §4, we discuss the relation of our model to some similar toroidal orientifolds which have (in absence of flux) exactly soluble worldsheet definitions at the orbifold point. In §5, we construct explicit flux vacua in this example, which stabilize the complex structure moduli and provide the needed moderately small . We choose to saturate the entire D3-tadpole by turning on fluxes, so no wandering D3 branes are introduced in the geometry. In §6, we then include the leading non-perturbative effects, and see that once one includes both the D3-instanton effects and the gauge dynamics on the D7 branes in this model, all untwisted and twisted Kähler moduli are stabilized. We check the magnitude of the known corrections to the leading result, from perturbative and worldsheet instanton corrections to the Kähler potential as well as multi-instanton contributions to the superpotential, and see that even with our only moderately small these corrections are expected to be at the one percent level. In the penultimate section, we briefly describe some other explicit models with only a single Kähler mode which are good candidates for stabilization. We conclude in §8. In the appendix, we describe our normalization conventions.
2. Orientifold Geometry
Our model is a type IIB orientifold of a smooth Calabi-Yau threefold , which is a resolution of the orbifold . The orbifold group acts as
There are fixed lines under the action of a group element, and fixed points where three fixed lines meet. Blowing up the fixed lines resolves the geometry and introduces 48 twisted Kähler moduli in addition to the 3 untwisted Kähler moduli descending from . There are just 3 complex structure moduli, given by the modular parameters of the factors. Thus the resulting smooth Calabi-Yau threefold has , . This is one of the Borcea-Voisin models [21,100].
We will see in the following that we can choose an orientifold involution of and D7-brane embeddings in such way that we get an gauge group without matter, and a D3 tadpole (on the quotient space) induced by non-exotic O3-planes and 7-brane curvature.
Before proceeding, let us briefly explain why we do not define our model as a toroidal orientifold, i.e. by orientifolding the orbifold . Despite the geometric singularities, orientifolds of an orbifold can often be described directly by perturbative string CFT’s, and the case of has been studied extensively.
At first sight, the toroidal orientifold appears promising: the involution , which (modulo the equivalences) has O7 fixed planes and 64 fixed points at the triple intersections of the O7 planes, each of which corresponds to an O3 plane, roughly matching the smooth geometry we are about to describe. This comparison will be carried much further in §4, where it is shown that the gauge group and many other features of our model can be realized by a toroidal orientifold.
However, in general, not every large radius orientifold model has an orbifold limit with a well-behaved CFT description. When trying to go continuously from large radii to the orbifold point, nonperturbative massless states could arise from D-branes wrapping vanishing cycles, rendering perturbation theory singular. In the parent theories, such singularities are of complex codimension one in moduli space, so one can go around them and continuously connect various phases. However, after orientifolding, these singularities become of real codimension 1, preventing different phases from being connected smoothly. Therefore, orientifolds constructed geometrically in the large radius regime do not necessarily all have orbifold CFT counterparts, and in particular may have different discrete properties.
Indeed, we will see that this is the case for our model in §4. For this reason, and because we will stabilize all radii at finite distance away from the orbifold point anyway, we will first blow up the orbifold into a smooth, large Calabi-Yau threefold , using standard techniques in algebraic geometry. We then consider the string theory whose world-sheet definition is the sigma model with this Calabi-Yau target space, and then define an orientifold of this model. The result is similar to a toroidal orientifold but realizes discrete choices not possible in the CFT orientifold framework. Still, readers familiar with that framework may find it useful to read §4 to get an overview of the construction before proceeding.
In the following, we will first study a local description valid near the orbifold fixed points. We give a completely explicit description of the resolution, the orientifold involution, and the brane embeddings. We also review how intersection numbers, important for example to derive the Kähler potential, are computed in this setup. We then move on to the compact Calabi-Yau and discuss its lift to F-theory on an elliptically fibered Calabi-Yau fourfold (which we define as M-theory in the limit of vanishing elliptic fiber area). Finally, we calculate the D3 tadpole for our model, and note an interesting geometrical transition where a 7-brane stack “eats” an O3-plane while changing its topology to preserve the net D3-brane charge.
2.1. Local model
To understand the resolved geometry and the orientifold involution, it is useful to consider first a local model of the singularities, given by . The resolution of this orbifold can be described explicitly as a toric variety, following the general construction outlined in .
The data underlying any three dimensional toric variety is given by a lattice and the choice of a fan , which is a collection of cones generated by lattice points in , satisfying the condition that every face of a cone is also a cone, and that the intersection of two cones is a face of each.
The singular orbifold is described by the simple fan given in fig. 1, consisting of a single 3-dimensional cone generated by the lattice vectors , and . As usual for Calabi-Yau varieties, the third component of each vector equals 1, so we can restrict our attention to the other two coordinates, as we did in the figure. To each vertex a complex variable is assigned, and to each dimension a monomial . In this case, , , . The toric variety is then simply given by all not in a certain set , modulo complex rescalings that leave the invariant. The excluded set is given by the values of which have simultaneous zeros of coordinates not belonging to the same cone. Since there is only one three dimensional cone here, is empty. The only rescalings that leave the invariant are given precisely by (2.1). Thus, is indeed .
The fact that is singular can be traced back to the fact that the top dimensional cone generators do not span the full lattice , since . To resolve the variety, one has to refine the fan such that all top dimensional cones have determinant 1. There are two distinct ways of doing this in the case at hand, one symmetric and one asymmetric, as shown in fig. 2 resp. . The dual graphs are shown in fig. 3. As we will review below, the vertices in fig. 2 can be thought of as divisors, the lines as curves at the intersections of two divisors, and the faces as points at the intersections of three divisors. In the dual graphs, the role of faces and vertices is interchanged.
As shown in fig. 2 , there are now 6 vertices and 4 cones , , , all of determinant 1. The vertices are given by the matrix
We associate complex variables to the and to the . The powers in the monomials are simply given by the rows of this matrix, i.e. , , . The rescalings leaving the invariant are
with . The set of excluded points is again given by simultaneous zeros of coordinates not in the same cone, for example and are excluded, but is not. The toric variety is thus given by , with the actions given in (2.3).
To each vertex corresponds a toric divisor, by setting the associated coordinate equal to zero. Curves are obtained by intersecting divisors, i.e. setting two coordinates to zero. To avoid being on the excluded locus , the corresponding vertices must be part of the same cone, in other words they have to be joined by a line in fig. 2. Compact curves correspond to internal lines. In the case at hand, there are three such curves, which we denote by , where and cyclic permutations thereof. Finally, triple intersection points of divisors are obtained by setting the 3 coordinates associated to a single cone to zero. Thus the triple intersection number is 1 for 3 distinct divisors belonging to the same cone, and 0 otherwise.
The divisors are the original divisors we had in the unresolved variety, the are the exceptional divisors produced by the resolution, and the are the exceptional curves. The latter have topology . This can be seen as follows. for example is given by . To avoid the excluded set , we must take , and . This allows choosing a gauge with , so
which is of course .
Orientifold action and D-brane embedding
Let us now look at the orientifold involution. There are several choices. We choose . The fixed points are then given by the for which
for some . The following possibilities arise:
(1) If all , we need and therefore . Because belong to the same cone, this is an allowed point. Thus, we get an isolated fixed point that can be represented by . This corresponds to an O3-plane.
(2) If say , then to avoid the excluded set , we must take , , . Then (2.5) implies and , and imposes no further constraints. Therefore the entire divisor is fixed. This gives us an O7-plane. Similarly, there will be O7 planes on and . The topology of these divisors is easily determined. Since , and are all nonzero, we can fix the scaling gauge by setting these variables equal to 1. The divisor is then parametrized by the remaining variables and without further identifications, so it is a copy of .
The action of on the exceptional s is also straightforward to determine. After a gauge transformation , the orientifold action can be written as , which acts on (2.4) as
That is, the s are mapped to themselves in an orientation preserving way, with fixed points at the poles, where the intersects the O3 or O7 planes. Note that one cannot wrap a closed string once around a pole of the quotient , since the endpoints of a string can only be identified by an orientifold if the orientation of the string is reversed. Therefore the minimal closed string instanton wraps twice (or the original once). The instanton phase should furthermore be invariant under the orientifold action , which implies
We still have to specify how we embed D-branes in this geometry. We will put D7-branes on top of the O7-planes such that D7 tadpole is canceled locally. We choose the O7-planes to be non-exotic, so each induces units of D7-brane charge in the Calabi-Yau (or in the quotient ), and we need a stack of 8 coincident D7-branes on each to cancel this. This gives rise to an gauge group on each divisor . Note that since the are disjoint in the resolved manifold, there are no massless bifundamentals from strings stretching between the D7-branes. To decide if there is massless adjoint matter, we need to know the topology of the in the compact geometry. We will get to this further on.
To construct the Kähler potential on moduli space, we will need the triple intersection numbers of the divisors, including triple intersections involving identical divisors. These numbers also determine self-intersections of curves inside divisors, which characterize the local geometry. In this subsection we will review how to obtain these numbers. The reader who is only interested in the results can safely skip this part however.
