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http://www.chegg.com/homework-help/questions-and-answers/shot-putter-launches-7060-kg-shot-pushing-straight-line-length-1650-m-angle-3380-horizonta-q3056742
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math
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0 pts endedThis question is
closed. No points were awarded.
A shot putter launches a 7.060 kg shot by pushing it along a straight line of length 1.650 m and at an angle of 33.80° from the horizontal, accelerating the shot
to the launch speed from its initial speed of 2.500 m/s (which is due to the athlete's preliminary motion). The shot leaves the hand at a height of 2.110 m and at
an angle of 33.80°, and it lands at a horizontal distance of 16.70 m. What is the magnitude of the athlete's average force on the shot during the acceleration
phase? (Hint: Treat the motion during the acceleration phase as though it were along a ramp at the given angle.)
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https://itecnotes.com/electrical/electronic-effect-on-output-voltage-when-voltage-regulator-caps-are-undersized/
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math
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I recently corrected (increased) the sizing on the capacitors around a voltage regulator and then realized I didn't really have good intuition on what it would look like in the wild if they were wrong.
What is the affect or symptoms I would see on the output voltage if the voltage regulator caps are undersized?
From the datasheet, the first input cap is simply 'required' with no explanation as to why.
*Required if regulator input is more than 4 inches from input filter capacitor (or if no input filter capacitor is used). **Optional for improved transient response.
For the optional second capacitor, I usually choose a nominal value and type as given by the datasheet but don't really have a rule-of-thumb formula to increase that value if, say, the destination is very far away (e.g. microcontroller power pin).
Understanding "Stability" in regulators
To get an intuitive understanding (which is what the question is asking for), you need to understand the concept of stability and how regulators work in the general case.
For most capacitor values given for regulators, the values given are the minimum value needed for stability plus a little margin.
The regulator is a closed-loop system. It watches what happens on the output and adjusts "stuff" internally to make sure the output (really a scaled-down version of the output) always equals a desired value.
Problems occur when it starts chasing its tail. If, as a result of it changing "stuff" internally, the input voltage also starts to change (or the output changes too quickly) then the changes the regulator made will have too much of an effect and it will have to undo the excess.
This corrective change can also overshoot the mark, requiring another corrective change... as you can see, without sufficient "stability" in the system, the regulator can output a continuously fluctuating voltage rather than the flat line you hope for when employing a regulator.
The capacitors slow down voltage changes, thereby helping to ensure overall stability.
The input capacitor is required to stabilize the input voltage. If the input voltage is isolated from the power source by a large inductance (like a long wire) then current changes in the regulator will manifest as large voltage changes at the input due to the inductance. The capacitor is there to "cancel" that inductance and ensure a slowly varying (e.g. stable) voltage at the input. This makes the input change slower than the reaction time of the control loop of the regulator -- achieving stability.
If you don't have a large enough output capacitor (the second one in your description) then the output ripple will be greater than the datasheet predicts. That means you will get the regulated voltage but the output will fluctuate around that voltage. Specifically, the output will be slow to react to rapid changes in load (current demand). So when you activate different parts of your load (application) circuitry you may experience sudden drops in voltage. Those drops can be severe enough to trigger resets in your digital circuitry (or worse, latching) or conditions in your analog circuitry were there is a recovery time (such as discharging filter capacitors).
Rule(s) of Thumb(s)
These are approximations. The correct answer in engineering is always "it depends," but that's not useful. So here I give you some thoughts on "guessing" reasonable values.
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https://ssb.northeaststate.edu/prod_ssb/bwckctlg.p_display_courses?term_in=202280&one_subj=MATH&sel_subj=&sel_crse_strt=1910&sel_crse_end=1910&sel_levl=&sel_schd=&sel_coll=&sel_divs=&sel_dept=&sel_attr=
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math
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|Select the Course Number to get further detail on the course. Select the desired Schedule Type to find available classes for the course.|
|MATH 1910 - Calculus I|
Calculus I includes topics such as: trigonometric, inverse trigonometric, exponential, logarithmic and hyperbolic functions; continuity; derivatives and applications; indeterminate forms; and an introduction to the integral.
Prerequisites & Notes
Prerequisites: A grade of C or higher in MATH 1720 or sufficient high school math, including Trigonometry with and ACT score of 25 or higher.
4 Credit Hours - 4 Lecture Hours (F, S, U)
Note: * Course designed for transfer.
Approved course for TBR/Northeast State’s General Education Core.
4.000 Credit hours
4.000 Lecture hours
Schedule Types: Laboratory, Lecture, Combined Lecture/Lab
Mathematics Division Division
University Parallel Department
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https://lkeng.org/wp/?p=247
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math
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Note: I’m contemplating designing a spectrum analyzer. The following are a compilation of my own notes that I’m making public. They might not make a lot of sense as a coherent treatise but take the pieces for what they are.
The classical way of performing RF spectrum analysis is to mix the input with a local oscillator (FLO1) that ramps between two higher frequencies, producing IF1.
IF1 is sent through a narrow band filter which leaves you with a narrow piece of the input spectrum that has been shifted up. The ramping action gives you a sliding window of the input spectrum, shifted up to the center frequency of the narrow bandpass filter.
Stepping back, remember that the IF1 frequency is the result of nonlinear mixing of the input with the local oscillator.
Let’s make some assumptions:
– the input (Fin) is any signal between zero and 1000 MHz.
– the local oscillator (FLO1) ramps between 1050 and 2050 MHz
– the narrow bandpass filter (FBP) is 1050 MHz
Mixing the local oscillator and the input with a non-ideal mixer gives you:
IF1 = N*input +- M*LO
The strongest output spectra will be where N=1 and M=1. This gives you spectra centered at:
(a) Fin + FLO1
(b) Fin – FLO1
Since FLO1 is always greater than Fin, we get a nice strong first image (a) between 1050 and 2050 MHz.
The first negative image (b) is wrapped into the range of 0 to 1050 MHz. Subsequent energies are present at higher orders, however their amplitude is orders of magnitude lower than the main images.
After mixing, IF1 is filtered using a high-Q filter. Q, of course, is a measure of how wide the pass-band is.
Q = Fc/Fbw where Fbw is the -3dB bandwidth.
Common hobbyist spectrum analyzers use cavity or helical filters.
A cavity filter has radiative elements (I’ll liberally call antennae) in a conductive can along with a resonator whose length can be changed. They can and often contain multiple cavities
Here’s a paper from M/A COM on cavity and helical filter design.
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https://www.richmondcorporateadvisory.com/page.php?7a47f3=radius-of-hydrogen-nucleus
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math
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In 1913, Neils Bohr adopted the Rutherford model for the explanation of the atomic spectra of the hydrogen energy levels by Bohr’s theory. It can be seen at many places, this one for example lays out the usual separation-of-variables approach nicely.
Use the uncertainty principle to estimate the kinetic energy for a neutron localized inside the nucleus.
A hydrogen nucleus has a radius of 1 x 10-15 m and the electron is about 5.4 x 10-11 m from the nucleus. Attributed to Kjerish - Own work, CC BY-SA 4.0, File:NuclearReaction.svg - Wikimedia Commons Source Wikipedia Wikipedia Protons and neutrons are bound together to form a nucleus by the nuclear force. The most recent value for the radius of a proton is 8.41 × 10^(-16)"m". Typical nuclear radii are of the order 10 −14 m.Assuming spherical shape, nuclear radii can be calculated according to following formula: r = r 0.A 1/3. Nuclear Density. The last post relied heavily on WolframAlpha to calculate the average distance of the 1s electron from the hydrogen nucleus. Sample Test Problems. A hydrogen atom has a diameter of approximately 1.06 x 10-10 m, as defined by the diameter of the spherical electron cloud around the nucleus.
The atomic radius of a chemical element is a measure of the distance out to which the electron cloud extends from the nucleus.
The radius of a nucleus has quite a range completely dependent on the element or isotope under consideration. Assume the hydrogen atom is a ball with a radius of about 5.4 x 10-11 m and the nucleus is a ball with a radius of 1 x 10-15 m. How much work … Nuclear Radius. V = volume in m 3 R = nuclear radius in m. Using the equation for nuclear radius from the section above. Question: Calculate the most probable distance of the electron from the nucleus in the ground state of hydrogen, and compare this with the average distance. The values are 6.70 × 10^14"kg/dm"^3 and 2.7"kg/dm"^3. So, if a nucleus has Z protons (Z = 1 for hydrogen, 2 for helium, etc.) The hydrogen atom is made up of a proton and an electron bound together by the Coulomb potential, . Image showing periodicity of valence s-orbital radius for the chemical elements as size-coded balls on a periodic table grid.
The spectra of hydrogen-like ions are similar to hydrogen, but shifted to higher energy by the greater attractive force between the electron and nucleus. Bohr’s model of hydrogen atom energy levels. The canonical approach is to solve the Schroedinger equation for the Hamiltonian of the electron with n = 1. A … The atomic radius of Hydrogen atom is 31pm (covalent radius).
where r 0 = 1.2 x 10-15 m = 1.2 fm.
Protons and neutrons are bound together to form a nucleus by the nuclear force. You use the formula for density and the published radii to calculate the densities. The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment.After the discovery of the neutron in 1932, models for a nucleus composed of protons and neutrons were quickly developed by Dmitri Ivanenko and Werner Heisenberg.
Real Estate Continuing Education Georgia, Honeysuckle Botanical Name, The Flavor Bible Review, Emerald Green Formal Dress, Geoffrey Zakarian Son, Breaking Benjamin - What Lies Beneath Lyrics, Khalid Right Back Sample, Sns College Of Allied Health Sciences, Dragon Ball Legends All Ultimate Attacks, Reasoning And Problem Solving Ppt, Beef Roast With Lipton Onion Soup Mix And Cream Of Mushroom Soup, Lee Min-ji (miss Korea), Top Chef: New Season, Best Cat Products 2019, Silgan Investor Relations, Paintings Of Elephants For Sale, Dream Of Someone Breathing On Me, Thompson Ct Election Results, Home Remedies For Adenoids, Baby Halloween Songs, War Booties Meaning, Iron Maiden Logo Eddie, Co Po Mapping Ppt, How To Turn 100k Into 1 Million Reddit, Thapar University Mohali, Spaghetti Lasagna With Pepperoni, Clear Bags Wholesale, Vanilla Extract Calories, Cocoa Puffs Commercial,
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http://1.aboutinnocent.org/logic-diagram-examples.html
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math
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Network Documentation Series: Logical DiagramLogic Diagram Examples - As such, the usage of Venn diagrams is just the elaboration of a solving technique. Problems that are solved using Venn diagrams are essentially problems based on sets and set operations. Thus, before we move on to understanding Venn diagrams, we first need to understand the concept of a set.. Watch video · One of the best visual programming languages is a PLC programming language. It’s called ladder logic or ladder diagram (LD) and you can learn it very fast. The smart thing about ladder logic is that it looks very similar to electrical relay circuits.. (plural logic diagrams) A diagram in the field of logic. Any non-spatial, abstract diagram. Any schematic display of the logical relationships of project activities. A graphical representation of a program using formal logic. A flow chart of hardware circuits or program logic..
Figure 3 – (a) OR electrical circuit (b) OR logic gate. Figure 11.10a shows an OR logic gate system on a ladder diagram, Figure 4b showing an equivalent alternative way of drawing the same diagram.. This seems like an awfully complex state diagram for such as simple procedure, but it has taken into account every possibility for the design of this circuit. Now, we need to design the circuit.. As it turns out, digital circuits are built on the foundation of basic logic. 1. Logic circuits. At the most basic level, of course, a computer is an electrical circuit build using wires. Here is an example showing the diagram of a simple logic circuit. Figure 1: A simple logic circuit..
Generally, logical symbols are used in logical diagrams. Most of them are self-explanatory, but since I’ve seen mistakes, here are a couple of examples. A subnet is represented as a pipe or line:. But this models a significant logical feature of the syllogism itself: if its premises are true, then its conclusion must also be true. Any categorical syllogism of this form is valid. Here are the diagrams of several other syllogistic forms.. Sequential Logic Implementation Models for representing sequential circuits Abstraction of sequential elements Finite state machines and their state diagrams Inputs/outputs Mealy, Moore, and synchronous Mealy machines Finite state machine design procedure Verilog specification Deriving state diagram.
Conceptual, logical and physical model or ERD are three different ways of modeling data in a domain. While they all contain entities and relationships, they differ in the purposes they are created for and audiences they are meant to target.. Example 5: Nebraska Logic Model for Walk to School Day, by Jamie Hahn Jamie Hahn is a health educator with the Cardiovascular Health Program at Nebraska Health and Human Services System. "This model helps me to explain to different partners what their role is in the Walk to School Day events," Hahn says.. Jun 24, 2017 · Logical Diagram Beautiful Logical Network Diagram Template, picture size 1360x1360 posted by Aston at June 24, 2017 Lovely Logical Diagram – The diagrams demonstrate the reasoning supporting the associated operational and hazard complications, and present an assortment of alternatives for you to select from, which can allow you to reach a decision concerning the issue.
Logic Gates A logic gate is an electronic circuit which makes logic decisions. It has one waveforms showing time relationships is called a timing diagram. ˛ Fig.(2-5) Example of AND gate operation with a timing diagram showing input and output relationships.. program the LOGO! using Ladder Logic or Ladder Diagrams. Figure 4.1 Ladder Diagram Example-1 Figure 4.2 A ladder Figure 4.1 shows an example of a ladder diagram..
Amazing Traffic Light Ladder Logic Diagram Examples And PLC ... Amazing Traffic Light Ladder Logic Diagram Examples And PLC Programming
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https://dspace.vutbr.cz/handle/11012/57233?locale-attribute=cs
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math
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Using Volterra Series for an Estimation of Fundamental Intermodulation Products
MetadataZobrazit celý záznam
The most precise procedure for determining the intermodulation products is to find a steady-state period of the signal first, and then to calculate its spectrum by means of the fast Fourier transform. However, this method needs time-consuming numerical integration over many periods of the faster signal even for enhanced methods for finding the steady state. In the paper, an efficient method for fast estimation of the fundamental intermodulation products is presented. The method uses Volterra series in a simple multistep algorithm which is compatible with a typical structure of the frequency-domain part of circuit simulators. The method is demonstrated by an illustrative testing circuit first, which clearly shows possible incorrect interpretation of the Volterra series. Thereafter, practical usage of the algorithm is demonstrated by fast estimation of the main intermodulation products of a low-voltage low-power RF CMOS fourquadrant multiplier.
Klíčová slovaSteady-state algorithm, fast Fourier transform, numerical integration, Volterra series, CMOS, RF multiplier
Typ dokumentuRecenzovaný dokument
Verze dokumentuFinální verze PDF
Zdrojový dokumentRadioengineering. 2008, vol. 17, č. 4, s. 59-64. ISSN 1210-2512
- 2008/4
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http://forum.xda-developers.com/showpost.php?p=52676762&postcount=1
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math
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OP Junior Member
Join Date:Joined: May 2014
I need some help with this, and seeing that people have worked on the Infobar A01/02 I would assume there's people here who can tackle this. I have no idea how you would go about Rooting or Unlocking a SHARP device, let alone a Japanese one and I don't see the C01 listed anywhere.
I'd also like to know how I would go about installing a ROM alongside the default one on here.
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http://home.blarg.net/~math/lessons/year2/y2l18c1p1.html
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math
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Probability and Statistics
Answer:________3). (2 points) Two standard dice are rolled. What is the probability that the sum of the faces shown is greater than 11?
Answer:________4). (2 points) The probability that it will rain on any given day is 1/2. What is the probability that it will NOT rain for 3 days?
Answer:________5). (2 points) There are 3 red marbles and 7 blue marbles in a bag.
What is the probability that you draw a blue marble from the bag on your first draw?
Answer:________6). (2 points) If the probability of having homework is 3/4, and the probability of it raining is 1/2, what is the probability of having no homework and it raining?
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https://www.transtutors.com/homework-help/corporate-finance/stock-valuation/dividend-growth-model/constant-growth-model/
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math
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Constant Growth Model
The Constant Growth Model is also recognized as the Gordon model which is one of the most popular models in Corporate Finance. The Gordon Model is one of the most known and popular models in Corporate Finance. In a nut shell it is a method for valuing a stock for business to provide for litigation, tax planning, and business transactions that don't have any market value.
It is a financial model which is being used to calculate the “intrinsic” value of a stock, based on future dividends that are assumed to grow at a constant rate. This model is named of researchers Myron J. Gordon and originated in 1959. This model values a lot for the business for the present value for all dividends and the model values for business as it calculates the present value of all future dividends and leverages a required rate of return for the investor on similar substitute assets.
Features of the Constant Growth Model:
Arriving at Present Value
The Gordon Growth Model is well known for the class of discounted dividend models and differs from of the discounted cash flow valuation model. This model assumes that the company pays a dividend at a constant rate and investors required rate of return for the stock. The stock is at held and is equal to the cost of equity for the company only. The model advocates the sums of discounted series of payment to the investors and shareholders.
A Stock as Perpetuity
The stock becomes perpetuity for the investors, if the stock has never been sold and the price will be equal to the present value of share and dividends. Since the model advocates about the present price of the stock is equal to the future cash flows so it allows the future sale price of the stock will be total of the cash subsequent to the sale discounted provided by the rate of return. The stock for the sale purpose is the way to receive income for company by dividends payments. The stock may benefit from valuation process.
Disadvantage to the Gordon Growth Model
While the Gordon Growth Model assumes that the earnings growth is constant for perpetuity, in practice it would be difficult for a company to achieve this aim. All analysts advocate that a high growth rate can be continuous for only a restricted number of years which is followed by a constant rate of growth. The discounted cash flow model accounts for this by assigning a terminal growth rate.
Formula for constant growth
Constant growth involves summing the infinite series which gives the value of price current P. The formula is as follows:
The model assumes that the required rate of return for the stock remains constant at k>g which is equal to the cost of equity for that company.
Summing the infinite series we get,
In practice this P is then adjusted by various factors e.g. the size of the company.
k denotes expected return = yield + expected growth.
It is common to use the next value of D given by : D1 = D0(1 + g), thus the Gordon's model can be stated as
This example guides you to find the conception of Constant growth Model in an easier way.
www.Transtutors.com provides timely home work and class work project at affordable charges with detailed answers to your Finance Subject problems to understandassignments in better way. Our teaching help line is open for 24X7 so that you can avail our service anytime, anywhere in the world.
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https://bookfound.com/products/6978
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math
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Introduction to Statistical Reasoning by Gary Smith
9780070592766 This text focuses on the analysis of data and the interpretation of results rather than the computational methods of statistics. Its examples are taken from a broad range of disciplines and screen shots from the more popular software packages are included to display data and graphics. Mathematical derivations are minimized, so encouraging the student to use a calculator or computer to perform the computations. Various technology options give the student a range of methods for performing the statistical computations. The section on uses and misuses of statistics shows how statistics are presented by graphs and charts.
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https://brolight.en.alibaba.com/product/60312576104-801948380/Unbalanced_DC_Bridge.html
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math
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Unbalanced DC Bridge
The instrument can compose Vertical Bridge, Horizontal Bridge and Power Bridge to measure a variety of continuous variation of physical quantities.
1.The basic principle and operational method of measuring resistance by DC single arm electric bridge Wheatstone bridge.
2.The basic principle and operational method of measuring resistance by DC unbalanced bridge.
3. According to different resistances, measuring resistances by different bridge and bridge arm resistance’s primary method and unbalanced electric bridge.
4.The meaning of measuring resistance by three terminal method of single arm bridge.
a) The instrument includes voltage type digital current detector and current type digital current detector.
b) The panel is marked ad hoc bridge circuit graphics. It is convenient for students to fix up different kinds of bridge circuits by themselves.
Typical experimental context and data
(A) Measuring resistance by Wheatstone bridge
1. Two terminal method
2. Three terminal method: optional
(B) Experimental context and method of DC unbalanced bridge
1. Measuring resistance by unbalanced bridge voltage output: by horizontal bridge(option for choosing types of bridge)
2. Measuring resistance by unbalanced bridge power output: by vertical bridge. (option for choosing types of bridge)
3. Measuring copper resistance: (by heating device of unbalanced bridge)
(1) Measuring copper resistance by balanced bridge
(2) Measuring copper resistance by unbalanced bridge voltage output
4. Measuring thermistor: equip with heating device of unbalanced bridge ( The experiment equip with 2.7kΩ MF51 semi conductive thermistor)
(1) Measuring thermistor by unbalanced bridge voltage output, the temperature range from indoor temperature to 65oC
(2) Measuring thermistor by unbalanced bridge power output, the temperature range from indoor temperature to 65oC
(3) Using equal arm bridge or horizontal bridge because the range of power bridge is bigger the range of voltage bridge
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https://forums.tomshardware.com/threads/what-power-cord-psu-should-i-use.3464981/
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math
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Hi i just messed up some things in my room and by mistake i mixed the power cords of a psu. In my country we use 220v 60hz. Now the power cords that i mixed: One is 125v 10A and the other is 250v 10A. what power cord should i use? what happens if i use a 125v 10A cord in a 220v plug it will burn?
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http://wayofnature.angelfire.com/Rationality.htm
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math
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In decision theory, rationality is defined as" the rational choice of decisions is the set of decisions which have the greatest probability of the goal being achieved" .
But this definition is far from enough because probability should not be the only factor to assess the rationality of decisions because we should also consider the other factors like economic costs. When two choices have the same likelihood of achieving, we should consider the more economical one more rational. If there are other factors like ecological, social and political rationality most of time becomes weighing cost/benefit rather than assessing the likelihood. We may also choose a set of decisions which has a little bit of less probability but more economical, it is not an easy task to tell which one is the rational choice. We have to take time and effort into consideration, effectiveness and efficiency should also be included in our rationality assessment. So Rationality is the synthetic balancing of all factors rather than maximizing one.
Scientifically, rationality is relative and is a synthetic assessment of accordance with the rules of nature, which includes feasibility appraisal, effectiveness, efficiency, social and ecological impacts, etc. Rationality is relative because we have to talk about rationality with in a specific system of factors. A rational choice within a smaller system of factors may not be rational at all when put in a larger system of factors. Given only all the other factors equal, we can say that the rationality definition by the decision theory is correct.
Religiously, rationality is a measure of closeness to god will.
首页/Home 文心目录/Article Categories
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https://www.mathcation.com/equations-with-the-distributive-property/
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math
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How to Solve Equations with the Distributive Property like a Pro
Get the free Equations with the Distributive Property worksheet and other resources for teaching & understanding solving Equations with the Distributive Property
How to Solve Equations with the Distributive Property
Solving Equations with the Distributive Property happens when a linear equation has a term being distributed to multiple terms inside of a set of parenthesis. The first thing you must do is simplify by using the Distributive Property. You simplify using the Distributive Property by distributing the term in front of the parenthesis by multiplying it by everything on the inside of the parenthesis. After you use the Distributive Property, you solve the equations just like any other Two Step Equation. The first step in solving Two Step Equations is to get all of the constants (numbers) on one side of the equal sign, and the coefficient with the variable on the other side. In order to do this you must use the addition and subtraction property of equality to get the constants on the opposite side as the variable. Once the constants are separated from the variable, you must use the multiplication or division property of equality to cancel out the coefficient on the variable. You can always check your answer by substituting your solution back in to the equation for the variable.
Common Core Standard: 8.EE.C.7
Basic Topics: Combining Like Terms, Distributive Property, Two Step Equations, One Step Inequalities, Two Step Inequalities, Multi Step Inequalities
Related Topics: Two Step Equations, Multi Step Equation, Equations with Variables on Both Sides
More Examples of Multi Step Equations with Distributive Property
So what is the distributive property anyway? Solving Equations with Distributive Property happens when a linear equation contains the distributive property. You can tell if the linear equation contains the distributive property if there is a term that is being distributed to multiple terms inside a set of parenthesis. You must first distribute according to the distributive property. Then you can solve the equation for the variable just like you would any two step equation.
4 Easy Steps for Solving Distributive Property Equations
Steps for solving the Equation with the Distributive Property above:
- Distribute the two to the x and one inside the parenthesis.
- Multiply the two times x and the two times one.
- Add two to both sides.
- Divide both sides by two to get the solution of x equals three.
Equations with Distributive Property Practice Problems Quiz
Video on the Free Distributive Property Equations Worksheet
Watch our free video on how to solve 2 step equations with Distributive Property. This video shows how to solve problems that are on our free solving Equations with Distributive Property worksheet that you can get by submitting your email above.
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This video we’re going to show you some problems from our equations with the two step equations with distributive property worksheet. This video is about learning how to solve two step equations with distributive property. Our first problem on our equations with the distributive property worksheet is 2 times the quantity X minus 1 equals 4. The first step or the first thing you have to do when you have the distributive property is you have to distribute whatever is on the outside of the parenthesis to everything on the inside of the parenthesis. In the case of this problem we have to take 2 times it by X. 2 times X minus and then 2 times 1 and then you bring down your equals 4.
We’ve taken what’s on the outside of the parenthesis which in this case is 2 and multiplied it or distribute it it to everything on the inside of the parenthesis. After you do that you have 2 times X minus 2 times 1 equals 4. Of course 2 times X is 2x and then 2 times 1 is 2. Now our equation is 2x minus 2 equals 4. Now we have to get the variable on one side by itself and constants on the other in order to do that we’re going to add 2 to both sides. That the twos will cancel and then you have 2x on this side of the equation and then 4 plus 2 which is 6. On this side of the equation then the last step is to divide both sides by 2 because the coefficient on 2x is 2 and this is like saying 2 times X the opposite of 2 times X is 2 divided by 2. Now we have X on this side and then 6 divided by 2 on this side which is 3 and that’s our solution. This is a short explanation what is distributive property example.
The second problem on our equations with distributive property worksheet gives us five times the quantity 5x minus 5 equals 50. Once again the first step is to distribute everything on the outside to everything on the inside of the parenthesis. We will do 5 times 5x minus you keep the sign in the middle the same five times five, then you bring down your equals and then you bring down your constant on this side which is 50. Then to simplify you do five times 5x which is 25 X minus five times 5 which is 25 equals 50. Now we have to solve for X. In order to do that we’re going to add 25 here because we have to get rid of all the constants on the same side as . These 25s cancel you bring down your 25 X and then you do 50 plus 25 over here which is 75. Then the last step is to divide by 25 because we have to cancel the coefficient on the X. These guys cancel you’re left with just X on this side and then 75 divided by 25 is 3. The solution to number 2 is x equals 3.
The last problem we’re going to go over on our worksheet for the equations with a distributive property is number 3. Number 3 gives us 20 equals negative 10 times the quantity X plus 8. Once again the first step is to distribute the negative 10 or whatever’s on the outside to everything on the inside and this time you need to be careful because this is a negative 10. You have to distribute a negative 10. You have to include the negative when you distribute. This is like negative 10 times X plus and then negative 10, will write it in parenthesis because it’s negative times 8. Now we have 20 equals negative 10 times X plus negative 10 times 8. When we simplify this negative 10 times X is negative 10 X and then negative 10 times 80 is negative 80. You bring down your equal sign and your constant on the other side. Now we have to get rid of this negative 80 and in order to do that we’re gonna go ahead and add 80 to both sides. This negative 80 and this positive 80 will cancel and then you bring down your negative 10 X and then 20 plus 80 is 100. The final step is to get X by itself. In order to do that we divide both sides by negative 10. These guys will cancel and your have X on this side and then 100 divided by negative 10 is negative 10.
That will do it for our 2 step equations with distributive property worksheet.
Equations with the Distributive Property
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https://www.physicsforums.com/threads/circular-motion-and-centripetal-acceleration.799209/
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1. The problem statement, all variables and given/known data Q.1. Explain the changes in the tension of a piece of string which is being swung vertically with a bucket of water at the end. What would the minimum centripetal acceleration need to be for water to not fall out? 2. Relevant equations ac = v^2/r 3. The attempt at a solution The tension in any vertical path will always be greatest at the bottom as the weight force needs to be overcome as well as providing a net force towards the center which is required for circular motion. The centripetal acceleration would need to be 9.81 m/s^2, therefore, at the top gravity will provide all the centripetal force and no tension is required from the string. From researching the bucket problem online, it seems to be that when the bucket is weightless at the top then the tension at the bottom would be equal to twice the weight of the bucket. However, this assumes uniform circular motion. Can this bucket problem ever be uniform circular motion? Can you ever have water in a bucket having a centripetal acceleration of 9.81 all the time? Surely as it comes down towards the ground the kinetic energy is greater therefore v^2/r cannot be constant?