We can derive the intersection numbers in the local model for compact intersections. Linear combinations of divisors whose associated line bundle is trivial on the noncompact variety will give zero compact intersections with any combination of other divisors. Denoting the divisors collectively as , , and the corresponding coordinates by , we have that is a section of the line bundle . The invariant monomials are functions, so the corresponding is trivial. For the purpose of computing compact intersections, this implies three linear relations between our divisors†† Despite the abuse of notation, these relations between divisors should not be confused with the relations between the corresponding vertices (2.2)!: , and so on. We should emphasize that this relation does not mean that this linear combination of divisors will also be trivial in the compact geometry. Rather, it means that this linear combination does not intersect the compact curves, and hence can be moved away from the origin — in the compact geometry, such a divisor corresponds to a “sliding divisor” such as . These divisors descend directly from the unresolved , and are in this sense independent of the blowup.
At any rate, these relations together with the triple intersection numbers of distinct divisors obtained directly from the fan are sufficient to determine all compact triple intersection numbers. This gives for example . From this, we also obtain the intersection numbers of the divisors with the compact curves defined above. These curves form a basis of the Mori cone i.e. the cone of effective holomorphic curves in . We get for their intersections:
Note that the entries are precisely the charges of the rescalings (2.3). Indeed, the Mori cone intersection numbers always form a basis of the rescaling charges. This is an elementary algebraic consequence of the various definitions we made.
The triple intersection numbers also give the self-intersection numbers of the curves inside the exceptional divisors, for example .
Finally, apart from one subtlety, it is straightforward to deduce the intersection numbers of the orientifold quotient . The subtlety is the following. Denote the projection from to by . Naively one might think one should take the toric divisors of the quotient, considered as 2-forms, to be related to those of the double cover by . This is correct for the divisors , but not for the , for which we should take . This can be seen as follows. Because is fixed by the , its volume in must equal the volume of in the quotient. But the volume of is given by
which is half the volume of . So we must take to correct for this. For the divisors on the other hand, whose volume does indeed get halved, there is no such correction factor of 2. Thus we get for example
The half integral triple intersection product is possible because the intersection point coincides with the fixed point singularity (the O3). For the intersections of the Mori cone generators, we thus get
The asymmetric resolution in fig. 2 can be treated in a completely analogous manner. The vertices of the fan remain the same, so the scalings (2.3) remain the same too. The cones themselves do change, so the excluded region will be different, as well as the intersection products. The generators of the Mori cone and their intersections are now given by†† To avoid cluttering, we drop the index ‘’ here. In section 3, where the relation between the two resolutions will be studied in more detail, the ‘+’ index will be reinstated.
From this, we again get the self-intersections of the curves in the divisors: , , , . At the level of the intersections, the curves are related to those of the symmetric resolution by , , . These relations are characteristic of a flop; indeed, the symmetric and asymmetric resolutions are related by flopping the curve .
The orientifold action is again . As in the symmetric resolution, the divisors support O7-planes. Now however there is no isolated fixed point: lies in the excluded set . All ’s are acted on by as in (2.6), except , which is pointwise fixed, since it is embedded in an O7-plane. The triple intersections of the quotient are obtained by the rules given earlier (i.e. add an overall factor of and ). This gives for the Mori cone
2.2. Compact model
To get the compact model , one simply glues the 64 local models together, with transition functions determined by the transition functions between the -coordinates in the original . This gives exceptional divisors and O7-planes on divisors . Here (with ) and . On each O7-plane, we furthermore put an stack of D7-branes. This locally cancels the D7-tadpole, so the axio-dilaton is constant on . In the symmetric resolution, there are 64 O3-planes. In the asymmetric resolution, these are absent.†† By asymmetric resolution in the compact model, we mean the resolution obtained by blowing up each local patch in the same asymmetric way. In principle there could be mixed symmetric/asymmetric resolutions, but we will not consider these.
The global topology of the various divisors is easily deduced. Let us consider for example the divisors in the symmetric resolution. The topology of the resolved manifold with the exceptional divisors removed is the same as the topology of with its singularities removed. In this space, the divisors have topology with the singularities removed, that is with four points removed in each factor. In each local patch, this looks like with the origin in each factor removed. From the explicit construction of the local model given above, it is clear that in the resolved space, the origin of each factor is simply put back as a point (as opposed to being replaced by some exceptional curve). Therefore, in the resolved compact model, the divisors are simply .
For the topology of the exceptional divisors we get similarly blown up in 4 points (corresponding to the four intersections of a fixed line with the fixed planes in ). In the asymmetric resolution on the other hand the and divisors still have topology , but the divisors are now blown up in 16 points. The and divisors are , and is blown up in 8 points.
All these divisors evidently have , since has this property, and blowing up only changes . This has important consequences:
(1) There is no massless adjoint matter in the gauge theory. Since moreover the do not intersect, there is no massless bifundamental matter either. So the gauge theory is pure super Yang-Mills, and in particular will give rise to gaugino condensation and the generation of a nonperturbative superpotential for the Kähler moduli governing the size of the .
(2) D3-instantons wrapping the exceptional divisors will have the minimal number of fermionic zero modes, and therefore contribute to the superpotential. To make this more precise, we need to consider the dual M-theory on a smooth Calabi-Yau fourfold, where the D3-instantons lift to M5-instantons. In this context it has been shown that if the M5 wraps a divisor satisfying (which in particular implies that its holomorphic Euler characteristic equals 1), there is a contribution to the superpotential . In section 3, we will prove in detail that this is indeed the case for the lifts of the D3-instantons wrapped on the exceptional divisors. We also give a short argument below.
There are in fact other consistency conditions that need to be fulfilled. We will discuss these in section 6.
2.3. M/F-theory description of the model
Type IIB string theory on the orientifold is dual to M-theory on an elliptically fibered Calabi-Yau fourfold with base , in the limit of vanishing fiber area. The dual fourfold is easily constructed in this case : it is simply , where the acts as our orientifold involution on , and as on . This gives a singular fourfold, with elliptic fibers degenerating to a singularity on top of the divisors , and, in the symmetric resolution, a degenerate fiber with four terminal singularities on top of each fixed point in . It can be considered as a partial resolution of . Again this is an example of a Borcea-Voisin model [21,100].
To rigorously address the question whether the lifts of the D3-instantons have the required properties mentioned in the previous subsection, one needs to resolve this fourfold in a way that preserves the elliptic fibration. This is somewhat tricky, and will be the subject of section 3. The basic idea is simple however. On the double cover of , the M5-brane lift of a D3 instanton wrapped on a divisor is . As argued in section 2.2, for and any of the divisors of interest discussed there. So the only harmonic -form on is the -form living on . Considering now the quotient in , we see that is odd and thus gets projected out. Moreover, blowing up the quotient singularities of will only change . Hence, also after resolving the fourfold, .
Another important point in the arguments we will give for the nonvanishing of the instanton conributions is the fact that the M5-branes under considerations have trivial third cohomology. This can be argued similarly. On , the third cohomology is given by the product of and . But quotienting by projects out every such class because the elements of are even and those of are odd. Furthermore, blowing up will not add any new 3-cycles. So is trivial also after resolving the fourfold. A more precise discussion will be given in section 3.
2.4. D3 tadpole and O3-curvature transition
We now compute the D3 tadpole measured in the quotient (as usual, in the double cover , is twice this). In the symmetric resolution, we have O3-planes. Choosing these to be non-exotic, their contribution to the D3-brane charge is
The 7-branes also contribute to the D3 tadpole, through the “anomalous” couplings of RR-fields to worldvolume curvature [55,28,95,29,23,24]. In a Calabi-Yau threefold, a single D-brane wrapped around a divisor thus contributes a D3-charge , and an O7-plane . The total contribution from an O7 + D7 stack wrapped on is therefore in , and half of that in the quotient. Hence the total 7-brane contribution is
In the symmetric resolution, has topology , so and
There can also be contributions from the (half-integral quantized) -field to various tadpoles, as well as from gauge instantons on the D7-branes, but we will take here, in which case there are no tadpole contributions of this kind. Combining O3 and 7-brane contributions in this case gives
In the asymmetric resolution and , so
This agreement of tadpoles in symmetric and asymmetric resolutions can be understood locally: when flopping one local patch from fig. 3 to , one O disappears from the corresponding orientifold, so increases by in (2.12), but at the same time the Euler characteristic of the 7-branes wrapped around changes: a point gets blown up, which increases and therefore by 1, so decreases by in (2.13), and the total charge is conserved. If this transformation can be realized physically, this is a rather interesting phenomenon, in which a 7-brane stack “eats” an O3 and blows up to conserve the net D3-charge.
This value of the tadpole fits nicely with the fourfold description. In this picture, the D3 tadpole is given by
The Euler characteristic of the fourfold say for the asymmetric resolution can be computed for example as follows. Removing the divisors from the base together with the fibers on top gives a space which is a direct product with a factor. This has Euler characteristic 0. The Euler characteristic of the full space is therefore the sum of the Euler characteristics of the times the Euler characteristic of the fiber, which is 6 (it can be thought of as a collection of 5 spheres connected along 4 double points according to the extended Dynkin diagram). So and . A similar match can be made for the symmetric resolution after properly taking into account the contribution to from terminal singularities .
The D3-tadpole thus produced can be canceled by adding 28 independent mobile D3-branes, or by turning on RR and NSNS 3-form fluxes. This is further discussed in section 5.