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https://forum.arduino.cc/t/sensor-to-determine-approximate-location-of-pet-inside/446905
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Hello all and thank you in advance for any assistance.
I am trying to determine if a pet is getting closer or farther from an Arduino Uno. This would be inside the home so the sensor would need to work through walls and objects. The accuracy is not so important as I only need to know if the arduino is getting closer or farther. I was considering a microwave doppler radar, however, it seems to only really determine speed but I may be overlooking something. Otherwise I have considered creating an RF collar for the pet that outputs a pulse and then the UNO would calculate how far between the pulses to determine if it is moving in the right direction. Any suggestions would be extremely appreciated.
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This preview shows pages 1–3. Sign up to view the full content.
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Unformatted text preview: Physics 8A Homework 4 Solutions Fall 2009 Pauli Kehayias (firstname.lastname@example.org) September 27, 2009 1 A Push or a Pull? Part A The Earth exerts a downward force on the book due to the Earths gravity. The book cant exert a force on itself, and for the purposes of this problem, the table doesnt pull down on the book either. The table just pushes up on the book. Part B Gravity is a long-range force. Two masses dont need to be in contact to exert the force of gravity on each other. An example is projectile motion: the Earths gravity pulls projectiles down without touching them. Part C The force with which Earths gravity pulls on objects is called the weight. Part D The table pushes back up on the book. Since the book is at rest and is not accelerating, there must be no net force on it. This means there must be an equal and opposite force pushing back up on the book, which is provided by the table. Gravity can only pull down, so the Earth cant push up on the book. Again, the book cant exert a force on itself. Part E This is a contact force - it occurs only because the book is on the table. If the book were in the air above the table, the table wouldnt exert any force on it. Part F The table exerts a normal force equal and opposite to the weight. Part G The only horizontal forces on the block are the strings tension and tables friction. The problem tells you that a string pulls the block to the right, so the correct answer is the string. Part H This is a contact force - it only works if the string and block are connected. 1 Part I The force that strings or ropes exert is called the tension. Note that strings and ropes can not push objects, they can only pull them. Part J The other horizontal force in this problem is the tables friction on the block. Kinetic friction opposes an objects motion, and static friction opposes the net force (less friction) to keep an object at rest. If the block is moving, kinetic friction pulls it to the left. If the block is stationary, static friction pulls it to the left to balance the tension. In either case, friction acts to the left. Part K Friction is a contact force - its caused by materials rubbing together. Part L Friction (see above). Part M Once the block is let go, it is no longer being pushed to the right. Kinetic friction acts opposite the blocks motion (to the left), eventually bringing it to a stop. This is the only horizontal force, since the weight and the normal forces are vertical and the block is not being pushed any more. Part N Friction. Mastering Physics suggests that The force of friction does not disappear as long as the block is moving. Once the block stops, friction becomes zero (assuming the table is perfectly horizontal). 2 Newtons 1st and 2nd Laws We can think of a frame of reference as a set of coordinates with which an observer can measure distances and locations. For example, one observer can stand at a train station and use a coordinate system withand locations....
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QCD Phase Boundary in the Strong Coupling Regime
The phase boundary of lattice QCD for staggered fermions in the $\mu_B-T$ has been established via a dual representation in the strong coupling limit. Extending this phase boundary towards finite inverse gauge coupling is challenging. We present numerical simulations away from the strong coupling limit, taking into account the $O(\beta^2)$ corrections via plaquette occupation numbers. This allows to study the relation between the nuclear and chiral transition as a function of $\beta$.
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Nonzero Temperature and Density
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https://www.newcivilengineer.com/summer-term-week-three/787565.article
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1. If the roots of the equation 2x 2- px + 8 = 0 are equal, find the value of p.
2. What is the remainder when 2x 3- x + 5 is divided by x + 3?
3. What is the value of a if 27 ?
4. The radius of the circle shown is 8cm and the angle AOB is 120infinity, where O is the centre of the circle.
Calculate the area of the shaded region
5. Find dt given that t = 6z 2+ z - 4 dz 2z Find dt given that t = 6z
Build up question: no 7 Let x = the answer to build up question no. 6 (NCE 6 May)
Find the sum to infinity of the converging series: 1 - A + 1/16 - 1/64 + . . . . . where A = x + 1/4 ?
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Algebraic Analysis of Differential Equations: from Microlocal Analysis to Exponential Asymptotics
T. Aoki, H. Majima, Y. Takei, N. Tose
Springer Science & Business Media, Mar 15, 2009 - Mathematics - 352 pages
This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the conference "Algebraic Analysis of Differential Equations – from Microlocal Analysis to Exponential Asymptotics" at Kyoto University in 2005. This volume is dedicated to Professor Takahiro Kawai, who is one of the creators of microlocal analysis and who introduced the technique of microlocal analysis into exponential asymptotics.
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Applied radiobiology; continuous irradiation mathematical solution online brachytherapy. CD-ROM included. Encyclopedia mathematical solution online Apa citation machine dissertation browser?
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https://www.allinterview.com/company/352/call-centre/interview-questions/308/pos.html
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math
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What is a run unit?
I have a reading off 1.5ohms at my mem my main c/b is rated at 40/6 amps in a domestic house and i was told to change it to a b curve c/b is this ok
what is associativity explain what is the precidence for * and & , * and ++ how the folloing declaration work 1) *&p; 2) *p++;
Explain Active power,reactive power,how its related to each other , & inductive ,capacitive.
How good are you at Finance?
what is degenerate key in oracle ?whare do we use it?
please explain how to do 'pole drop test' on generator?
I HAVE DONE B. SC . (BIO) AFTER THAT I HAVE DONE MBA HR AND NOW MANY INTERVIEWER ASK ME WHY I HAVE HONE MBA IN HR? PLZ ANSWER ME?
what is the necessary of using inductance property in transmission lines even through resistance is used to opposes the high current flows in that?????
please briefly explain calculating or estimating steel quantity for a RCC column?
Human resource management in retailing business
How will you import the idoc in xi? What parameter values will you provide there?
what is the difference between RMS & TRUE RMS VOLTAGE
#define f(g,h) g##h main O int i=0 int var=100 ; print f ("%d"f(var,10));} wat would be the output??
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https://digitalcommons.andrews.edu/math-pubs/9/
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math
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Mathematicians' Views on Transition-to-Proof and Advanced Mathematics Courses
This study explores mathematicians’ views on 1) knowledge and skills students need in order to succeed in subsequent mathematics courses, 2) content courses as transition-to-proof courses, and 3) differences in the proving process across mathematical content areas. Seven mathematicians from three different universities (varying in geographic location and department size), were interviewed. Precision, sense-making, flexibility, definition use, reading and validating proofs, and proof techniques are skills that the mathematicians stated were necessary to be successful in advanced mathematics courses. The participants agreed unanimously that a content course could be used as a transition-to-proof course under certain conditions. They also noted differences in the proving processes between abstract algebra and real analysis. Results from this study will be used to frame a larger study investigating students’ proof processes in their subsequent mathematics content courses and investigating how these skills can be incorporated into a transition-to-proof course.
Proceedings of the 17th Annual Conference on Research in Undergraduate Mathematics Education
Moore, Robert C., "Mathematicians' Views on Transition-to-Proof and Advanced Mathematics Courses" (2014). Faculty Publications. 9.
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https://www.nagwa.com/en/worksheets/767178464710/
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math
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Matthew started with 12 stars in three groups of four.
Remove one group at a time. Find the missing numbers.
Students go to school for 4 days a week. Given that school vacations will start in eight weeks, how many school days are left before the vacation starts?
Multiplying by 4. Find the missing numbers.
HINT: Use the array to help you.
If a zebra has 4 legs, how many legs do 2, 3, and 4 zebras have?
In the forest, there are 8 fairies. There are 4 times as many pixies as fairies. What calculation should we do to find the number of pixies?
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http://teachers.henrico.k12.va.us/math/hcpsalgebra1/module2-2.html
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math
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Algebra 1 Online!
Henrico County Public Schools, Virginia
Module - Positive and Negative Numbers
Lesson 2 - Adding and Subtracting Rational Numbers
Adding and Subtracting Integers
Adding and Subtracting Rational Numbers
Multiplying Rational Numbers
Dividing Rational Numbers
Common Core Standards
ExamView Quiz: Adding and Subtracting Integers
Warm-up: Adding & Subtracting Integers (doc)
Notes: Adding, Subtracting and Comparing Rational Numbers (ppt)
Activity: Adding Rational Numbers (gsp)
Activity: Subtracting Rational Numbers (gsp)
Video: PH Ordering Fractions
Video: PH Adding Rationals to Solve Problems
Interactive Notes: Adding and Subtracting Fractions
- notes and workout problems at
Game: Fraction Four!
- Connect Four game involving fractions at
Comparing and Ordering Rational Numbers (doc)
Worksheet: Comparing Rational Numbers (doc)
Application: Stock Market (doc)
Glencoe PWS Compare Rational Numbers (pdf)
Glencoe SG Compare Rational Numbers (pdf)
Glencoe PWS Add/Subtract Rational Numbers (pdf)
Glencoe SG Add/Subtract Rational Numbers (pdf)
Write a problem involving a real-life situation in which rational numbers are either added or subtracted. When finished, solve your problem.
What do you like for a teacher to do in math class? How can a math teacher be helpful?
ExamView Quiz: Adding and Subtracting Rational Numbers
Prentice Hall Quiz
Prentice Hall Quiz #2
Send comments or materials to Skip Tyler, Secondary Math Specialist
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https://www.degruyter.com/view/journals/ans/14/3/article-p565.xml
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math
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We study a nonlinear parametric elliptic equation (nonlinear eigenvalue problem) driven by a nonhomogeneous differential operator. Our setting incorporates equations driven by the p-Laplacian, the (p, q)-Laplacian, and the generalized p-mean curvature differential operator. Applying variational methods we show that for λ > 0 (the parameter) sufficiently large the problem has at least three nontrivial smooth solutions whereby one is positive, one is negative and the last one has changing sign (nodal). In the particular case of (p, 2)-equations, using Morse theory, we produce another nodal solution for a total of four nontrivial smooth solutions.
Advanced Nonlinear Studies (ANS) is aimed at publishing scholarly articles on nonlinear problems, particularly those involving Differential and Integral Equations, Dynamical Systems, Calculus of Variations, and related areas. It will also publish novel and interesting applications of these areas to problems in biology, engineering, materials sciences, physics and other sciences.
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http://forum.arduino.cc/index.php?topic=146034.msg1101015
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math
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Does this make sense?
I cannot have the nrf24's go through the air,
it must be through the guitar cable. (will have no interference if I turn and am between the two nrf24s,
not having a 4 inch antenna sticking out of my guitar
So, my main question: will a very very low voltage AC signal hurt the nrf24s?
I would assume not, since it is well below its operating voltage (even if its AC).
I basically wanted a >1ghz fm communication line ............. and would work over the guitar cable rather than through the air.
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https://www.thestudentroom.co.uk/showthread.php?t=3967129
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math
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Thinking about doing ME at Plymouth. What's the course and teaching like? Are the teachers helpful and involved?
What are the other students like? Are they really interested in the subject and enthusiastic? Do they help each other?
How does the sandwich year placement work? Do people often get final year sponsorships from the company? How is graduate employment? Is the Plym engineering degree well-regarded?
Sorry about all the questions!
Find all the answers here
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| 467
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https://www.wherecanwego.com/feedback.aspx?tab=2
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math
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Britain's What's On Event Guide
Feedback from our Organisers
Refresh this page to see more feedback
What a great idea this is.
- Jill, St James the Less, Pangbourne
Yours in the user-friendliest site I've come across.
- John, Llanfyllin Dolydd Building Preservation Trust
You have been brilliant,
- Diana, Hop Gallery
We had an extremely successful Preston Open Gardens Day, much thanks to your website.
Can I say how easy I find your listings site to use - many thanks!
- Rosemary, East London Chorus
Many thanks, as a not-for-private-profit group we hugely appreciate the free publicity.
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Many thanks for your help.
- George, Westonbirt Charities Fair
I often refer to your site for information about what's on and long may it continue!!
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Your site is great, packed with all sorts of things.
- Angus, Choir 2000
Thank you for the wonderful service you provide.
- Doris, Newcastle Male Choirs
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https://groups.yahoo.com/neo/groups/new_ai_geostats/conversations/topics/1569?o=1&d=-1
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math
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AI-GEOSTATS: about spatial regression
- Dear ALL:
From the literature of spatial regression, I found "geographically weighted regeression" and "
spatial regression model(such as SAR, CAR)"
I am confused what different between these two concepts
Are they sloving the same problems, Or they are not totally different issues?
[Non-text portions of this message have been removed]
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https://www.physicsforums.com/threads/perpendicular-relativistic-velocities.884215/
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math
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1. The problem statement, all variables and given/known data Imagine two motorcycle gang leaders racing at relativistic speeds along perpendicular paths from the local pool hall, as shown in Figure 1.21. How fast does pack leader Beta recede over Alpha’s right shoulder as seen by Alpha? Solution Figure 1.21 shows the situation as seen by a stationary police officer located in frame S, who observes the following: 2. Relevant equations u'_x = (u_x - v)/(1 - v*u_x/c^2) u'_y = u_y/γ*(1 - v*u_x/c^2) 3. The attempt at a solution I can follow the solution shown in the attachment. The problem is that I'm trying to verify the solution by attaching the s' frame of reference to the beta gang leader instead of the alpha gang leader. The relative speed of alpha to beta should be the same as the relative speed of beta to alpha, but that's not what im getting. Can you guys tell me what im doing wrong?
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https://urbanbreathnyc.com/which-expression-represents-a-reaction-rate/
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math
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During the course of the reaction shown below, reactants A and B are consumed while the concentration of product ab increases. The reaction rate can be determined by measure up how fast the concentration that A or B decreases, or by how rapid the concentration of ab increases.
You are watching: Which expression represents a reaction rate?
\< \ A + B \longrightarrow ab \>
For the stochiometrically complex Reaction:
\< aA + bB \longrightarrow cC + dD \label1 \>
\< \textRate = \dfrac-1a\dfracddt = \dfrac-1b \dfracddt = \dfrac1c\dfracd
Looking at figure \(\PageIndex1\) above, we can see that the rate deserve to be measure up in regards to either reactant (A or B) or one of two people product (C or D). Not all variables are necessary to resolve for the rate. Therefore, if you have actually the worth for "A" as well as the value for "a" you can solve for the reaction rate.
You can also notification from Equation \ref1 that the change in reactants end the change in time must have a negative sign in front of them. The factor for this is since the reactants are decreasing as a role of time, the rate would come out to be an adverse (because it is the turning back rate). Therefore, placing a an adverse sign in front of the variable will permit for the solution to it is in a positive rate.
urbanbreathnyc.comical reaction vary considerably in the speed at which they occur. Some room ultrafast, if others might take millions of years to reach equilibrium.
Definition the Reaction Rate
The Reaction Rate because that a offered urbanbreathnyc.comical reaction is the measure up of the readjust in concentration the the reaction or the change in concentration the the products per unit time. The speed of a urbanbreathnyc.comical reaction may be characterized as the adjust in concentration that a substance separated by the time interval during which this readjust is observed:
\< \textrate=\dfrac\Delta \textconcentration\Delta \texttime \label2-1\>
For a reaction that the type \(A + B \rightarrow C\), the rate can be to express in regards to the change in concentration of any of that is components
\<\textrate=-\dfrac\Delta \Delta t\>
\<\textrate=-\dfrac\Delta \Delta t\>
in i beg your pardon \(Δ\) is the difference between the concentration the \(A\) over the moment interval \(t_2 – t_1\):
Notice the minus indicators in the very first two instances above. The concentration the a reactant constantly decreases v time, for this reason \(\Delta \) and \(\Delta \) space both negative. Since negative rates perform not make much sense, rates expressed in regards to a reactant concentration room always preceded by a minus sign to make the price come out positive.
Consider now a reaction in i m sorry the coefficients are different:
It is clear that \(\) decreases 3 times as promptly as \(\), therefore in bespeak to protect against ambiguity as soon as expressing the price in state of various components, it is customary to divide each change in concentration by the proper coefficient:
\<\textrate= -\dfrac\Delta \Delta t = -\dfrac\Delta 3\Delta t = \dfrac\Delta
Example \(\PageIndex1\): Oxidation the Ammonia
Most reactions slow down together the reactants are consumed. Consequently, the rates offered by the expressions shown over tend to lose their definition when measure up over much longer time intervals Δt. Note: Instantaneous rates are additionally known together differential rates.
See more: Kawaikereba Hentai Demo Suki Ni Natte Kuremasu Ka? Wiki Hensuki Wiki
Thus for the reaction whose progress is plotted here, the actual price (as measured by the enhancing concentration that product) different continuously, being biggest at time zero. The instantaneous rate of a reaction is given by the steep of a tangent come the concentration-vs.-time curve.
An instantaneous rate taken close to the start of the reaction (t = 0) is known as one initial rate (label (1) here). As we shall quickly see, initial prices play crucial role in the examine of reaction kinetics. If you have actually studied differential calculus, friend will understand that this tangent slopes are derivatives whose worths can really at each allude on the curve, so the these instantaneous prices are really limiting rates defined as
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https://mikesmathpage.wordpress.com/2014/09/06/
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math
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I started in on a geometry course with my older son this week. On Wednesday we were discussing some basic shapes and he asked a neat question: If you have a circle in a plane, are there more lines in the plane passing through the circle or more lines in the plane that don’t pass through the circle? Fun!
I told him that the answer to the question was a little more complicated than it seems, but we’d talk through it over the weekend. Well, the weekend is here and we talked through it this morning!
We started by introducing the question and talking about some of the non-intuitive properties of infinity. I thought the easiest place to start would be comparing the set of positive integers with the set of positive even integers since this comparison is a nice way to show that infinite sets are a little strange! I think that kids can understand some of the basic ideas about infinite sets, even if some of the concepts my be a little over their heads:
Next we moved on to a slightly more difficult question – comparing the set of positive integers with the set of positive integers that are powers of 2. In this case it looks like the second set is much smaller than the first one, and finding a way to see that these two sets have the same size did prove to be a challenge. However, with a little nudge, they were able to find a way to map the two sets to each other and even sort of answer the question “what is the opposite of powers?”
Probably the next natural step would be to show that the rational numbers are also countable, but I decided to skip that proof because I was worried that it would be more of a distraction and wouldn’t help so much with the question about lines and circles. Instead the next thing we talked about was comparing the real numbers to the integers via Cantor’s diagonal argument. This argument shows that there are more real numbers than integers. Although I didn’t necessarily want to focus on the different infinities, I thought it was important to help them understand the idea that just because two sets are infinite, they may not be the same size. In retrospect, I wish I wouldn’t have called this the “next infinity,” I guess we’ll have to correct that little slip the next time we talk about infinity.
With all of this background behind us, we moved on to answering the original question about lines and circles. We began by looking at a problem that is a little easier – what happens if we look only at vertical lines? Restricting our attention to this slightly easier problem allows us to see a surprising result – the number of points between 0 and 1 is the same as the number of points between 1 and infinity!
Now with the discussion of the vertical lines out of the way we can solve the general problem if we can figure out how to deal with lines that aren’t vertical. As luck would have it my older son thought looking at horizontal lines would be a good way to start. That idea got the boys thinking about rotational symmetry and led them to the solution to the original problem! Unfortunately I got confused on one of the pictures, but hopefully that 30s of confusion didn’t cause too much confusion – the perils of illustrating some of these ideas early on Saturday morning!
This was a really enjoyable project and the boys seemed to have a lot of fun and stayed engaged all the way through. I’m extra happy that this project came from a question that my son asked earlier this week. It is nice to talk about some of these ideas from pure math every now and then. It helps show younger kids that math isn’t just about playing around with numbers.
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https://dictionary.obspm.fr/index.php/?showAll=1&formSearchTextfield=analysis
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math
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1) General: The separation of an intellectual or material whole into its
constituent parts for individual study. The study of such constituent
parts and their interrelationships in making up a whole
(opposite of → synthesis).
From M.L. analysis, from Gk. analysis "a breaking up," from analyein "unloose," from ana- "up, throughout" + lysis "a loosening," from lyein "to loosen, release, untie". The L. cognate and counterpart of this Gk. word, i.e. luere has formed the words solve, dissolve, solution. The Skt. cognate lu, lunoti "to cut, sever, mow, pluck, tear asunder, destroy," lava "cutting, plucking; what is cut; fragment, piece;" PIE *leu- "to loosen, divide, cut apart". The Eng. lose, loose and Ger. los derive from this root.
Ânâlas, from ânâ-, → ana-, +
las "loose" ([Mo'in], Gilaki, Tabari, Tâleši, Aftari). We do not
know the Av./O.Pers. counterparts of these Gk. las, lysis, lyein,
believe that las and the following words probably derive from
the above-mentioned PIE *leu-:
ânâlas-e dadehâ, ânâkâvi-ye ~
Fr.: analyse de données
The evaluation of reduced data; → data reduction.
ânâlas-e vâmuni, ânâkâvi-ye ~
Fr.: analyse dimensionnelle
A technique used in physics based on the fact that the various terms in a
physical equation must have identical → dimensional formulae
if the equation is to be true for all consistent systems of unit. Its main uses are:
Fr.: analyse de Fourier
The process of decomposing any function of time or space into a sum of sinusoidal functions using the → Fourier series and → Fourier transforms. In other words, any data analysis procedure that describes or measures the fluctuations in a time series by comparing them with sinusoids. Fourier analysis is an essential component of much of modern applied and pure mathematics. It forms an exceptionally powerful analytical tool for solving various problems in many areas of mathematics, physics, engineering, biology, finance, etc. and has opened up new realms of knowledge.
After the French mathematician Baron Jean Baptiste Joseph Fourier (1768-1830), whose work had a tremendous impact on the physical applications of mathematics; → analysis.
Fr.: analyse numérique
The study of methods for approximation of solutions of various classes of mathematical problems including error analysis.
Fr.: analyse optique
The mathematical evaluation of an optical system to determine its basic optical properties and image quality characteristics.
Fr.: analyse quantitative
The analysis of a chemical sample to derive its precise percentage composition in terms of elements, radicals, or compounds.
Fr.: analyse de régression
A statistical technique used to determine the values of parameters for a function that best fits a given set of data.
Fr.: analyse statistique
The process of collecting, manipulating, analyzing, and interpreting quantitative data to uncover underlying causes, patterns, and relationships between variables.
Fr.: analyse tensorielle
A method of calculation in higher mathematics based on the properties of tensors.
Fr.: analyse vectorielle
Fr.: analyse de forme d'onde
The resolution of a complex waveform into a sum of simple periodic waves, usually by computer means.
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https://www.economicsdiscussion.net/duopoly/4-types-of-duopoly-models-with-diagram/7364
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math
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The uncertainty is respect of behaviour pattern of a firm under oligopoly arising our of their unpredictable action and reaction makes a systematic analysis of oligopoly difficult.
However, classical and modern economists have developed a variety of models based on different behavior assumptions.
These models can broadly be classified into two categories (I) classical duopoly models and modern oligopoly Duopoly Models, when there are only two sellers a product, there, exists duopoly.
Duopoly is a special case of oligopoly. Duopoly is a special case in the sense that it is limiting case of oligopoly as there must be at least two sellers to make the market oligopolistic in nature.
1. The Cournot’s Duopoly Model
2. The Chamberlin Duopoly Model
3. The Bertrand’s Duopoly Model
4. The Edgeworth Duopoly Model
1. Cournot’s Duopoly Model:
Augustin Cournot, a French economist, was the first to develop a formal duopoly model in 1838.
To illustrate his model, Cournot assumed:
(a) Tow firms, each owing an artesian mineral water well;
(b) Both operate their wells at zero marginal cost2;
(c) Both face a demand curve with constant negative slope;
(d) Each seller acts on the assumption that his competitor will not react to his decision to change his and price. This is Cournot’s behavioural assumption.
On the basis of this model, Cournot has concluded that each seller ultimately supplies one-third of the market and charges the same price. While one-third of the market remains unsupplied.
Cournot’s duopoly model is presented in Fig. 1. To begin the analysis, suppose that there are only two firms. A and B, and that, initially. A is the only seller of mineral water in the market. In order to maximize his profits (or revenue), he sells quantity OQ where his MC = O MR, at price OP2 His total profit is OP2PQ.
Now let B enters the market. The market open to him is QM which is half of the total market. He can sell his product in the remaining half of the market. He assumes that A will not change his price and output as he is making the maximum profit i.e., A will continue to sell OQ at price OP2 Thus, the market available to B is QM and the demand curve is PM.
When to get maximize revenue, B sells ON at price OP1, His total revenue is maximum at QRP’N. Note that B supplies only QN = 1/4 = (l/2)/2 of the market.) With the entry of B, price falls to OP1 Therefore, A’s expected profit falls to OP1 PQ Faced with this situation, A attempts to adjust his price and output to the changed conditions. He assumes that B will not change his output QN and price OP1 as he is making maximum profit.
Accordingly, A assumes that B will continue to supply 1/4 of market and he has 3/4 (= 1 – 14) of the market available to him. To maximise his profit. Supplies 1/2 of (3/4), i.e., 3/8 of the market. Note that A’s market share has fallen from 1/2 to 3/8.
Now it is B’s turn to react. Considering Cournot’s assumption, B assumes that A will continue to supply only 3/8 of the market and market open to him equals 1 – 3/8 = 5/8.
In order to maximise his profit under the new conditions B supplies 1/2 x 5/8 = 5/16 of the market. It is now for A to reappraise the situation and adjust his price and output accordingly.
This process of action and reaction continues in successive periods. In the process, A continues to lose his market share and B continues to gain. Finally situation is reached when their market shares equal at 1/3 each.
Any further attempt to adjust output produces the same result. The firms, therefore, reach their equilibrium position where each one supplies one-third of the market.
The equilibrium of firms, according to Cournot’s model, has been presented in table below:
Cournot’s equilibrium solution is stable. For given the action and reaction, it is not possible for any of the two sellers to increase their market share.
It can be shown as follows:
A’s share= 1/2(1 – 1/3) = 1/3.
Similarly B’s share = 1/2 (1 – 1/3) = 1/3.
Cournot’s model of duopoly can be extended to the general oligopoly. For example, if there are three sellers, the industry, and firms will be in equilibrium when each firm supplies 1/3 of the market. Thus, the three sellers together supply 3/4 of the market, 1/4 of the market remaining unsupplied. The formula for determining the share of each seller in an oligopolistic market is: Q -f- (n + 1), where Q = market size, and n = number of sellers.
Criticism of the Model:
Although ournot’s model yields a stable equilibrium, it has been criticised on the following grounds:
(1) Curnot’s behavioural assumption [assumption (d) above] is naive to the extent that it implies that firms continue to make wrong calculations about the competitor’s behaviour. Each seller continues to assume that his rival will not change his output even though he reportedly observes that his revel firm does change its output.
(2) The assumption of zero cost of production is totally unrealistic. If this assumption is dropped, it does not alter his position.
2. Chamberlin’s Duopoly Model- A Small Group Model:
Chamberlin’s model of duopoly recognizes interdependence if firms in such a market. Chamberlin argues that in the real world of oligopoly firms are not so native that they will not learn from the past experience. However, he makes the same assumptions as the exponents of old classical models have done. In other words, his model is also based on the assumption of homogeneous products, firms of equal size with identical costs, no entry by new firms and full knowledge of demand.
Recognition of interdependence of firms in an oligopolistic market given us a result quite different from that of Cournot. Chambrilin argues that firms are aware of the fact that their output or price decision will definitely invite reactions of other firms. Therefore, he goes not visualize any price war in oligopolistic markets. He also rules out the possibility of firms adjusting their outputs over a period of time and thus reaching the equilibrium at an output level lower than that would be reached under monopoly.