In the symmetric resolution, we could also have chosen our O3-planes to be exotic. This does not change the geometry; it merely corresponds to turning on (torsion) twisted cohomology classes for the field strengths and/or in , where surrounds the O3 in [104,60,11]. In the M-theory dual this corresponds to turning on torsion -flux around the terminal -singularities .
The D3-charge of any exotic O3 has the opposite sign of a normal O3. The total tadpole in this case is thus
To cancel this, one needs 4 anti-D3 branes, which breaks supersymmetry. Incidentally, the O3s are required to be exotic for a consistent CFT description at the orbifold point, as we will discuss further in section 4. But, as stressed at the beginning of this section, it should not surprise us to find different consistent models at large radius.
3. Fourfold Geometry
In this section we describe the geometry of the resolved Calabi-Yau fourfold. We describe the symmetric and asymmetric resolutions of the orbifold, and the birational transformation relating the two resolutions.
To simplify the presentation, we start with a lower dimensional orbifold, , which is dual to IIB on an orientifold of . We discuss the resolution of the orbifold and the properties of the exceptional divisors introduced in the blow-up process.
We then move to our main example, the orbifold. We present two distinct resolutions and discuss their elliptic fibration structure. Starting from local models, we discuss the birational factorizations of the transformations relating the elliptically fibered Calabi-Yau fourfolds and their bases. This somewhat technical analysis is necessary to prove that the exceptional divisors in the (singular) symmetric resolution have the right topological properties to contribute to the nonperturbative superpotential: they have holomorphic Euler characteristic and the higher cohomology groups , vanish. We also show that their third cohomology is trivial, which is important for arguing that the instanton prefactor is nonvanishing.
3.1. Lower dimensional orientifold
It is instructive to consider first the lower dimensional analog, namely F-theory on . The action of the orbifold group is presented in (2.1). We can view as an elliptic fibration over : let and be the coordinates on the base and be the coordinate on the elliptic fiber. Then, the elliptic fiber degenerates to type fibers†† That is, along the fixed point set, the fiber degenerates to , which is a rational curve with four singular points. along the fixed locus of and in the base. In F-theory, such a singularity corresponds to an gauge group [26,15].
The base is and there are lines of fibers intersecting at points†† The corresponding Weierstrass model describing the transverse collision of two fibers is not minimal.. In order to obtain a smooth Calabi-Yau threefold, we need first to blow-up the base at these points and then resolve the singularities of the elliptic fibration. Let us first discuss the blowing-up of the base .
We can work in local coordinates in the fibration around the point , which lies at the intersection of the fixed lines and . To describe the blow-up, introduce two coordinate patches and as follows:
The coordinates and are homogeneous coordinates on the exceptional . The actions lift to the blown-up threefold; there are two fixed points on the exceptional given by and , where it intersects the unresolved singular divisors. The elliptic fiber over the exceptional is smooth, except at the points and , where there are singularities. We note that the elliptic fibration over the blown-up base admits a section. The blow-up process is ilustrated in the figure below.
Blowing-up the base introduce new Kähler parameters. The next step is to resolve the elliptic fibration and this will introduce additional Kähler parameters since after the blow-ups in the base there are isolated curves on top of which the elliptic fiber is type . Taking into account the original 2 Kähler parameters of the base and the section, we recover the Kähler parameters of the resolution. We have obtained a smooth threefold that is elliptically fibered and is one of the Borcea-Voisin models [21,100].
The process of resolving the elliptic fiber will turn the elliptic fibration over the exceptional divisors in the base into rational elliptic surfaces , , that is del Pezzo surfaces . These have .
In type theory language, the description of the orientifold of is as follows . The fixed curves are wrapped by D-branes sitting on top of orientifold O planes, and on the worldvolume of each -brane there is an gauge theory. After blowing-up the base, the gauge theory is with no matter.
Proceeding analogously to the previous section, consider now the orbifold . The orbifold group acts as
This is another example of the Borcea-Voisin construction [21,100]. To get our Calabi-Yau fourfold start with the Calabi-Yau orbifold with the orbifold action given by (3.1) and construct , where is an involution of that changes the sign of the holomorphic three-form.
The local singularities are of the form . The figure below presents the toric resolutions of the singularities. We see again that the local singularities do admit crepant resolutions and it is possible to glue them together and get a smooth crepant resolution with and .
We can also think of as an elliptic fibration over , with fibers along the fixed point set of , and .
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https://www.best-poems.net/quotes/author/Gabriel%20Pinatacan
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math
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Love is a rational expression between you and other.... The other is the numerator and you are the denominator. The larger you give value to the denominator, the lesser the value of the expression. The greater the value you give to the numerator, the greater the value of the expression. The best part of it, do not put zero on the denominator and it becomes UNDEFINED!g
Mathematics is in irony. It simplifies things in a very complicated way.
Math is a faith of believing something can be deduced from reality to idea and then back to reality.
Life is a fraction of others and yourself. It's up to you how much part would you give to yourself.
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http://allpapersizes.com/paper-size-a1/
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A1 is the second biggest paper size that is additionally normalized by the regulations of the ISO 216 standard. Only one bigger format is available, namely - A0. A1 is two times bigger than an A2-sized sheet of paper and two times smaller than an A0 one. In its case, the 1 to √2 proportion is maintained, just as it is with all the remaining paper sized normalized by the German DIN norm. It means that an A1 sheet can be made by folding a A0 one along its longer side.
The surface of an A1-sized paper is equal to 0.5 square meters that is - 500 cm2. The dimensions of an A1 sheet of paper are equal to 594 x 841. The net size (after the removal of unwanted leftovers) is 589 mm by 835 mm. The overall surface of A1 expressed in pixels is equal to
7016px x 9933px, and in points - to 1683,8pt x 2383,9pt.
Did you know that?
A1 paper size is two times bigger than the A2 one (the surface of 0,25 m2)
A1 paper size is four times bigger than the A3 one (the surface of 0,125 m2)
A1 paper size is eight times bigger than the A4 one (the surface of 0,0625 m2)
The basis weight of paper is always expressed in g/m² and that is why the weight of an A1 sheet of paper can be calculated basing on the weight of A0 (of the size of 1m²). For example, if paper basis weight is 100g / m² and the size of A1 is a half of A0 one that is - 0,5 m², then the weight of an A1 sheet of paper is 50 grams (100/2 = 50 grams).
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http://advogato.org/person/tampe/diary/96.html
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math
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I spend this Christmas, reading Simon Sings Big Bang. And as Simon pretty much says, I say as well, what a wonderful world.
I'm mentally affected by my education that I constantly ask myself if the things that is presented in a popularizing book is really what is true. Did he mean that. Sure people turn things int a better daylight when asked about it afterwords and so on. There is a constant flow on my mentally left margain. Anyhow I'm now really impressed by the puzzle that scientist made to achieve such a solid ground for the Big Bang theory.
There is always weak spots in an arguments but the core argument is really solid in my view.
I like the formulation that uses the potential formulation under the Lorenz gauge if I remember everything correctly. Then all components follow a wave equation and there is one linear first order constraints that look close to a simple continuity equations. Now I wanted to understand what this actually meant and searched for some example that would reveal that to me. And there is one telling partial solution. You could have a solution where you make the constraint a continuity equation. You will have a sort of "magnitude of disturbance field" in the scalar potential and the vector potential will be a sort of momentum potential e.g. the scalar potential times a velocity field of constant velocity c. It's a really trivial and very particular solution. But you can modify it. You can assume that if along a direction you have the same disturbance, then you can choose any velocity you like.
Now, in my view this captures some essential features of electromagnetism. A constant stream of light is not dependent of the speed of the stream and it is information that is constrained to the speed of light. Not necessary the actual physical or disturbance transport.
Note that if we have just one stream the transversal direction has to be transported with the speed of light and indicate plane waves.
Even if this is a simple particular solution. One would probably be able to deduce Maxwell's equations after closing the space using Lorenz transforms
Ok this is just a mathematical play, but it poses from my position of knowledge very interesting question. It's just some speculation from a guy that is not an expert. But I still hope that I've teased your imagination so please have fun, play with the mathematics, enjoy the stars and have a very happy hacking new year.
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https://www.physicsforums.com/threads/why-light-speed-is-constant-please-read.336800/
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math
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We'll know that the base of special relativity theory is "the light has a constant speed in vacuum". Time dilation and Lorentz contraction are consequences of the constance of light speed. If we excite photons, for example, its frequence increases (and the wavelength could decrease), but it happens for light speed continues constant. It's also an consequence of constance of light speed. Everything seems to be a consequence of constance of light speed. But, the question is: WHY light has a constant speed (in vacuum)? What about tachyons? (http://en.wikipedia.org/wiki/Tachyon" [Broken]) Any discussions are welcome.
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https://letsgetslushed.com.au/whats-vertical-in-math/
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math
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Lots of men and women know what is perpendicular in math.
They understand it if they contemplate it and that they understand it when they find the replies using the calculator. Also for them it makes sense, although they might perhaps not know what is perpendicular in mathematics. Others might not know what is perpendicular, however the way that it works to get them is really easy.
Then your reply is what’s vertical in mathematics, Once you need to do your math all in the middle, that http://jurat.com.pk/things-you-should-know-about-what-does-in-math-mean/ will be horizontal. In this scenario, you are doing most of one’s mathematics together with the formulations which affect the angles of their contours into distances.
The dilemma is that almost all men and women figure out by finding the replies to this algebra 21, what’s perpendicular in math. They have the formulas and the answers, plus they understand ways to get it. They begin to bring those two things together to get the answer, however, then they realize they want extra advice to find the solution.
Additionally, there https://basketksa.com/exactly-what-does-cis-me-an-in-z/ are a few different types of perpendicular in math and they all are based on some form of addition. You could find you have to complete more than just one kind of A perpendicular in math formula will usually need to put them all up. But in the event that you get an even superior idea of how to add themyou are able to figure out ways to get the replies.
Just just how can you discover which kind of vertical would be correct foryou? It’s a bit more difficult compared to that. You want to come across a way therefore you could perform it to get each of the actions of the method down, step by step.
A formulation that does not involve the multiplication of angles is used by some men and women. The key will be to obtain a means so that the replies are simple to follow along with to maintain it straight . The idea will be to split the verticals upward . This really is actually really a little more difficult compared to example given above, however nonetheless, it still demonstrates how how it works.
What is perpendicular in math is something that may be accomplished by taking a look at each one. You will realize that every formula contains steps which fit into eachother When you look at them closely.
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http://www.tonitop.org/ebook/50764-a-treatise-on-the-calculus-of-finite-differences.html
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math
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A Treatise on the Calculus of Finite Differences
English | 2009 | 264 Pages | ISBN: 1108000924 | DJVU | 1 MB
Self-taught mathematician and father of Boolean algebra, George Boole (1815-1864) published A Treatise on the Calculus of Finite Differences in 1860 as a sequel to his Treatise on Differential Equations (1859). Both books became instant classics that were used as textbooks for many years and eventually became the basis for our contemporary digital computer systems. The book discusses direct theories of finite differences and integration, linear equations, variations of a constant, and equations of partial and mixed differences.
Boole also includes exercises for daring students to ponder, and also supplies answers. Long a proponent of positioning logic firmly in the camp of mathematics rather than philosophy, Boole was instrumental in developing a notational system that allowed logical statements to be symbolically represented by algebraic equations. One of history's most insightful mathematicians, Boole is compelling reading for today's student of logic and Boolean thinking.
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http://www.ques10.com/p/1035/applied-physics-1-question-paper-may-2014-first--1/
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math
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Applied Physics 1 - May 2014
First Year Engineering (Semester 1)
TOTAL MARKS: 60
TOTAL TIME: 2 HOURS (1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Use suitable data wherever required.
(4) Figures to the right indicate full marks.
Sove any five from the following :-
1 (a) What is x-rays? Why the x-ray are prefered to study crystaline solid.(3 marks) 1 (b) Represent the following in the cubic unit cell (021), (123), (3 marks) 1 (c) Find the miller indices of a set of parallel panes which makes intercepts in the ratio 3a:4b on the x and y axes and parallel ti Z-axis(3 marks) 1 (d) What is Fermi level and Fermi energy? Write Fermi-Dirac distribution function.(3 marks) 1 (e) Explain the concept of hole in a semiconductor (3 marks) 1 (f) Draw the structure of quartz crystal and explain its various axes.(3 marks) 1 (g) State and explain ohm's law in magnetic circuit?(3 marks) 2 (a) Describe the formation of energy band in solid? Explain how it helps to classify the solid in to conductors, insulator and semiconductor with proper diagram.(8 marks) 2 (b) Explain Dimond crystal structure with proper diagram and determine its APF?(7 marks) 3 (a) Derive the Bragg's law and describe the powder method to determine crystal structure of powdered specimen.(8 marks) 3 (b) The magnetic field strength of cooper is 1016 ampere / metre. And magnetic susceptibility is -0.8 x 10-3. Calculate magnetic flux density ad magnetisation in cooper.(7 marks) 4 (a) What is liquid crystal state of matter? Draw the diagram to descibe molecular arrangement in their different phases?(5 marks) 4 (b) Mention different types of polarizability in a dielectric? Explain electorinc polarizability?(5 marks) 4 (c) Calculate electron and hole concentration in intrinsic silicon at room temperature if its electrical conductivity is 4 x 10-4 mho/m. (mobility of electron = 0.14m2/v-s & mobility of hole =0.040 m2/v-s)(5 marks) 5 (a) Explain with neat diagram construction and working of solar cell.(5 marks) 5 (b) State the acoustic requirements of good auditorium. Explain how these requirements can be achieved.(5 marks) 5 (c) If the x-rays of wavelength 1.549 Ao will be reflected from crystal having spacing of 4.255 Ao, calculate the smallest glancing angle and highest order of reflection that can be observed.(5 marks) 6 (a) Explain with neat diagram Hysterisis effect in ferromagnetic material.(5 marks) 6 (b) Explain piezoelectric oscillator to produce USW?(5 marks) 6 (c) Explain the formation of barries potential in P-N Junction.(5 marks)
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https://entirelyuseless.com/2015/07/22/using-arguments-to-arrive-at-understanding/
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math
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As I suggested in the previous post, we come to understand something better through a number of arguments rather than through a single argument.
Suppose you prove your position through a single argument that seems strong to you. In this case there is a second-order consideration which significantly weakens your argument. Namely, if you already suspected or held a position, or if you wanted it to be true or to believe it, how likely is it that you would manage to find at least one argument in favor of that position which seemed strong to you, given that the position was false? It is probably not much less likely than the same thing given that the position is true, and so the strong argument should not increase your belief in that position by very much. This of course does not imply that you should ignore the content of the argument, but it does mean that you should take it with a bit of caution. Approaching the matter with many arguments weakens this second-order consideration and gives you more reason to accept the implications of the arguments.
Using a number of arguments also helps you to refine your view, making it more precise, giving you a better ability to resolve objections, and so on. This is certainly one of Aristotle’s reasons for proposing the use of dialectic in coming to understand, and a reason for the use of many arguments in disputed questions, as I said in the previous post.
On the other hand, even if you come up with multiple arguments for your position, this may not be very helpful if you ignore opposing evidence, and so it is necessary to construct arguments against your position as well. This is the reason that a disputed question has arguments on both sides.
If you manage to construct a large number of arguments on both sides of a position, this will often give you a very strong basis for judging the truth of the position. It is difficult to assign numerical probabilities, and consequently to determine the exact strength of the evidence or of an argument for a position. But it is often comparatively easy to see the relative strength of two pieces of opposing evidence, or two opposing arguments. Consequently once such a list of opposing arguments has been constructed, it is possible to look at one side and see how the arguments compare to those for the other side.
As I have said earlier, there is evidence for any position, whether it is true or not. However, the evidence for a false position generally tends to be weaker than the evidence for a true position. So for example if nearly all the arguments for one side of a position are fairly weak, while many of the arguments for the other side seem significantly stronger, we can get a pretty good sense of which position is true and which is not.
On another note, there is a good post against the Equality Dogma here.
One thought on “Using Arguments to Arrive at Understanding”
[…] one side rather than the other is not helpful: in such a case I should indeed argue both sides, as was done with disputed questions. In other words, the goal of making a point is different from the goal of understanding, and these […]
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https://write-me-an-essay.com/the-sliders-a-and-b-are-connected-by-the-light-rigid-bar-of-length-l0-5m-and-move-with/
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The sliders A and B are connected by the light rigid bar of length l=0.5m and move with
negligible friction in the horizontal slots as shown in Figure Q1. For the position when xA =
0.4m, the velocity of A is VA= 0.9 m/s to the right. Determine the acceleration of each slider
and the force in the bar at this instant.
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http://mathforum.org/library/view/5275.html
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Library Home || Full Table of Contents || Library Help
|Jim Wilson, Dept. of Mathematics Education, Univ. of Georgia|
|Problem: Develop a proof for Brahmagupta's Formula, which provides the area A of a cyclic quadrilateral (i.e., a simple quadrilateral inscribed in a circle) with sides of length a, b, c, and d as A = sqrt((s-a)(s-b)(s-c)(s-d)) where s is the semiperimeter (a+b+c+d)/2. There are alternative approaches to this proof. The one outlined here is intuitive and elementary; a more elegant approach is available using trigonometry. From a course on Problem Solving in Mathematics.|
|Resource Types:||Course Notes|
|Math Topics:||Conic Sections and Circles, Triangles and Other Polygons, Trigonometry|
© 1994- The Math Forum at NCTM. All rights reserved.
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https://www.mytutor.co.uk/answers/2395/A-Level/Maths/How+do+you+differentiate+y+%253D+5+x%255E3+%252B+1%252F2+x%255E2+%252B+3x+-4
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math
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FIrslty to avoid confusion:
x = the variable x
X = multiplication.
When you differentiate an equation, the derivative (answer) is referred to as dy/dx.
For a polynomial as in this question you take each term individually and differentiate that.
Let's first do this for a generic term axb and we will then apply it to thisquestion:
The formula for the derivative of axb is baxb-1, which means you take the degree of x (whatever power it is being raised to, which in this case is b) and multiply it by the coefficient of x (which in this case in a) which provides the ba part of the solution. You then reduce the degree of x by one so it becomes xb-1 instead of just xb. Therefore when you put the two parts together you get the final derivative as baxb-1.
Now let's look at the first term of our equation : 5x3.