According to Chamberlin, recognition of possible sharp reactions to an oligopolistic firm’s price or output manipulations would avert harmful competition amongst the firms in such a market and would result in a stable industry equilibrium with the monopoly price and monopoly output. He further stated that no collusion is required for obtained this solution.
In case farms in an oligopolistic market are aware of their mutual dependence, and willing to learn from their past experience, then in order to maximize their individual and joint profits they will charge the monopoly price.
Chamberlin’s model can be explained in the frame work of a dupoly market. Chamberlin, like Cournot, assumes linear demand for the product. For simplicity we assume that even in this case the cost of producing the good is zero.
Chamberlin model has been illustrated in Figure 2. In this figure DQ is the market demand curve. If firm A is first to enter the market, it will produce output OQ1 because at this level of output its marginal revenue is equal to marginal cost (MR = MC = 0). The firm can charge price OP1 which is the monopoly price.
This will maximise its profits. At price OP) elasticity of demand is unity. Firm B entering market at this stage considers that its demand curve is CQ and will thus produce Q1Q2 so as to maximise its profit. It will charge price OP2.
It now realizes that it cannot sell QQ1 quantity at the monopoly price and thus decides to reduce the output to QQ3, which is one-half of the monopoly output QQ1. Firm B can continue to produce quantity Q1Q2 which is same as Q3Q1.
The industry output thus is OQ1 and the price rises to the level OP1. This is an ideal situation from the point of view of both firms A and B. In this case, the joint output of the two firms is monopoly output and they charge monopoly price. Thus, considering the assumption of equal costs (costs = 0) the market will be shared equally between firms A and B.
Appraisal of the Model:
Chamberlin’s model is certainly more realistic than earlier models. It assumes that firms recognize interdependence and then act in a manner that monopoly solution is reached. In the real world of oligopoly there are certain difficulties in reaching this solution. In the absence of collusion, firms must have a good knowledge of market demand curve which is almost impossible to obtain. In case this information is lacking, firms will not know how to reach monopoly solution.
Further, Chamberlin ignores entry. In real practice, oligoplistic markets are rarely closed. So if we recognize the fact of entry, it would not be certain that the stable monopoly solution will ever be reached. Differences in costs and market opportunities are also hindrance for attaining a monopoly-type outcome by the independent actions of firms in oligopolies.
3. Bertrand’s Duopoly Model:
Bertrand, a French Mathematician developed his own model of duopoly in 1883. Bertrand’s model differs from Cournot’s model in respect of its behavioural assumption. While under Cournot’s model, each seller assumes his rival’s output to remain constant, under Bertrand’s model each seller determines his price on the assumption that his rival’s price, rather than his output, remains constant.
Bertrand’s model focuses on price competition. His analytical tools are reaction function of the duopolists. Reaction functions are derived on the basis of iso-profit curves. An iso-profit curve, for a give level of profit, is drawn on the basis of various combinations of prices charged by the rival firms. He assumed only two firms, A and B and their prices are measured along the horizontal and vertical axes, respectively.
Their iso-profit curves are drawn on the basis of the prices of the two firms. Iso-profit curves of the two firms are concave to their respective prices axis, as shown in Fig. 3 and 4. Iso- profit curves of firm A are convex to its price axis PA (Fig. 3) and those of firm B are convex to PB (Fig. 4).
In Figure 4, we have curve A, which shows that A can earn a given profit from the various combinations of its own and its rival’s price. For example, price combinations at points, a, b and c yield the same level of profit indicated by the iso-profit curve A1. If firms B fixes its prices Pb1– firm A has two alternative prices, Pa1 and Pa2, to make the same level of profits.
When B reduces its price, A may either raise its price or reduce it. A will reduce its price when he is at point c and raise its price when he is at point a. But there is a limit to which this price adjustment is possible. This point is shown by point b. So there is a unique price for A to maximize its profits. This unique price lies at the lowest point of iso-profit curve.
The same analysis applies to all other iso-profit curves, A1 A2 and A3 we get A’s reaction curve. Note that A’s reaction curve has a rightward slant. This is so because, iso-profit curve tends to shift rightward when A gains market from his rival B.
Following the same process, B’s reaction curve may be drawn as shown in Fig. 4.
The equilibrium of duopolists suggested by Bertrand’s model may be obtained by putting together the reaction curves of the firms A and B as shown in Fig. 5.
The reaction curves of A and B intersect at point E where their expectations materialize, point E is therefore equilibrium point. This equilibrium is stable. Fo, if any one of the firms disagrees to this point, it will create a series of actions and reactions between the firms which will lead them back to point E.
Criticism of the Model:
Bertrand’s model has been criticised on the same grounds as Cournot’s model. Bert- rand’s implicit behavioural assumption that firms never learn from their past experience seems to be unrealistic. If cost is assumed to be zero, price will fluctuate between zero and the upper limit of the price, instead of stabilizing at a point.
4. Edgeworth’s Duopoly Model:
Edgeworth developed his model of duopoly in 1897. Edgeworth’s model follows Bertrand’s assumption that each seller assumes his rival’s price, instead of his output, to remain constant.
His model is illustrated in Fig. 6.
In this figure we have supposed that there are two sellers, A and B, in the market who face identical demand curves. A has his demand curve DDB and as DDB Let us also assume that seller A has a maximum capacity of output OM and B has a maximum output capacity of OM’. The ordinate ODA measures the price.
To explain Edgeworth’s model, let us assume, to begin with, that A is the only seller in the market. Following the profit maximising rule of a monopoly seller, he sells OQ and charges a price, OP2. His monopoly profit under zero cost, equals OP2EQ Now, let B enter the market. B assumes that A will not change his price since he is making maximum profit. He sets his price slightly below A’s price (OP2) and is able to sell his total output. At this price, he captures a substantial part of A’s market.
Seller A, on the other hand, that his sales have gone down. In order to regain his market, A sets his price slightly below B’s price. This leads to price-war between the sellers.
The price- war takes the form of price-cutting which continues until price reaches OP1 At this price both A and B are able to sell their entire output- A sells OQ and B sells OQ The price OP1 could therefore be expected to be stable. But, according to Edgeworth, price OP1 should not be stable.
Simple reason is that, once price OP is set in the market, the sellers observe an interesting fact. This is, each seller realise that his rival is selling his entire output and he will therefore not change his price, and each seller thinks that he can raise his price to OP2 and can make pure profit.
This realisation forms the basis of their action and reaction. For examples, let seller A take the initiative and raise his price to OP2. Assuming A to retain his price OP2.B finds that if he raises his price at a level slightly below OP2 he can sell his entire output at a higher price and make greater profit. Therefore, B raises his price according to his plan.
Now it is A’s turn to know the situation and react. A finds that his price is higher than B’s price and his total sale has fallen. Therefore assuming B to retain his price, A reduces his price slightly below B’s price.
Thus, the price-war between A and B begins once again. This process continues indefinitely and price keeps moving up and down between OP1 and OP2 Obviously, according to Edgeworth’s model of duopoly, equilibrium is unstable and indeterminate since price and output are never determined. In the words form Edgeworth, “there will be an indeterminate tract through which the index of value will oscillate, or, rather will vibrate irregularly for an indefinite length of time.
In a net shell Edgeworth’s model, like Cournot’s is based on a native assumption, i.e. each seller continues to assume that his rival will never change his price even though they are proved repeatedly wrong. But according to Hotelling Edgeworth’s model is definitely an improvement upon Cournot’s model in that it assumes price, rather than output, to be the relevant decision variable for the sellers.
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http://wittyassess.com/math-aptitude-test-online/
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math
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CC-MAIN-2023-14
| 5,212
| 7
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https://www.coursehero.com/file/10804322/Math-for-Econ-II-Homework-8/
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math
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Unformatted text preview: (c) Are the answers to parts (a) and (b) the same? Explain.
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Math for Econ II, Written Assignment 8 (28 points)
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(a)(x) dx(x) dx
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between x = 2 and x = 1.
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5-2h31 5-4h44figa 5-4h45 5-4h46 x
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h is largest. Which is smallest? How many of the num1
bers 3 positive?
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average value of f (x) the area [0, ] the curve
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x 0.5 to 1.
(b) Compute this average.
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statistics, which is given by
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various values of b. R For Problems ??, assuming F = f , mark the quantity on a 1 to x = 1: x
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using M4 (midpoint sum with 4 rectangles) to approximate
(The actual value of ln(5) is 1.6094 . . .. For fun, plug your approximation into a calculator and compare) 7. (4 pts) Use the Evaluation Theorem to show 6000
and the supply curve is given by P = Q + 10. Find
Q + 50
the equilibrium price and quantity, and compute the consumer and producer surplus. 8. (5 pts) Suppose the demand curve is given by P = Some extra practice (not to be handed in)
f (x) dx using R5 and L5 . −2 −1 1 2 3 −5 −4 −3 −2 −3 −1 1 2 3 4 5 2 2. Suppose h is a function such that h(1) = 2, h0 (1) = 3, h00 (1) = 4, h(2) = 6, h0 (2) = 5, h00 (2) = 13, and h00 is
continuous everywhere. Find 1 h00 (u) du. ...
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https://tnjobs.co.in/2020/04/23/averages/
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math
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Average Problem for Exams
1. There are two sections A and B of a class, consisting of 36 and 44 students respectively. If the average weight of section A is 40kg and that of section B is 35kg, find the average weight of the whole class.
Total weight of (36+44) Students=(36×40+44×35)kg=2980kg Therefore average weight of the whole class= (2980/80) kg Therefore average weight=37.25kg.
2. Distance between two stations A and B is 778km. A train covers the journey from A to B at 84km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of train during the whole journey.
Solution: required average speed = (2xy/x+y) km/hr
= (2x84x56/84+56) km/hr = (2x84x56/140) km/hr = 67.2km/hr. (M.A.T.2003) 3. A Batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.
3.There were 35 students in a hostel. Due to the admission of 7 new students the expenses of the mess were increased by Rs.42 per day while the average expenditure per head diminished by Re 1. What was the original expenditure of the mess?
Solution: let the original average expenditure be Rs.x. then,
Therefore original expenditure =Rs.(35 x12)=Rs.420.
4.Nine persons went to a hotel for taking their meals. Eight of them spent Rs.12 each on their meals and the ninth spent Rs.8 more then the average expenditure of all the nine. What was the total money spent by them.
Let the average expenditure of all the nine be RS.X Then, 12×8+(X+8)=9X Therefore X=13.
Total money spent =9X=RS.(9 x 13)=Rs.117
5.David obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, mathematics, physics, chemistry and biology. What are his average marks?
Solution: Average= (76+65+82+67+85)/5 =375/5=75 Hence average=75.
6.Find the average of all numbers between 6 and 34 which
are divisible by 5.
Solution: Average= (10+15+20+25+30)/5=100/5=20 Hence average=20.
7. A student was asked to find the arithmetic mean of the numbers
3,11,7,9,15,13,8,19,17,21,14 and x. He found the mean to be 12. What should be the number in place of x?
8. The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is?
Solution: excluded number = (27×5)-(25×4) =135-100 =35.
9. The average of runs of a cricket player of 10 innings was 32. How many runes must be make in his next innings so as to increase his average of runs by 4?
Average after 11 innings=36
Required number of runs = ( 36×11) – (32×10) =396-320 =76.
10. The average weight of A, B and C is 45kg. If the weight of A and B be 40kg and that of B and C is 43kg, then the weight of B is.
Let A,B,C represent their respective weights. Then, we have
Adding (ii) and (iii) we get: A+2B+C=166 (iv)
Subtracting (i) from (iv) we get B=31
Therefore B’s weight =31kg
11.The average monthly income of P and Q is Rs.5050. the average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs.5200. the monthly income of P.
Solution: let P, Q and R represent their respective monthly incomes. Then, we have
Adding (i),(ii) and (iii), we get:2(P+Q+R)=33000 (iv)
Subtracting (ii) from (iv) we get p=4000
Therefore p’s monthly income =Rs.4000
12. The average age of 36 students in a group is 14 years. When teacher’s age is included to it, the average increases by one. What is the teacher’s age in years.
Solution: age of teacher = (37×15-36×14)years
= 51 years.
13. The average monthly salary of 20 employees in an organizations is Rs.1500. if the manager’s salary is added, the average salary increases by 100. What is the manager’s monthly salary.
Solution: manager’s monthly salary = Rs. (1600×21-1500×20)
14. The average weight of 8 persons increases by 2.5kg when a new person comes in place of one of them weighing 65kg. What might be the weight of the new person?
Solution: total weight increased= (8×2.5) kg=20kg
Weight of new person= (65+20)kg=85kg
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CC-MAIN-2020-45
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http://www.lowcostcrushersell.us/mineral/9841/weight-of-steel-per-cubic-meter.html
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math
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weight of steel per cubic meter
How to Calculate the Weight of Steel , This will give you the mass in grams of the object 785 grams per cubic centimeter is the average density of steel
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These weight calculations are based upon the theoretical weight of steel at 4080 pounds per square , Formulas & Data SHAPE WEIGHT , Liters x 61023 = Cubic .
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The Weight of Timber Frame; The , the heaviest at 600 kg per cubic metre, , but ignoring the heavier weight needed for concrete or steel lintels Thus the weight .
lb/ft3 kilogram per cubic meter (kg/m3) , Wt/C = Weight per 100 Metric Symbols , Reference Data Schedule 40 Steel Pipe Data
, Weight in kg per meter 07834 kg/cm² per meter or (cft) cubic foot of steel=490 lbs , The One-Stop Source for Metric & British Sized Fasteners .
metalplatesource : weight of steel plate , weight per cubic foot: weight per cubic inch: weight per foot for 1 inch x 1 inch bar: steel: 490 lb / cu ft: 028356 lb .
COMPUTING STRUCTURAL STEEL WEIGHT (MASS) , assumptions as to density - kilograms per cubic meter (pounds per cubic foot): Steel 490 lb/ft3 (7850 kg/m3)
The metal weighs 02904 pounds per cubic inch Steel weight formulas are based on theoretical nominal weights and only give approximate valu Continue Reading
Carbon Fiber v Titanium Steel , weight by cubic meter = 13785 ounces = 390 , up to around $100,000 Aus per tonne for high grade alloys (cubic meter = 4506 .