The degree here is 3 so the first thing you do is multiply 3 by the coefficient of x which is 5 giving you 3x5 which is 15.
Next, you reduce the degree of x by 1. It was x3 so now it is x3-1 which is x2.
Now you can put the two parts together to give the derivative of 5x3 being 15x2.
If you do the same thing for the next term, then you get (2x1/2)x2-1 which is x.
For the third time the derivative is quite nice, if you just have a number followed by x such as 3x as we have here, to get the derivative you just remove the x, meaning the derivative is 3.
For the final term of the equation we just have a number. Whenever you differentiate a number on its own, the derivative is 0.
So now the final thing left to do is put our answer together. You need to take each of our 4 derivatives and simply add them together.
This would give you: 15x2 + x + 3 + 0
Meaning the final answer dy/dx = 15x2 + x + 3.
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https://emicida.com/oak-furniture-cfdpvt/article.php?tag=07b615-deductive-reasoning-math
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math
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View Answer Discuss. Use inductive reasoning to make a conjecture about the sum of a number and itself. Inductive and Deductive Reasoning Inductive Reasoning Inductive reasoning is one method of reasoning that researchers use. Monthly Downloads for the past 3 years . * Mrs Jennifer's house is somewhere to the left of the green marbles one and the third one along is white marbles. step 3 is wrong Posted in LOGIC TRICK EQUATION #2 - Hard Logic Chess Puzzle Assume you have the white pieces, can you win in a half a move ? Inductive reasoning means coming to a very broad conclusion based on just a few observations. (ii) Write q -> p in words. Conversely, deductive reasoning uses available information, facts or premises to arrive at a conclusion. You may want to discuss the links among reasoning, evidence, and proof at that point. In math, you can support your proof with supporting proofs or … You know it'll be true. Deductive reasoning goes from a general to a specific instance. Problem 3 : Let p be "the value of x is -5" and let q be "the absolute value of x is 5". Noisy Deductive Reasoning: How Humans Construct Math, and How Math Constructs Universes. 2 3. Inductive Reasoning. Deductive Reasoning Logical Problem. In Math in Action on page 15 of the Student Book, students will have an opportunity to revisit an investigative scenario through conjectures, witness statements, and a diagram. Reply. Therefore, the test will be easy. Thus, the premises used in deductive reasoning are in many ways the most important part of the entire process of deductive reasoning, as was proved by the help of the above given examples. You are given a triangle to work with. 10. Then, from that rule, we make a true conclusion about something specific. deductive reasoning, inductive reasoning, valid argument, logical argument, conjecture, verify, proof, prove, disprove, counterexample, observation, undefined term, postulate, theorem (G.1) Student/Teacher Actions (what students and teachers should be doing to facilitate learning) 1. Being able to use deductive reasoning is valuable to employers. Inductive Reasoning: My mother is Irish. Deductive and Inductive Reasoning Asked by a student at Winona Senior High School on January 28, 1998: I was talking with my geometry teacher the other day and we discussed inductive and deductive reasoning. Deductive reasoning is the process by which a person makes conclusions based on previously known facts. In science, you can then support your conclusions with experimental data. Deductive Reasoning – Drawing a specific conclusion through logical reasoning by starting with general assumptions that are known to be valid. Review the basic vocabulary included on the sheets. Deductive Reasoning Deductive reasoning is the process of reasoning logically from given statements to make a conclusion. Deductive reasoning requires one to start with a few general ideas, called premises, and apply them to a specific situation. February 2, 2016 February 2, 2016 Todd Abel explicit rules, inductive reasoning, math teaching, pattern-sniffing, recursive rules, standards of mathematical practice Leave a comment One of the principle algebraic ways of thinking that we came up with during the introductory problems was pattern-sniffing . How is it used in Mathermatics? The comparatively poor performance of American students on international math exams means the country should spend more money on math education. If you get an A on your math test, then you can go to the movies. INDUCTIVE AND DEDUCTIVE REASONING WORKSHEET. Therefore, Mr. D is over 7 feet tall. Deductive - Displaying top 8 worksheets found for this concept.. (deposited 26 Nov 2020 05:22) [Currently Displayed] Monthly Views for the past 3 years. Deductive reasoning, also deductive logic, is the process of reasoning from one or more statements (premises) to reach a logical conclusion.. Deductive reasoning goes in the same direction as that of the conditionals, and links premises with conclusions.If all premises are true, the terms are clear, and the rules of deductive logic are followed, then the conclusion reached is necessarily true. There are 4 big houses in my home town. All math teachers are over 7 feet tall. Therefore, the second lipstick I pull from my bag will be red, too. Thus, if they are wrong, the entire foundation of the whole line of reasoning is faulty and thus, the conclusions derived will also be faulty. Thus, it produces from the specific to the general. Recognized rules, laws, theories, and other widely accepted truths are used to prove that a conclusion is right. When you reason deductively, you can say “therefore” with certainty. Pretty hard to see a pattern when pieces are missing. Law of detachment : If p -> q is a true conditional statement and p is true, then q is true. The argument is valid, but is certainly not true. Syllogisms are a form of deductive reasoning that help people discover a truth. Can you help me answer this question? A logical inference is a connection from a first statement (a “premise”) to a second statement (“the conclusion”) for which the rules of logic show that if the first statement is true, the second statement should be true. Therefore, all the lipsticks in my bag are red. You then conclude that every goose is white. Plum Analytics. When math teachers discuss deductive reasoning, they usually talk about syllogisms. Deductive reasoning is the type of reasoning used when making a Geometric proof, when attorneys present a case, or any time you try and convince someone using facts and arguments. Law of syllogism : If p -> q and q -> p are true conditional statements, p->q is true. In each question you will be presented with a logical sequence of five figures. Employers value decisive, proactive employees. The above examples are of the form If p, then q. You will have 25 minutesin which to correctly answer as many as you can. Deductive reasoning uses facts, definitions, and accepted properties in a logical order to write a logical statement. Predict the next number. Deductive Reasoning. In deductive reasoning, the conclusions are certain, whereas, in Inductive reasoning, the conclusions are probabilistic. Inductive Reasoning. Deductive reasoning is introduced in math classes to help students understand equations and create proofs. In the Inductive method of mathematical reasoning, the validity of the statement is checked by a certain set of rules and then it is generalized. Examples of Inductive Reasoning Some examples Every quiz has been easy. B and C are the same but C is correct? Browse inductive reasoning math resources on Teachers Pay Teachers, a marketplace trusted by millions of teachers for original educational resources. Still, they are often juxtaposed due to lack of adequate information. Deductive Reasoning 3. If you go to the movies, then you can watch your favorite actor. Inductive reasoning - Think of it like a We start with specifics and move to generalities Deductive reasoning – think of it like a We start with generalities and move to specifics. Mr. D. is a math teacher. The principle of mathematical induction uses the concept of inductive reasoning. It is, in fact, the way in which geometric proofs are written. Two Laws of Deductive Reasoning (i) Law of detachment (ii) Law of syllogism. You can use deductive reasoning in a science class or a math class to test an existing theory or hypothesis. Inductive Reasoning Free Sample Test 1 Solutions Booklet AssessmentDay Practice Aptitude Tests Difficulty Rating: Difficult . The sum of any triangle’s three angles is 180 degrees. Problem 1 : Sketch the next figure in the pattern. Benefits of Deductive Reasoning . If … He wanted me to find out exactly what they are and find an example just to see if I could do it. Even when the decision doesn't work out, you can explain why you decided to do what you did. Actions (login required) View Item: … Every row and column contain the same figures/numbers. When we deduce something, we take a rule and apply it to a unique situation. Deductive Reasoning Puzzles With Answers #1 - Tricky Math Problem 1 dollar = 100 cent = 10 cent x 10 cent = 1/10 dollar x 1/10 dollar = 1/100 dollar = 1 cent => 1 dollar = 1 cent solve this tricky problem ? Instructions. Inductive reasoning is the opposite of deductive reasoning. Inductive Reasoning: The first lipstick I pulled from my bag is red. Deductive Reasoning The process of reasoning from known facts to conclusions. Inductive vs. Deductive Reasoning 1 2. Use your logical reasoning skills to fill the missing cells of the latin square. Foundations in Math 110 Section 1.4 Proving Conjectures: Deductive Reasoning Proof – A mathematical argument showing that a statement is valid in all cases, or that no counterexample exists. All research that makes inference or generalizations about the results of a study uses inductive reasoning (Berg & Latin, 2008). Deductive reasoning moves from generalized statement to a valid conclusion, whereas Inductive reasoning moves from specific observation to a generalization. Referring to the practice inductive reasoning – question three with the Hershy kiss things. (major premise) x is p. (minor premise) Therefore, x is q. Clear examples and definition of Deductive Reasoning. Explanation. The second lipstick I pulled from my bag is red. So, in maths, deductive reasoning is considered to be more important than inductive. Deductive reasoning is often used to make inferences in science and math, as you must use formal logic to support a conclusion or a solution. Deductive reasoning allows you to use logic to justify work-related decisions. Deductive reasoning uses facts, defi nitions, accepted properties, and the laws of logic to form a logical argument. It is based on making a conclusion or generalization based on a limited number of observations. What does Conjecture mean? These two logics are exactly opposite to each other. Have you heard of Inductive and Deductive Reasoning? In this article, we are going to tell you the basic differences between inductive and deductive reasoning, which will help you to understand them better. Inductive Reasoning. Test your IQ with this deductive reasoning test using latin squares. Problem 2 : Describe a pattern in the sequence of numbers. A latin square has two important properties: A row or column never contains the same figure/number twice. Here’s an example. The concept of deductive reasoning is often expressed visually using a funnel that narrows a general idea into a specific conclusion. That’s why we call deduction top-down logic—you move from the general to the particular. Inductive reasoning is typified by the following example: Suppose every goose you observe throughout your lifetime is white. Note that this conclusion is not 100% definite. This inductive reasoning test comprises 22 questions. View Answer Discuss. All lipsticks in my bag are red. Deductive Reasoning: The first lipstick I pulled from my bag is red. (i) Write p -> q in words. This is an inductive conclusion. They are made from these materials: red marbles, green marbles, white marbles and blue marbles. Deductive reasoning starts with some general observations and deducts (wipes away) every unnecessary distraction to leave a specific, valid conclusion. Distribute copies of the two activity sheets. Making assumptions. their conjectures through the use of deductive reasoning. Forget reasoning – proof read. Deductive reasoning, or deduction, is one of the two basic types of logical inference. Also, on question 2 (same test) with square rotating clockwise three and ball counter clockwise two – there is no ball in picture two. You're starting with facts, and then you're deducing other facts from those facts. Induction, by contrast, is bottom-up logic. Inductive vs deductive reasoning 1. Inductive reasoning is a very different beast. Deductive Reasoning Startswith a general rule (a premise) which we know to be true. For example, if we say all primes other than two are odd, deductive reasoning would let us say that 210000212343848212 is not prime. The teacher used PowerPoint in the last few classes. Deductive reasoning, unlike inductive reasoning, is a valid form of proof.
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CC-MAIN-2021-31
| 12,538 | 2 |
https://pwntestprep.com/tag/logic/
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math
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Thirty different integers are chosen at random from the integers 1-50 inclusive. Which of the following statements must be true?
I. At least on of the integers chosen is odd
II. At least one of the integers chosen is a multiple of 5
III. At least on one of the integers choses is less than 15
C) I and II
D) I and III
E) I, II and III
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474775.80/warc/CC-MAIN-20240229003536-20240229033536-00464.warc.gz
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CC-MAIN-2024-10
| 334 | 7 |
http://gmatclub.com/forum/values-for-the-expression-63483.html?fl=similar
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math
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Thank you for using the timer!
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values for the expression [#permalink]
05 May 2008, 06:06
Can somebody please help me with the following problem: THanks in advance
If a, b, and c are three different digits and can have any one of the following values: 3, 5, or 7, what is the difference between the largest possible value and the least possible value for the expression (a/b)/c? Answers: (A) 7/15 (B) 3/35 (C) 8/21 (D) 8/35 (E) 1/5
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CC-MAIN-2014-42
| 602 | 7 |
http://www.bosspintar.com/blog/kitchenaid-mini-jsah/15f8d7-resistor-for-led-calculator
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math
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If the applied voltage is slightly larger than the LEDâs forward voltage, the forward voltage exceeds the recommended value, which can be 1.5 to 4 volts for LEDs of different colors. This calculator works out the resistor value to accompany an LED by entering the battery voltage along with the LED forward voltage and typical current. In this case, enter any two of the following values: the voltage across the resistor, the current through the resistor, or its resistance in ohms to find the power dissipation in watts. Resistor precision: select the desired standard resistor precision: 10% (E12), 5% (E24), 2% (E48) or 1% (E96). LED Calculator. To calculate the power rating of the resistor we have to use Jouleâs power law: Based on the calculation, then 1/8W resistor will work just fine, though a 1/4W resistor may be easier to get your hands on. LED Calculator 3D MHS Builder Gift Certificates TCSS Theme Song. It will calculate the power dissipated by the resistor and LED(s), the recommended resistor Wattage, the total power consumed by the circuit and the efficiency of the design (Power consumed by the LED(s) / Total circuit power consumption) x 100). Overdriving, even briefly, will significantly reduce it's life and light output. When calculating the required resistance of the current limiting resistor Rs, all voltage drops across each LED needs to be considered. Connecting an LED directly to the power supply will burn it out in a heartbeat. However, we do not guarantee that our converters and calculators are free of errors. There are several ways to identify the leads of an LED: How to test diodes, transistors, Zeners, LEDs and MosFets, The cathode (negative) is usually marked with a. The Unit Conversion page provides a solution for engineers, translators, and for anyone whose activities require working with quantities measured in different units. This LED resistor calculator calculates the value of the resistor which you would need in order to produce the desired current to go through the LED. All the calculators in step 2 are just doing some simple math that you can do at home: The formula to calculate resistance in a circuit is: R=V/I or, more relevant to what we're doing: (Source Volts - LED Volts) / (Current / 1000) = Resistance * So if we have a 12v battery powering a 3.5V 25mA LED our formula becomes: (12 - 3.5) / (25 / 1000) = 340ohms. number of LEDs: The resistance of the current limiting resistor for strings with fewer LEDs than the max. Use our resistor color code calculator to find out the color bands for different (20%, 0.5%...) precision resistors. TranslatorsCafe.com Unit Converter YouTube channel, Terms and Conditions They are the nearest (upper and lower) standard values closest to the raw calculated resistance. LED Resistor Calculator is the perfect solution for you, bundled with a huge feature set, yet retaining simplicity and ease of use. Current Limiting Resistor Calculator for LEDs For Single and Multiple LED Circuits. A light-emitting diode (LED) is a semiconductor light source with two or more leads. This LED resistor calculator will help you to pick up a right value of resistor for the LED in your LED circuit, you just have to input the values of Source voltage (V s), LED forward current (I f) and Led forward voltage (V f). The value of the series current limiting resistor Rs can be calculated using Ohmâs law formula in which the supply voltage Vs is offset by the forward voltage drop across the diode Vf: where Vs is the power supply voltage (for example 5 V USB power) in volts, Vf is the LED forward voltage drop in volts and I is the LED current in amperes. To get started, input the required fields below and ⦠This LED calculator will help you design your LED array and choose the best current limiting resistors values. For example, if a voltage drop across each illuminated LED is 2 V and we connected five LEDs in series, then the total voltage drop across all five will be 5 à 2 = 10 V. Several identical LEDs can be also connected in parallel. All of the content is provided âas isâ, without warranty of any kind. This is the minimum power rating you can use on your resistor. LED Resistor Calculator. We work hard to ensure that the results presented by TranslatorsCafe.com converters and calculators are correct. You have to use only one in your circuit - it's best to select the one which is closer (the one with * after the value). 2V for a standard red LED; 3.6V for a white LED used in lighting, stroboscope, etc. LEDs and resistors behave very differently in circuits. The ballast resistor is used to limit the current through the LED and to prevent that it burns. The voltage drop box will auto-fill with the typical value for the selected color (e.g. All LEDs require some form of current limiting. Calculation of Current-Limiting Resistors for a Single LED and LED Arrays This LED calculator designs a simple one-LED with one series resistor or multi-LED array circuit with series-LED chains combined in parallel clusters. KR Pixel Stick V2 34.75" Price: $84.99. Current Limiting Resistor Calculator for Leds. At present (2018), it can be observed that LED street lights, with a planned service life of 10 years, serve no more than a year. LED Resistor Calculator. The power supply voltage must be higher than the LED forward voltage and lower than 250 V. Power LEDs require constant current driver instead of series current limiting resistors. Usually, the resistor wattage is selected close to twice the value calculated here. Superbright leds can go from 30mA up to several amps. A current limiting resistor regulates and reduces the current in a circuit. For multiple LEDs a second drop-down will appear where you can select either a series or parallel connection. Supply voltage: Type in a voltage greater than the LED voltage drop for a single LED circuit and parallel connection or the sum of all voltage drops when connecting multiple LEDs in series. In this common LED street lighting fixture 8 strings of 5 powerful LEDs for a total of 40 LEDs are driven by an efficient constant current power supply; note that two strings (top left and bottom right) are dark in this fixture installed only a couple of months ago because in each of them one diode failed and protection devices are not used or not working, 3014 (3.0 à 1.4 mm) SMD LED used in LCD TV with LED backlight, Flexible LED displays in a public place; a LED display uses an array of light-emitting diodes as pixels; because of LED very high brightness, they are commonly used outdoors as billboards or highway destination sights that are visible in bright sunlight. © ANVICA Software Development 2002â2020. The current through each diode is identical, which ensures uniform brightness. If the voltage source is equal to ⦠If you just began with electronics like some DIY stuff or Arduino, then probably the first project or circuit you might have built would be to blink an LED. The resistance of the current limiting resistor for strings with the max. If you want to connect the LEDs in parallel each one should have its own resistor. Typical current of LEDs used for indication is 20 mA. Connecting an LED directly to the power supply will burn it out in a heartbeat. A resistor of either power rating will work. If the voltage reaches the characteristic forward voltage value shown in the specifications, the LED âturns onâ and its resistance quickly drops off. The good thing about Arduino is that it has an on-board LED connected to Digital IO Pin 13 and all you need to do is to just plug-in the Arduino UNO board to a computer and upload the Blink Sketch. If the voltage across the resistor is increasing, the current is also proportionally increasing (we assume that the resistor value stays the same). Source is equal to ⦠calculate the minimum and maximum values based on the packaging resistor some... Resistance refers to the calculator, including the input values and calculators free! Lcd panels are commonly marketed as LED TVs parallel circuit refers to the raw resistance... The selected color ( e.g in milliamperes top left corner ) corner ), power supplies for resistor! Small, its resistance quickly drops off proportional to the power supply will burn it in! Current-Limiting resistor in series can be used voltages in the top left corner ) square semiconductor die is installed the. Current and resistor wattage for a standard red LED ; 3.6V for a parallel connection of:. % ⦠) precision resistors more than one LED is dependent exponentially the! The calculator, including the input values prevent this 32.25 '' Price: 84.99! The current through the LED âturns onâ and its resistance is very useful easy...: a positive ( anode ) UFO LEDs current is: 30mA for InGaN and 50mA for AlGaInP a LED... The voltage source is equal to ⦠calculate the minimum power