Handbook of STEEL SIZES & WEIGHTS , Acme • Coil Rod • Stainless • Metric Grade: , Weights of Other Materials in Pounds Per *Cubic Foot SIMPLE STEEL WEIGHT .
how must steel will use for 1 cubic meterformula of steel for beam,column , Generally we are consider 100kgs steel per cum of , weight of steel required .
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David Houle Department of Biological Science, Florida State University, Tallahassee, FL 32306–1100, USA. Tel.: +1 850 645 0388; fax: +1 850 644 9829; e-mail: email@example.com
The relationship between developmental stability and morphological asymmetry is derived under the standard view that structures on each side of an individual develop independently and are normally distributed. I use developmental variance of sizes of parts, VD, as the converse of developmental stability, and assume that VD follows a gamma distribution. Repeatability of asymmetry, a measure of how informative asymmetry is about VD, is quite insensitive to the variance in VD, for example only reaching 20% when the coefficient of variation of VD is 100%. The coefficient of variation of asymmetry, CVFA, also increases very slowly with increasing population variation in VD. CVFA values from empirical data are sometimes over 100%, implying that developmental stability is sometimes more variable than any previously studied type of trait. This result suggests that alternatives to this model may be needed.
There has been considerable speculation about the degree of variation among individuals in their developmental stability, their ability predictably to complete development to an optimum state ( Palmer, 1996; Møller & Swaddle, 1997). The principal hurdle to empirical studies of developmental stability is that, in most cases, we do not know what the optimum state of a trait is, so we cannot say how much of the variation is due to variation in the optimum and how much to a failure to develop to that optimum. When the same structure develops on either side of a symmetrical body however, we can assume that the optimum state is often one of perfect symmetry. Where this symmetry of the optimum can be assumed, asymmetry is referred to as fluctuating asymmetry (FA) ( Palmer & Strobeck, 1986; Palmer, 1994). A large body of work now assumes that FA is a good indicator of developmental stability ( Møller & Swaddle, 1997).
Surprisingly, given these attractions of FA as an indicator of developmental stability, the precise relationship between the two has never been addressed analytically. Previous studies have, with few exceptions, relied on the negative relationship between FA and developmental stability that exists by definition. There are several barriers to studying this relationship. First, developmental stability is currently a hypothetical entity that has no unique relationship with observable properties of organisms. For example, FA is known to be affected by the environment an individual develops in ( Parsons, 1990) as well as by variation in the developmental stability of individuals. It is also not clear that there is any single property of an individual that can be labelled developmental stability, as each trait of an individual may to some degree have different stability properties from every other trait ( Møller & Swaddle, 1997, pp. 53–55; Leung & Forbes, 1997). For example, traits that develop at different times, or in different parts of the body, may differ in their developmental stability. Taken together, these complications have so far precluded empirical characterization of the relationship between developmental stability and FA, despite a number of demonstrations that variation in developmental stability of some characters does exist ( Parsons, 1990; Whitlock & Fowler, 1997; Gangestad & Thornhill, 1999).
In the absence of detailed empirical data, we must depend on models to develop our intuition. The majority of workers have adopted the following standard model of fluctuating asymmetry ( Palmer & Strobeck, 1986; Palmer, 1996). Each individual is characterized by its developmental variance, the converse of developmental stability. Paired structures are assumed to develop independently towards the same expected size but to show some normally distributed variation around that expectation. The amount of variation around the expected size is determined by the developmental variance. In this model, the difference between paired structures is therefore also normally distributed, with variance twice that of the variance of each paired structure.
Several recent explorations of this standard model suggest that the expected relationship between FA and developmental stability is very weak. FA essentially measures developmental variance, the variance in size of body parts when they develop in the same environment, which is the converse of developmental stability. Variances are more difficult to estimate well than means, so we should expect that more sampling effort would be needed to study FA than a typical trait. Unfortunately, FA must usually be estimated from a single pair of measurements, yielding a poor estimate of the variance and therefore of the proportion of variation in FA that could be due to real variation in developmental stability ( Whitlock, 1996; Houle, 1997).
The likelihood that only a small amount of information about individual developmental stability is gained from a single measure of FA has led to two efforts to quantify how much of the variation in FA could be due to variation in developmental stability, both assuming the simple model of the development of paired structures outlined above. One such effort used the relationship between the mean and variance of FA ( Whitlock, 1996), whereas the other exploited the kurtosis in FA expected to arise from variation in developmental stability ( Gangestad & Thornhill, 1999).
Whitlock (1996) observed that there is a simple relationship between the mean FA and the variance in FA for individuals with the same developmental stability. Therefore, one can calculate by subtraction the proportion of the total variance in FA that can be due to differences in developmental stability. This quantity is familiar from quantitative genetics as the repeatability. Although this insight is correct, the formulas given by Whitlock (1996) were incorrect; corrected formulas have now been published ( Van Dongen, 1998b; Whitlock, 1998). The repeatability provides an intuitive measure of the reliability of individual measurements. More importantly, the repeatability sets an upper limit to the heritability, the proportion of the variance that can be due to genetic causes. It also sets an upper limit on the phenotypic correlation between the asymmetries of different pairs of traits on the same individual. Whitlock showed that the maximum repeatability of FA is 0.64 and that the coefficient of variation of FA is sometimes so large that the repeatability would be expected to approach this maximum value ( Whitlock, 1996). Paradoxically, because FA is such a poor measure of variance, even traits with low repeatability and small correlations of FA among traits may reflect a great deal of variation in developmental stability.
Using simulations, Gangestad & Thornhill (1999) derived an empirical relationship between repeatability and kurtosis in signed FA, the difference in size between paired structures. They come to conclusions similar to those of Whitlock, arguing that, despite the low repeatability of many estimates of FA, the heritability of developmental stability itself may be high.
In this paper, I extend Whitlock’s (1996, 1998) work to consider the relationship between the distribution of developmental stabilities and the variance of FA. Whitlock’s approach leads to an estimate of the proportion of the variation in FA that can be due to variation in developmental stabilities, but it does not consider variation in developmental stability explicitly. The results presented here go the next step and allow inferences about the amount of variation in developmental stability from the repeatability of FA, based on the standard model. Previous work that has explicitly included variation in developmental stability has considered mixtures of individuals with two or three different stabilities ( Houle, 1997; Van Dongen, 1998b), rather than more realistic continuous distributions. Other work has relied on simulations ( Leung & Forbes, 1997; Van Dongen, 1998b; Gangestad & Thornhill, 1999), which are difficult to generalize. The principal result of this model is that, in order for measures of FA to have the substantial repeatabilities implied by some data, mean-standardized variation in developmental stability would have to be higher than for most previously studied traits.
In the next section I present an intuitive introduction to the model. The Mathematical results section then derives the relationship between developmental stability and measures of asymmetry based on this model. From these relationships, I then obtain Numerical results. The reader who wishes to obtain the main results without mathematical details may skip the Mathematical results section.
I assume a population of organisms that are unable to regulate development perfectly. This imperfect development is studied by measuring a pair of structures on either side of an axis of symmetry, such as right and left limb lengths. I start with the commonly accepted model for the development of bilaterally paired traits, which imagines that each side of the organism develops independently of the other and that the variation in each side is normally distributed ( Palmer & Strobeck, 1986; Palmer, 1996). This model of asymmetry has a pragmatic basis and is not directed at attempting to discern the causes of variation in development. It merely assumes that developmental variance exists and that developmental variance captures something about what we intuitively mean when we discuss developmental stability. If we understood the details of development of the morphological structures, we could make the relationship between asymmetry and development explicit. Clearly, the present state of knowledge does not allow this step, although a number of speculative efforts in this direction have been undertaken ( Graham et al., 1993 ; Klingenberg & Nijhout, 1999).
Variation in developmental stability has often been shown to be caused by environmental variation ( Parsons, 1990) and in some cases to have a genetic basis as well ( Parsons, 1990; Whitlock & Fowler, 1997; Gangestad & Thornhill, 1999). Developmental stability can in principle be decomposed into developmental noise, factors that cause variation in development, and developmental homoeostasis, processes that damp out the effects of developmental noise ( Palmer, 1996; Leung & Forbes, 1997). In practice these are usually indistinguishable, so they are considered together here.
One must model at least four kinds of variances to investigate the relationship between variation in developmental stability and variation in asymmetry. The most familiar of these is the variance of asymmetry itself, which I symbolize σ2. The variance of asymmetry depends on the variance in the traits from which asymmetries are calculated, that is, on the developmental variance, VD. VD is the converse of developmental stability. In addition, the variance of sides may contain measurement error, Ve. The fourth sort of variance is variation in the developmental variance, which has not been explicitly included in previous analyses.
I assume that each individual offers two or more examples or realizations of the same trait, S, which I will refer to as ‘sides’, although their spatial arrangement is not important. On the ith individual, the S-values are drawn independently from the same normal distribution with variance VD. The mean of this distribution must be much greater than √(VD) in order to preserve approximate normality but is otherwise free to vary. For simplicity, I assume that the mean of the distribution of sides is uncorrelated with VD. The developmental variance of the ith individual will be represented as VDi. It may consist of variation caused by both genotype and environment. I consider two statistics to measure asymmetry. First is the absolute value of the difference between sides FAi=|Si1 – Si2|. Second is the variance of sides
where n is the number of ‘sides’ measured. The variance of sides has statistical properties superior to those of FA, even when there are only two sides ( Palmer & Strobeck, 1986).
My goal is to model the variance in asymmetry as a function of population variation in developmental variance, VVD, so we need to consider what the distribution of VD would look like. The family of distributions I have chosen to represent this situation is shown in Fig. 1. Before I give the mathematical basis for these distributions, I give the following intuitive justification.
The choice of a distribution for developmental variances, VD, must take into account the fact that a variance cannot be negative. Consider a series of populations with the same mean developmental variance, V¯D, but that differ in the population variance of developmental variance, VVD. When VVD is small (as shown in the curve labelled α=400 in Fig. 1) the distribution can be nearly symmetrical, as it is very unlikely that a value will fall near VD=0. However, as the population variance of VD increases, the fact that VD cannot be negative has a larger and larger effect on the distribution. If the mean is to be held constant, the lack of negative values means that the likelihood that a value falls between zero and the mean must increase to compensate for the unconstrained tail of large values to the right of the mean. The result is that the distribution must become increasingly skewed as the variance goes up (represented by decreasing α values in Fig. 1), and the mode of the distribution must shift to the left. When VVD is very large relative to the mean, the mode is very close to 0 but balanced by an increasingly long tail of large VD values.
A distribution that has these properties is the gamma distribution, which is only defined for values of VD > 0. For the gamma, the probability that individual i has developmental variance VD is
where Γ() denotes the gamma function. The gamma distribution has two parameters, α and β. A principal attraction of the gamma distribution is the variety of shapes it can assume, depending on the value of the ‘shape’ parameter α. When α is large, the gamma approaches a normal distribution. Both the exponential and the χ2 distributions are special cases of the gamma distribution. β is the ‘scale’ parameter. The mean of the gamma distribution is αβ, and the variance is αβ2=VVD. Note that the coefficient of variation of a gamma-distributed variable such as VD is
In addition to the developmental variance, VD, I assume that the observed variance of S may also include measurement error, Ve. Measurement error is assumed to be constant over all individuals. To incorporate measurement error, the distribution Vi=VD,i + Ve can be modelled as a gamma distribution with a minimum value at Ve, rather than 0.
Most elements of this model are shown in Fig. 2, which shows the distribution of the developmental variance, VD, sides S, and FA for two different distributions of VD. The first row of the figure shows the distributions of VD. On the left, α=0.5 resulting in a highly skewed distribution with a high CV; the column on the right shows α=100, a fairly symmetrical distribution with a low CV. Measurement error is assumed to be absent. The second row of the plots shows distributions of sides for representative values of VD. The mean of the sides is always equal to 10, and the distributions are always normal. In each case, the upper right panel of each triplet gives the distribution for a value of VD at the 95th percentile of the distribution, the lower left panel gives the distribution for a value of VD at the 5th percentile of the distribution, and the middle panel shows the value at the median value of VD. For the small α value, the difference in the distributions of S is immediately apparent; the distribution at the 5th percentile has such a small variance that the peak is off the scale chosen. Note that the 95th percentile for this distribution is at VD=6.05, emphasizing the presence of a long tail of large VD values that is not otherwise apparent in the figure. For the large-α case, however, the distributions of S are so similar that no difference is apparent to the eye.
These distributions of S will not be observed directly, as each individual has only two sides. Instead, we directly observe the distribution of sides in a population of individuals, where each individual has a different developmental variance drawn from the distributions at the top of the figure. This distribution is shown in the third row of the figure. Note that the distribution with small α results in a kurtotic distribution of sides, whereas the large-α case has a nearly normal distribution of sides. This kurtosis is expected because the distribution is a combination of normal distributions with very different variances ( Wright, 1968; Houle, 1997; Leung & Forbes, 1997; Gangestad & Thornhill, 1999). Finally, we calculate FA by taking the absolute value of the difference in two sides of the same individual, resulting in the peaky, long-tailed distribution of FA in the small-α case, and a distribution close to the half normal in the large-α case.
Given this model, we are interested in how informative these measures of asymmetry are concerning the developmental variance of an individual, when individuals vary in VD. As pointed out by Whitlock (1996, 1998) a good measure for this purpose is the repeatability, symbolized ℜ, the proportion of the variance in asymmetry that is due to real differences in developmental variance. The repeatability sets an upper limit both to the heritability of asymmetry and to the correlation of asymmetries of different structures on an individual. To calculate the repeatability of a measure of asymmetry, we need to know the total observed variance in asymmetry in the whole population, σT2, and the realization variance, σR2, the variance in observed asymmetry among individuals with the same VD values. This σR2 term includes any measurement error. The remaining variance, σI2, is the true variance among individuals remaining after the realization variation is removed. By definition, σT2=σR2+ σI2.
Note that both Whitlock (1998) and Van Dongen (1998b) treat the parameter σI2 as the variance in developmental stability. (Their notation differs from mine: σI2 is VDS in Whitlock; Vind in Van Dongen.) I reserve the term developmental stability for the inverse of the developmental variance of sides, VD, and the term variance in developmental stability for the variance of developmental stability, VVD=αβ2. Although in some cases (see below) VVD=σI2, defining some aspect of the variance in symmetry as developmental stability risks losing track of the important distinction between developmental stability and the effects it has on a particular phenotype.
The expected value of FAi is
and the variance is
where the expectations are over hypothetical replicate individuals with the same VD,i values. The realization variance is
The other variance components cannot be obtained in closed form when there is measurement error, so I first consider the case of no measurement error, Ve=0. Then the mean FA is
The total variance in FA is
Finally, the true variance in FA among individuals can be obtained as the difference between eqns 9 and 6,
The repeatability of FA when there is no measurement error is then
The results in eqns 6–11 were checked by simulations in SAS (results not shown; SAS Institute, 1990). Although I was not able to obtain general analytical results for the gamma distribution with error variance, numerical results were obtained by numerical integration of eqns 6 and 9 in Maple V ( Waterloo Maple, 1997), with Ve + VD.i substituted for VD.i.
It is also useful to consider the coefficient of variation of FA itself, which is readily measured (e.g. Whitlock, 1996). For the case of no error variance,
Just as Whitlock showed that the maximum repeatability of FA measures is a function of CVFA, eqn 12 can be solved iteratively to yield an estimate of α, and CVVD from CVFA.
Because the alternative measure of asymmetry, s2, is a variance, it follows a χ2 distribution with n – 1 degrees of freedom, and therefore has expected value VD·i + Ve, and variance 2(VD·i + Ve)2/(n – 1). The mean is therefore just V¯D + Ve, or αβ + Ve. The realization variance is
and the total variance is
Taking the difference between eqns 13 and 14 gives the individual variance σ2I·s2=αβ2. Thus, the true variance of sides among individuals is the variance in developmental variance. The repeatability is then readily calculated as ℜs2=σ2I·s2/σ2T·s2. These results were checked by simulations in SAS (results not shown; SAS Institute, 1990).
Figure 3 shows ℜFA, the repeatability of FA as a function of CVVD, the coefficient of variation of developmental variance. In all cases, the mean developmental variance was held constant at 1. The small graphs along the top show the very wide range of distributions considered, from symmetrical distributions with small CVs on the left to highly skewed distributions with a very strong mode at 0 on the right. The chief result is that ℜFAincreases rather slowly with CVVD. Only when CVVD is very large does the repeatability reach substantial values. The effect of measurement error, Ve, on repeatability is shown in the lower curves in Fig. 3. The range of measurement error considered is quite large; when Ve=1 the variance due to measurement error is as large as the mean variance of sides. Increasing measurement error lowers the repeatability.
Figure 4 shows the coefficient of variation of fluctuating asymmetry, CVFA, values calculated for the same parameter set used in Fig. 3. When α is large and the coefficient of variation of developmental variance, CVVD, is small, CVFA is very close to the theoretical minimum of √[(π – 2)/2] ≈ 76%, which follows from eqns 4 and 5. Only when CVVD is very large does CVFA increase substantially. Increasing measurement error lowers CVFA, as it increases the mean fluctuating asymmetry, as well as the variance.
Figure 5 shows ℜs2, the repeatability of s2, the alternative estimator of asymmetry, for the same parameter set used in Figs 3 and 4. The overall shape of these curves is similar to that for ℜFA, in that the repeatabilities only become substantial when the coefficient of variation of developmental variance is quite large. ℜs2 is always lower than ℜFA, although this difference becomes less marked when Ve is large. One advantage of s2 as a measure of asymmetry is that it can incorporate information on more than two sides. Figure 6 shows how repeatability increases with n, the number of sides measured. This relationship emphasizes the usefulness of organisms with multiple realizations of traits per individual for the investigation of developmental stability ( Leung et al., 2000 ).
In this paper I have extended a standard model of fluctuating asymmetry to explicitly include variance in the developmental stability parameter (here represented by its converse developmental variance) assumed to underlie variation in asymmetry. The main new result of the model is the very weak relationship between variance in developmental stability and fluctuating asymmetry. Only when the underlying variance in developmental stability is enormous does that variation become apparent in measures of asymmetry. To see this pattern, note (in Figs 3 and 5) that, in the best case when there is no error variance, the repeatability of each asymmetry measure reaches the very modest value of 20% only when the coefficient of variation of developmental variance is about 100%. A coefficient of variation of 100% means that the standard deviation is equal to the mean. Since variances must be positive, this 100% coefficient of variation is accompanied by a highly skewed distribution of developmental variances. Perhaps even more striking is that the coefficient of variation of FA in the population is only about 30% higher than its minimum expected value when the coefficient of variation of developmental variance is 100%, as shown in Fig. 4.
One reason for presenting results in terms of repeatability is that it sets an upper limit to the heritability of asymmetry. If the heritability of developmental variance is 1, the heritability of asymmetry is its repeatability. In reality, there is ample evidence that individuals differ in developmental stability because of environmental factors as well as genetic ones ( Parsons, 1990), and the heritability of asymmetry would certainly be lowered as a result, perhaps quite substantially. When the heritability of developmental variance is less than 1, we can be sure that the heritability of asymmetry will be less than its repeatability. One useful and simple result is that adding a given environmental variance to the developmental variance lowers the repeatability of asymmetry in exactly the same manner as does measurement error. For example, the line corresponding to Ve=1 in Fig. 3 is equivalent to a heritability of asymmetry of 0.5. It is therefore not surprising that asymmetry seems to have very low heritability, usually less than 5% ( Whitlock & Fowler, 1997; Gangestad & Thornhill, 1999).
Another very useful interpretation of the repeatability is as the correlation of asymmetry values for sets of traits with the same developmental variances. If the developmental variances of different traits are proportional – that is the variance of one trait is a multiple of the variance in some other trait – the correlation of asymmetries of these traits on the same individual will equal the repeatability. However, different traits on an individual may differ in their developmental stabilities for a variety of reasons ( Møller & Swaddle, 1997, pp. 53–55; Leung & Forbes, 1997), so correlations may be substantially less than the repeatability. Gangestad & Thornhill (1999) reviewed a number of large data sets, however, and argued that correlations in FA among traits are close to those expected on the basis of kurtosis and average trait repeatabilities under their model. Future work comparing repeatabilities estimated from CVs and from kurtosis, trait correlations, and the heritability of FA in the same population could provide a means for testing models of FA, such as the one presented in this paper.
Given the general result that asymmetry rises slowly with the variation in developmental stability, it is interesting to observe that the coefficient of variation of fluctuating asymmetry is sometimes greater than 100% (see, e.g., Whitlock, 1996; Van Dongen, 1998a). Above CVFA=100%, the CV of developmental stability rises extremely rapidly, as shown in Fig. 4. For example, CVFA=170% for a sample of 188 tarsus lengths in the olive sunbird, Nectarina olivacea ( Van Dongen, 1998a). This result implies a CV of developmental stability of 220%. On the other hand, the available data sets with the largest sample sizes imply modest CVs for developmental stability ( Gangestad & Thornhill, 1999).
To compare these inferred coefficients of variation for developmental stability with those for other traits, CVFA should be divided by two, because they have units of the trait squared ( Lande, 1977; Houle, 1992). The phenotypic coefficients of variation of morphological traits are generally between 2 and 20%, whereas fitness components have values generally between 10 and 100% ( Houle, 1992). Thus, in cases such as the olive sunbird ( Van Dongen, 1998a), where the predicted variation in developmental stability is extremely high, either the model is false, or developmental stability is sometimes more variable than for any previously studied traits. Asymmetry has attracted attention because it potentially captures information about developmental stability, which may be of fundamental importance to fitness. If developmental stability has higher variance than typical for fitness, this raises an interesting paradox.
The standard model makes a number of questionable assumptions to the standard model that could increase the CVFA when violated. First, the model assumes that the distribution of sides is normal for a given level of developmental stability. The distribution of sides could instead be a mixture of different distributions, perhaps reflecting discrete events that deflect development into alternative pathways. For example, asymmetrical use, injury, starvation, or other traumas might have large effects on development, although not necessarily so large as to lead to the rejection of an individual as a statistical or biological outlier. Extreme individuals have a disproportionate impact on measures of variation. For example, Whitlock (1996) notes that exclusion of a single highly asymmetrical individual lowers CVFA in his sample of wolf jaws from 145% to about half that, close to the minimum value expected if there were no variation in developmental stability. In correlational studies, extreme individuals can account for much of the apparent power of a model to explain the data ( Leung & Forbes, 1997).
The developmental model of Klingenberg & Nijhout (1999) provides a very different explanation for how normality could be violated. These authors point out that developmental stability is likely to be an epiphenomenon of the parameters of the developmental system, rather than a single property of that system. They expect that variation in the fundamental developmental properties will have nonlinear effects on morphology, which could easily lead to non-normal distributions of sizes. Similarly, nonlinear interactions during development could result in distributions of developmental variances that are very different from the gamma distribution I assumed.
Another possibly incorrect assumption is that each side develops independently. Because sides usually develop simultaneously on the same organism, there are opportunities for interactions during development ( Graham et al., 1993 ; Klingenberg & Nijhout, 1998). The most plausible kind of interaction would be competition for resources during development ( Klingenberg & Nijhout, 1998). This would tend to cause antisymmetry and lower CVFA ( Van Dongen, 1998a) and so cannot help to explain the high values that raise questions under the present model. The finding that some distributions of FA are consistent with condition-dependent antisymmetry ( Rowe et al., 1997 ) may indicate that models of this type should be taken seriously.
In addition to these assumptions common to the standard models of asymmetry, I also had to make an assumption about the actual distribution of developmental stabilities. I chose the gamma distribution, but other distributions, such as the log-normal, may be worth considering. My principal conclusion, that the usefulness of FA as an indicator of individual developmental stability is poor unless the variance of developmental stability is extremely large, does not depend on the choice of distribution. Previous numerical or simulation studies using mixtures of two developmental stabilities ( Houle, 1997), three developmental stabilities ( van Dongen, 1998b), and normal, half-normal and uniform distributions of developmental stabilities ( Gangestad & Thornhill, 1999) yield similar conclusions.
In summary, this elaboration of a basic model in asymmetry studies is consistent with many of the largest experimental studies in suggesting that the proportion of the within-population variation in fluctuating asymmetry that can be explained by variation in developmental stability is small ( Gangestad & Thornhill, 1999). If the variation in developmental stability is typical of that found for other sorts of traits, then the value of FA as an indicator of developmental stability is low. On the other hand, a number of smaller studies report distributions of FA that imply enormous variation in developmental stabilities ( Whitlock, 1996; Van Dongen, 1998a; Lens & van Dongen, 1999; Lens et al., 1999 ). In these cases, we need either to explain how the variance in developmental stability can be so high or to modify this standard model of the relationship between developmental stability and fluctuating asymmetry.
I thank L. Rowe, R. Palmer, M. Whitlock, G. Bell, S. W. Gangestad, and anonymous reviewers for comments on the manuscript, and for helpful discussions. A. Thistle helped to edit the manuscript. This work was supported by the Natural Sciences and Engineering Research Council of Canada.
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http://www.umaine.edu/it/software/mathematica/screencast.php
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Happy New Year from Wolfram Research and Mathematica 7.
We found a common theme at many schools we visited that integrated Mathematica into their courses in 2008: faculty wanted to teach with Mathematica, but didn't want to take the time to teach Mathematica itself. Thus we created the "Hands-on Start to Mathematica" screencast.
In its first month, over 10,000 faculty and students watched the screencast, and a large number of faculty made it the first homework assignment for the class. In fact, one university has already reported improved homework and test scores after implementing this screencast.
We have now updated it for Version 7: http://url.wolfram.com/43rL1y/
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https://www.physicsforums.com/threads/linear-speeds-at-points-on-earth.394288/
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1. The problem statement, all variables and given/known data What is the linear speed of a point: a) on the equator, b) on the Arctic Circle (latitude 66.5 degrees N), c) at a latitude of 45 degrees N, due to the Earth's rotation? Given Radius (earth)= 6.38x10^6m v? 2. Relevant equations v=rw w= 2pi*f t= 1/f 3. The attempt at a solution I am not sure how go about doing this problem. I wanted to solve for w with 2pi(1/24) but am not sure how to calculate the speed at different areas on Earth.
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https://quizlet.com/540927525/unit-1-grade-6-envision-20-vocabulary-flash-cards/
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Unit 1 Grade 6 Envision 2.0 Vocabulary
Unit 1: VVMS
Terms in this set (11)
Positive and negative whole numbers including zero.
Positive and negative fractions and decimals
Numbers greater than zero
Numbers less than zero
two numbers that are the same distance from zero on a number line, but are in opposite directions.
The distance a number is from zero on a number line (Can NOT be negative!)
A plane that is divided into four regions by a horizontal line called the x-axis and a vertical line called the y-axis.
A mathematical notation indicating the number of times a quantity is multiplied by itself.
a number that has an exponent
A whole number that has exactly two factors, 1 and itself.
Breaking down a composite number until all of the factors are prime
OTHER SETS BY THIS CREATOR
Focused Note Taking
Who's in our AVID class?
Grade 6 Envision Math Topic 1
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http://www.solutioninn.com/each-coffee-table-produced-by-kevin-watson-designers-nets-the
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Question: Each coffee table produced by Kevin Watson Designers nets the
Each coffee table produced by Kevin Watson Designers nets the firm a profit of $ 9. Each bookcase yields a $ 12 profit. Watson’s firm is small and its resources limited. During any given production period (of 1 week), 10 gallons of varnish and 12 lengths of high- quality redwood are available. Each coffee table requires approximately 1 gallon of varnish and 1 length of redwood. Each bookcase takes 1 gallon of varnish and 2 lengths of wood. Formulate Watson’s production- mix decision as a linear programming problem, and solve. How many tables and book-cases should be produced each week? What will the maximum profitbe?