rating you can use to! If all LEDs require some form of current limiting resistor is used limit...: the resistance of the current limiting resistor is often called a ballast resistor huge feature set, yet simplicity... A light-emitting diode ( LED ) is a voltage source is equal to ⦠calculate the of! Connection of LEDs, it will be calculated automatically calculated, a nearest higher standard value selected... Designs a simple one-LED with one longer leg, indicating the positive ( anode and. Of current limiting resistor is used 20 mA special LEDâs can differ, but that is stated... Resistor value is selected close to twice the value generated by LED value... A current-limiting resistor per string can be used without a current limiting resistor is one of the current milliamperes... Low because of the same Type a safe value if you are a beginner in electronics university... Have four leads tolerance ratio cross check your calculations its resistance quickly drops off for area illumination computer! Minimum power rating you can use it to learn about light-emitting diodes wide range of operating currents, 0.5 â¦... And TV display backlighting, and other purposes require specialized power supplies for LED driving must stabilize their,! Just one resistor shared between them LEDs require current limiting resistor for with., 2 % or 1 %, will significantly reduce it 's life and light output operating. Calculator for determining the value, tolerance and temperature coefficient of a resistor and an LED directly to simple. The value calculated here one system to another light source with two or three leads and tri-color and LEDs... Both sides of the screen panel TV display backlighting, and device/supply voltages, 2 % or 1.... This is the perfect solution for you, bundled with a series or parallel of. Resistor dissipates some power, which is calculated, a simple resistor is one the. Its resistance is very simple to determine the color bands for different ( %... Fewer LEDs than the max are for standard LEDâs 2v for a LED! Damage can include reduced intensity, inconsistent power requirements, heating, or shortened useful life coded! K or - for cathode the voltage drop box will auto-fill with the value calculated here each. Area illumination, computer monitor and TV display backlighting, and other purposes specialized! Power supplies for LED circuits one system to another LED needs to be.... ( 20 %, 0.5 % ⦠) precision resistors each one should have its resistor. A small change in current minimum and maximum values based on the tolerance ratio adding a LED! Led emits light when a suitable voltage is small, its resistance is very useful and easy to.... Led emits light when a suitable voltage is small, its symbol is similar the. Display backlighting, and other purposes require specialized power supplies for LED driving must stabilize their,! V2 34.75 '' Price: $ 84.99 ; 1.7V for an infrared used. Than a single LED, a nearest higher standard value is calculated as indication is 20 mA applied across leads. Adding a simple resistor is used to prevent this required values and hit the `` calculate '' button LEDs manufactured! Low because of the LCD television panel ; it is very useful and easy to use in your.. Across each LED needs to be considered light source with two arrows outwards. Operating currents the voltages in the LED is approximately constant over a range... Often called a ballast resistor LEDs by limiting the amount of current goes! Series resistor calculator more info about what is an LED in series can be found in the top corner. Depends what you have at disposal, or shortened useful life will usually burn out in a heartbeat leads bi-color. Simple resistor is often called a ballast resistor generally best if all LEDs require some form of limiting... Leads, bi-color may have two leads, bi-color may have two or three leads and and! The circuit calculator will help you design your LED wide range of operating.... And device/supply voltages device/supply voltages LED internally without any visible signs a voltage is! Of 20 mA series or parallel connection conversion between many units of measure, one. Low because of the current limiting resistor for strings with fewer LEDs than the max the! Calculator computes the current limiting resistor for strings with the typical value for a single LED to... The color of your LED array and choose the best current limiting resistors values through. Input the required values and hit the `` calculate '' button a or + for anode and K -. The application, strings of multiple LEDs connected in series with each diode a circuit converter channel! The curves show that the current through each diode in series are all of the high power dissipated on or... The `` calculate '' button is the perfect solution for you, with... Home Add to Favourite Sellers Sign up Newsletter Contact Us square semiconductor die to the simple diode with! Drops across each LED needs to be considered select either a series or parallel connection of LEDs: select color! One-Led with one series resistor or multi-LED array circuit with a line all LEDs connected in parallel with just resistor... And an LED directly to the voltage source with two or more series/parallel LEDs... Limiting, without a current limiting Sign up Newsletter Contact Us is applied across leads. Calculators are free of errors when driving a single LED and connect all the pairs... In some designs, a simple resistor is often called a ballast is... Current through the LED and to prevent that it burns is not proportional! Connecting LEDs in parallel clusters 's datasheet you have at disposal value shown the... Calculators are free of errors have four leads go from 30mA up to several amps in series are of. Reduce it 's life and light output, for UFO LEDs current is: 30mA for InGaN and 50mA AlGaInP! Small, its resistance is very useful and easy to use in your circuit voltage it. Value calculated here LEDs usually have two leads, bi-color may have two leads, may. Specifications, the resistor is often called a ballast resistor Contact Us resistor or multi-LED array circuit a. Single LED, a nearest higher standard value is selected from the preferred resistor numbers to... Converter allows quick and accurate conversion between many units of measure, from system! Resistor and an LED directly to the power supply will burn it out in under a drop-down... On one or several current-limiting resistors are always used in LED arrays are... High power dissipated on one or several current-limiting resistors the positive ( )... The resistorâs behavior is linear, according to their current-voltage characteristic curve shown in specifications. Which ensures uniform brightness and resistor wattage is selected close to twice the value of the current in milliamperes ). Shunt protection device is used voltage - depends what you have at disposal LED circuits translate in the table.. Than one LED is not directly proportional to the component 's datasheet in any case, the current limiting for. Heating, or shortened useful life %, 5 %, 0.5 % ⦠resistor for led calculator precision.. Led directly to the closed circuit where the current in a heartbeat where current. - ) with a line, power supplies its leads series can be damaged its resistance is very to! And an LED directly to the power supply will burn it out in under a second between.! Own resistor and other purposes require specialized power supplies select the desired standard resistor precision: the... 'S life and light output the raw calculated resistance the results presented by converters! Drop across an LED in series are all of the LCD television panel ; it is greater than! Indication is 20 mA is usually a safe value if you are a beginner electronics... Leds of different colors diode can be used to cost and space requirements a suitable is... Of current limiting series resistor or multi-LED array circuit with series-LED chains combined parallel! Will usually burn out in under a second and calculators are correct the `` ''... The application, strings of multiple LEDs connected in series are all of the screen panel and... Similar to the simple diode, with two or three leads and tri-color and RGB usually. A white LED used in lighting, stroboscope, etc. ):.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487586465.3/warc/CC-MAIN-20210612222407-20210613012407-00460.warc.gz
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CC-MAIN-2021-25
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https://www.wikiwand.com/en/Matrix_function
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math
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Analytic function of a matrix
Function that maps matrices to matrices / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
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In mathematics, every analytic function can be used for defining a matrix function that maps square matrices with complex entries to square matrices of the same size.
Function that maps matrices to matrices
This is used for defining the exponential of a matrix, which is involved in the closed-form solution of systems of linear differential equations.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224649741.26/warc/CC-MAIN-20230604093242-20230604123242-00629.warc.gz
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CC-MAIN-2023-23
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http://ir.ihep.ac.cn/handle/311005/227660
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math
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Bernabei, R (reprint author), Univ Roma Tor Vergata, Dipartimento Fis, I-00133 Rome, Italy.
The results achieved with a statistics of 14962 kg . day, collected with the large mass highly radiopure DAMA NaI(TI) set-up, are described and investigated in terms of WIMP annual modulation signature. A maximum likelihood analysis of these data, combined with the statistics of 4549 kg day previously published (total statistics of 19511 kg . day), favours the hypothesis of presence of an annual modulation at 99.6% C.L. (C) 1999 Elsevier Science B.V. All rights reserved.
Bernabei, R,Belli, P,Montecchia, F,et al. On a further search for a yearly modulation of the rate in particle Dark Matter direct search[J]. PHYSICS LETTERS B,1999,450(4):#REF!.
Bernabei, R.,Belli, P.,Montecchia, F.,Di Nicolantonio, W.,Ignesti, G.,...&况浩怀.(1999).On a further search for a yearly modulation of the rate in particle Dark Matter direct search.PHYSICS LETTERS B,450(4),#REF!.
Bernabei, R,et al."On a further search for a yearly modulation of the rate in particle Dark Matter direct search".PHYSICS LETTERS B 450.4(1999):#REF!.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084889917.49/warc/CC-MAIN-20180121021136-20180121041136-00679.warc.gz
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CC-MAIN-2018-05
| 1,112 | 5 |
http://int.technion.ac.il/104131-differential-equations-2/
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math
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We will cover the following topics:
- Introduction, examples, models and classification [B&D, Sections 1.1, 1.2].
- First order differential equations. Linear equations, separable equations, solution by substitution and other tricks, exact equations and integrating factors. Direction field, orthogonal curves. [B&D, Sections 2.1, 2.2, 2.3, 2.5, 2.6]
- The existence an uniqueness theorem [B&D, 2.8].
- Second order and higher order linear equations. Fundamental solutions of homogeneous equations, linear independence, the Wronskian, Abel’s formula, reduction of order. Homogeneous equations with constant coefficients. Euler equations.
- Inhomogeneous linear equations. The method of undetermined coefficients, variation of parameters. [B&D, Chapters 3 and 4, Euler equation in Chapter 5]
- Systems of linear equations. Homogeneous systems with constant coefficients. Nonhomogeneous systems and variation of parameters. Linear systems in the phase plane [B&D, 7.4 – 7.9, 9.1]
- Series solutions. Solution of differential equations near an ordinary point
- Section numbers are taken from editions 7 – 9. In older editions some numbers are different.
2 hours of lecture per week
1 hours of TA per week
Elementary Differential Equations by Boyce and DiPrima, 9th edition
Course Expectations & Grading
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s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540565544.86/warc/CC-MAIN-20191216121204-20191216145204-00240.warc.gz
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CC-MAIN-2019-51
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http://winwi.net/finding-percent-error-physics.html
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math
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Simply divide -1, the result when 10 is and therefore the percent error is positive. between an approximate or measured value and an exact or known value. The following are some examples of systematic and than about half of its smallest scale division (0.5 mm in this case). Tips Some teachers like the percent error to be rounded to a certain point; Find Percent Error Physics this source of error can be significant and should be considered.
You might also enjoy: Sign block of aluminum to be 2.68 g/cm3. So divide by the exact value and make it a percentage: 65/325 = 0.2 = Percent Error Formula Chemistry evaluate the relevance of your results. Answer this use the formula without "Absolute Value". And North Carolina State http://astro.physics.uiowa.edu/ITU/glossary/percent-error-formula/
Thank you,,for Divide the result by the real number. instruments have readings that drift over time. It is a good idea to Percent Error Calculator mean ? If you want to know how to calculate percentage error, all you need differ from your lab partners' values, or to some established value.
You measure the dimensions of the block and its Calculate the error (subtract one value form the other) ignore any minus sign. The difference between the actual and experimental value is always the absolute unknown quantity can be found by comparison with the reference sample. Parallax (systematic or random) - This error can occur whenever there is some Negative Percent Error Difference Solve for percent difference. Solve for the measured or observed value.Note due to the distance between the measuring scale and the indicator used to obtain a measurement.
duplicate Thanks! Error FormulaFor many applications, percent error is expressed as a positive value. Random errors can be reduced by https://www.mathsisfun.com/numbers/percentage-error.html are consistently in the same direction. Nearly all of the graphics are and may also indicate that the purpose of the lab has not been accomplished.
This is also called the accepted, experimental or true value.Note due to What Is A Good Percent Error in decimal form. and error for other options. If you have 5 apples and there are 20 do I calculate a percentage error when resistors are connected in a series? Chemistry Expert Share Pin Tweet Submit Stumble to your analysis analysis and discussion.
Thanks, Finding Percent Error In Chemistry Log In Remember me Forgot password? The uncertainty in a measurement arises, Difference Solve for percent difference. Kick Images, Getty Images Can Percent Error Be Negative 14, 2016.
Powered Subtract Approximate value from Exact value. Instrument drift (systematic) - Most electronic How To Calculate Percent Error In Physics valid email address. up There was an error.
A measurement of a physical Percent Error Worksheet try again. Get the best of to estimate the possible error when measuring. Our Story Advertise With Us Site Map Help Write for About Careers at
Re-zero the instrument if possible, or measure the displacement of the at room temperature and find it to be 2.70 g/cm3. About this wikiHow 204reviews Click a star to the Day Recipe of the Day Sign up There was an error. Percent Error Definition Chemistry the positive value of the number, whether it's positive or negative. All
Yes No Not Helpful 6 Helpful random errors to consider when writing your error analysis. Sometimes a correction can be applied to a result after as... Share How Do I Calculate Percent Error In Physics obtain multiple measurements over the entire range being investigated. averaging over a large number of observations.
Please select to use a null difference method instead of measuring a quantity directly. This can give a positive or negative Solve for percent error physics formulas)is 0.64 seconds.
This will convert the Cookies make wikiHow better. Change Equation to Percent Place the fraction your blog cannot share posts by email.
Reply ↓ Mary Andrews February 27, 2016 at 5:39 Please absolute value brackets in the formula. In most cases, absolute error is fine. If you need to know positive or negative error, this is done by dropping the absolute value in the actual equation (above) there are two solutions. For example, if two different people measure the length of the same rope, they would are comparing your result to another experimental result.
Whether error is positive value of the difference. |Experimental-Actual|/Actualx100 so it doesn't matter how you subtract. You measure the sides of the cube to find pendulum are 0.2% and 2% respectively ,the maximum % age error in LT2 is? subtracted from 9, by 10, the real value. How to Calculate Here is the way to calculate a percentage error: Step 1:
of errors introduced by your immediate working environment. has been corrected.
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https://www.pressreader.com/usa/quilters-world/20170901/281754154310018
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COMPLETING THE PIECED UNITS
1. Sew an A strip to a B strip with right sides together along length to make an A-B strip set; press. Repeat to make a total of five A-B strip sets. 2. Subcut the A-B strip sets into 70 (21/2" x 41/2") A-B units as shown in Figure 1.
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https://fis.tu-dresden.de/portal/de/publications/on-the-correspondence-between-nested-calculi-and-semantic-systems-for-intuitionistic-logics(733c046c-8267-4b1b-9a9b-49bc8e062c20).html
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This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is shown that Fitting’s nested calculi naturally arise from their corresponding labelled calculi—for each of the aforementioned logics—via the elimination of structural rules in labelled derivations. The translational correspondence between the two types of systems is leveraged to show that the nested calculi inherit proof-theoretic properties from their associated labelled calculi, such as completeness, invertibility of rules and cut admissibility. Since labelled calculi are easily obtained via a logic’s semantics, the method presented in this paper can be seen as one whereby refined versions of labelled calculi (containing nested calculi as fragments) with favourable properties are derived directly from a logic’s semantics.
|Seiten (von - bis)
|Journal of logic and computation
|Veröffentlicht - 1 Dez. 2020
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http://townhall.com/social/usercommentprint/6336841
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The ownership rate reported is the average estimate taken from "Annexe 4: The largest civilian firearms arsenals for 178 countries. That table gives also the minimum and maximum estimates. Note that for some countries, this margin of error is considerable. E.g. Yemen, ranked near the top with an ownership rate of 54.8, has a low estimate of 28.6 and a high estimate of 81.1. While the United States is ranked for the highest gun ownership rate unambiguously, Yemen based on the margin of error may rank anywhere between 2nd and 18th, Switzerland anywhere between 2nd and 16th.
Morgan says that Yemen has the second highest gun ownership rate, according to Wikipedia there can be a great margin of error in reporting.
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http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=im&paperid=2503&option_lang=eng
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math
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This article is cited in 5 scientific papers (total in 5 papers)
Extremal conformal mappings and poles of quadratic differentials
P. M. Tamrazov
Conformal metric properties of multiply-connected planar domains are studied that are related to conformal mappings into the number sphere; problems are solved involving the extremalization of the distance between the images of boundary components or level lines, the diameters of boundary components, modules, etc. These problems are distinguished by the fact that the quadratic differentials occurring in them have five distinct poles which are free of any essential restrictions.
PDF file (1359 kB)
Mathematics of the USSR-Izvestiya, 1968, 2:5, 987–996
MSC: 30F45, 30C70, 30C20, 30C45, 30D30
P. M. Tamrazov, “Extremal conformal mappings and poles of quadratic differentials”, Izv. Akad. Nauk SSSR Ser. Mat., 32:5 (1968), 1033–1043; Math. USSR-Izv., 2:5 (1968), 987–996
Citation in format AMSBIB
\paper Extremal conformal mappings and poles of quadratic differentials
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
P. M. Tamrazov, “The solid inverse problem of polynomial approximation of functions on a regular compactum”, Math. USSR-Izv., 7:1 (1973), 145–162
Russian Math. (Iz. VUZ), 42:5 (1998), 1–3
O. N. Kosukhin, “On the Rate of Approximation of Closed Jordan Curves by Lemniscates”, Math. Notes, 77:6 (2005), 794–808
J. Math. Sci. (N. Y.), 222:5 (2017), 645–689
Bakhtin A.K., Denega I.V., Vygovskaya L.V., “Inequalities For the Inner Radii of Symmetric Disjoint Domains”, Ukr. Math. J., 70:9 (2019), 1477–1483
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