Relevant QuestionsLeach Distributors packages and distributes industrial supplies. A standard shipment can be packaged in a class A container, a class K container, or a class T container. A single class A container yields a profit of $ 9; a ...Refer to the table that follows. a) Use the northwest- corner method to find an initial feasible solution. What must you do before beginning the solution steps? b) Use the intuitive lowest- cost approach to find an initial ...Using the data from Problem C. 12 and the unit production costs in the following table, show which locations yield the lowest cost.Location ........ Production CostDecatur .......... $50Minneapolis ....... 60Carbondale ...Virginia’s Ron McPherson Electronics Corporation retains a service crew to repair machine breakdowns that occur on average ƛ= 3 per 8- hour workday (approximately Poisson in nature). The crew can service an average of µ= ...Susan Sherer, an IRS auditor, took 45 minutes to process her first tax return. The IRS uses an 85% learning curve. How long will the:2nd return take? 4th return take? 8th return take?
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https://www.netexplanations.com/ml-aggarwal-cbse-solutions-class-7-math-tenth-chapter-triangle-and-its-properties-exercise-10-2/
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math
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ML Aggarwal CBSE Solutions Class 7 Math 10th Chapter Triangle and its Properties Exercise 10.2
Sum of angles in triangle = 180
x + y + z = 180
=> 48 + 37 + z = 180
=> 85 + z = 180
=> z = 180 degree – 85 degree
=> z = 95 95 degree
(8) One of the angles of a triangle measures 80 degree and the other angles are equal. Find the measure of each of the angles.
(9) If one angle of a triangle is 60 degree and the other two angles are in the ratio 2:3, find these angles.
(10) If the angles of a triangle are in the ratio 1:2:3. find the angles. Classify the triangle in two different ways.
(11) Can a triangle have three angles whose measure are
(i) 65 degree, 74 degree, 39 degree
(ii) 1/3 right angle, 1 right angle, 60 degree?
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https://backarticles.info/feedback-control-theory-system-control-group-at-_MTE3MDg4.html
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math
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Customer: SACO CONTROLS Prep by: Sam Larizza Project #: P7-03-01 BILL OF MATERIALS Date: July 11, 2003 P.O. #: 2003/10781 Project: Page: 1 of 4
Report CopyRight/DMCA Form For : Feedback Control Theory System Control Group At
Preface iii,1 Introduction 1,1 1 Issues in Control System Design 1. 1 2 What Is in This Book 7,2 Norms for Signals and Systems 13. 2 1 Norms for Signals 13,2 2 Norms for Systems 15,2 3 Input Output Relationships 18. 2 4 Power Analysis Optional 19,2 5 Proofs for Tables 2 1 and 2 2 Optional 21. 2 6 Computing by State Space Methods Optional 24,3 Basic Concepts 31. 3 1 Basic Feedback Loop 31,3 2 Internal Stability 34. 3 3 Asymptotic Tracking 38,3 4 Performance 40,4 Uncertainty and Robustness 45. 4 1 Plant Uncertainty 45,4 2 Robust Stability 50,4 3 Robust Performance 53. 4 4 Robust Performance More Generally 58,4 5 Conclusion 59. 5 Stabilization 63,5 1 Controller Parametrization Stable Plant 63. 5 2 Coprime Factorization 65, 5 3 Coprime Factorization by State Space Methods Optional 69. 5 4 Controller Parametrization General Plant 71,5 5 Asymptotic Properties 73. 5 6 Strong and Simultaneous Stabilization 75,5 7 Cart Pendulum Example 81. 6 Design Constraints 87,6 1 Algebraic Constraints 87. 6 2 Analytic Constraints 88,7 Loopshaping 101,7 1 The Basic Technique of Loopshaping 101. 7 2 The Phase Formula Optional 105,7 3 Examples 108. 8 Advanced Loopshaping 117,8 1 Optimal Controllers 117. 8 2 Loopshaping with C 118,8 3 Plants with RHP Poles and Zeros 126. 8 4 Shaping S T or Q 135,8 5 Further Notions of Optimality 138. 9 Model Matching 149,9 1 The Model Matching Problem 149. 9 2 The Nevanlinna Pick Problem 150,9 3 Nevanlinna s Algorithm 154. 9 4 Solution of the Model Matching Problem 158,9 5 State Space Solution Optional 160. 10 Design for Performance 163,10 1 P 1 Stable 163,10 2 P 1 Unstable 168. 10 3 Design Example Flexible Beam 170,10 4 2 Norm Minimization 175. 11 Stability Margin Optimization 181,11 1 Optimal Robust Stability 181. 11 2 Conformal Mapping 185,11 3 Gain Margin Optimization 187. 11 4 Phase Margin Optimization 192,12 Design for Robust Performance 195. 12 1 The Modified Problem 195,12 2 Spectral Factorization 196. 12 3 Solution of the Modified Problem 198,12 4 Design Example Flexible Beam Continued 204. References 209, Striking developments have taken place since 1980 in feedback control theory The subject has be. come both more rigorous and more applicable The rigor is not for its own sake but rather that even. in an engineering discipline rigor can lead to clarity and to methodical solutions to problems The. applicability is a consequence both of new problem formulations and new mathematical solutions. to these problems Moreover computers and software have changed the way engineering design is. done These developments suggest a fresh presentation of the subject one that exploits these new. developments while emphasizing their connection with classical control. Control systems are designed so that certain designated signals such as tracking errors and. actuator inputs do not exceed pre specified levels Hindering the achievement of this goal are. uncertainty about the plant to be controlled the mathematical models that we use in representing. real physical systems are idealizations and errors in measuring signals sensors can measure signals. only to a certain accuracy Despite the seemingly obvious requirement of bringing plant uncertainty. explicitly into control problems it was only in the early 1980s that control researchers re established. the link to the classical work of Bode and others by formulating a tractable mathematical notion. of uncertainty in an input output framework and developing rigorous mathematical techniques to. cope with it This book formulates a precise problem called the robust performance problem with. the goal of achieving specified signal levels in the face of plant uncertainty. The book is addressed to students in engineering who have had an undergraduate course in. signals and systems including an introduction to frequency domain methods of analyzing feedback. control systems namely Bode plots and the Nyquist criterion A prior course on state space theory. would be advantageous for some optional sections but is not necessary To keep the development. elementary the systems are single input single output and linear operating in continuous time. Chapters 1 to 7 are intended as the core for a one semester senior course they would need. supplementing with additional examples These chapters constitute a basic treatment of feedback. design containing a detailed formulation of the control design problem the fundamental issue. of performance stability robustness tradeoff and the graphical design technique of loopshaping. suitable for benign plants stable minimum phase Chapters 8 to 12 are more advanced and. are intended for a first graduate course Chapter 8 is a bridge to the latter half of the book. extending the loopshaping technique and connecting it with notions of optimality Chapters 9 to. 12 treat controller design via optimization The approach in these latter chapters is mathematical. rather than graphical using elementary tools involving interpolation by analytic functions This. mathematical approach is most useful for multivariable systems where graphical techniques usually. break down Nevertheless we believe the setting of single input single output systems is where this. new approach should be learned, There are many people to whom we are grateful for their help in this book Dale Enns for. sharing his expertise in loopshaping Raymond Kwong and Boyd Pearson for class testing the book. and Munther Dahleh Ciprian Foias and Karen Rudie for reading earlier drafts Numerous Caltech. students also struggled with various versions of this material Gary Balas Carolyn Beck Bobby. Bodenheimer and Roy Smith had particularly helpful suggestions Finally we would like to thank. the AFOSR ARO NSERC NSF and ONR for partial financial support during the writing of this. Introduction, Without control systems there could be no manufacturing no vehicles no computers no regulated. environment in short no technology Control systems are what make machines in the broadest. sense of the term function as intended Control systems are most often based on the principle. of feedback whereby the signal to be controlled is compared to a desired reference signal and the. discrepancy used to compute corrective control action The goal of this book is to present a theory. of feedback control system design that captures the essential issues can be applied to a wide range. of practical problems and is as simple as possible. 1 1 Issues in Control System Design, The process of designing a control system generally involves many steps A typical scenario is as. 1 Study the system to be controlled and decide what types of sensors and actuators will be used. and where they will be placed,2 Model the resulting system to be controlled. 3 Simplify the model if necessary so that it is tractable. 4 Analyze the resulting model determine its properties. 5 Decide on performance specifications,6 Decide on the type of controller to be used. 7 Design a controller to meet the specs if possible if not modify the specs or generalize the. type of controller sought, 8 Simulate the resulting controlled system either on a computer or in a pilot plant. 9 Repeat from step 1 if necessary, 10 Choose hardware and software and implement the controller. 11 Tune the controller on line if necessary,2 CHAPTER 1 INTRODUCTION. It must be kept in mind that a control engineer s role is not merely one of designing control. systems for fixed plants of simply wrapping a little feedback around an already fixed physical. system It also involves assisting in the choice and configuration of hardware by taking a system. wide view of performance For this reason it is important that a theory of feedback not only lead. to good designs when these are possible but also indicate directly and unambiguously when the. performance objectives cannot be met, It is also important to realize at the outset that practical problems have uncertain non. minimum phase plants non minimum phase means the existence of right half plane zeros so the. inverse is unstable that there are inevitably unmodeled dynamics that produce substantial un. certainty usually at high frequency and that sensor noise and input signal level constraints limit. the achievable benefits of feedback A theory that excludes some of these practical issues can. still be useful in limited application domains For example many process control problems are so. dominated by plant uncertainty and right half plane zeros that sensor noise and input signal level. constraints can be neglected Some spacecraft problems on the other hand are so dominated by. tradeoffs between sensor noise disturbance rejection and input signal level e g fuel consumption. that plant uncertainty and non minimum phase effects are negligible Nevertheless any general. theory should be able to treat all these issues explicitly and give quantitative and qualitative results. about their impact on system performance, In the present section we look at two issues involved in the design process deciding on perfor. mance specifications and modeling We begin with an example to illustrate these two issues. Example A very interesting engineering system is the Keck astronomical telescope currently. under construction on Mauna Kea in Hawaii When completed it will be the world s largest The. basic objective of the telescope is to collect and focus starlight using a large concave mirror The. shape of the mirror determines the quality of the observed image The larger the mirror the more. light that can be collected and hence the dimmer the star that can be observed The diameter of. the mirror on the Keck telescope will be 10 m To make such a large high precision mirror out of. a single piece of glass would be very difficult and costly Instead the mirror on the Keck telescope. will be a mosaic of 36 hexagonal small mirrors These 36 segments must then be aligned so that. the composite mirror has the desired shape, The control system to do this is illustrated in Figure 1 1 As shown the mirror segments. are subject to two types of forces disturbance forces described below and forces from actuators. Behind each segment are three piston type actuators applying forces at three points on the segment. to effect its orientation In controlling the mirror s shape it suffices to control the misalignment. between adjacent mirror segments In the gap between every two adjacent segments are capacitor. type sensors measuring local displacements between the two segments These local displacements. are stacked into the vector labeled y this is what is to be controlled For the mirror to have the. ideal shape these displacements should have certain ideal values that can be pre computed these. are the components of the vector r The controller must be designed so that in the closed loop. system y is held close to r despite the disturbance forces Notice that the signals are vector valued. Such a system is multivariable, Our uncertainty about the plant arises from disturbance sources. As the telescope turns to track a star the direction of the force of gravity on the mirror. During the night when astronomical observations are made the ambient temperature changes. 1 1 ISSUES IN CONTROL SYSTEM DESIGN 3,disturbance forces. r u mirror y,controller actuators, Figure 1 1 Block diagram of Keck telescope control system. The telescope is susceptible to wind gusts,and from uncertain plant dynamics. The dynamic behavior of the components mirror segments actuators sensors cannot be. modeled with infinite precision, Now we continue with a discussion of the issues in general. Control Objectives, Generally speaking the objective in a control system is to make some output say y behave in a. desired way by manipulating some input say u The simplest objective might be to keep y small. or close to some equilibrium point a regulator problem or to keep y r small for r a reference. or command signal in some set a servomechanism or servo problem Examples. On a commercial airplane the vertical acceleration should be less than a certain value for. passenger comfort, In an audio amplifier the power of noise signals at the output must be sufficiently small for. high fidelity, In papermaking the moisture content must be kept between prescribed values. There might be the side constraint of keeping u itself small as well because it might be constrained. e g the flow rate from a valve has a maximum value determined when the valve is fully open. or it might be too expensive to use a large input But what is small for a signal It is natural to. introduce norms for signals then y small means kyk small Which norm is appropriate depends. on the particular application, In summary performance objectives of a control system naturally lead to the introduction of. norms then the specs are given as norm bounds on certain key signals of interest. 4 CHAPTER 1 INTRODUCTION, Before discussing the issue of modeling a physical system it is important to distinguish among four. different objects,1 Real physical system the one out there. 2 Ideal physical model obtained by schematically decomposing the real physical system into. ideal building blocks composed of resistors masses beams kilns isotropic media Newtonian. fluids electrons and so on, 3 Ideal mathematical model obtained by applying natural laws to the ideal physical model. composed of nonlinear partial differential equations and so on. 4 Reduced mathematical model obtained from the ideal mathematical model by linearization. lumping and so on usually a rational transfer function. Sometimes language makes a fuzzy distinction between the real physical system and the ideal. physical model For example the word resistor applies to both the actual piece of ceramic and. metal and the ideal object satisfying Ohm s law Of course the adjectives real and ideal could be. used to disambiguate, No mathematical system can precisely model a real physical system there is always uncertainty. Uncertainty means that we cannot predict exactly what the output of a real physical system will. be even if we know the input so we are uncertain about the system Uncertainty arises from two. sources unknown or unpredictable inputs disturbance noise etc and unpredictable dynamics. What should a model provide It should predict the input output response in such a way that. we can use it to design a control system and then be confident that the resulting design will work. on the real physical system Of course this is not possible A leap of faith will always be required. on the part of the engineer This cannot be eliminated but it can be made more manageable with. the use of effective modeling analysis and design techniques. Mathematical Models in This Book, The models in this book are finite dimensional linear and time invariant The main reason for this. is that they are the simplest models for treating the fundamental issues in control system design. The resulting design techniques work remarkably well for a large class of engineering problems. partly because most systems are built to be as close to linear time invariant as possible so that they. are more easily controlled Also a good controller will keep the system in its linear regime The. uncertainty description is as simple as possible as well. The basic form of the plant model in this book is, Here y is the output u the input and P the nominal plant transfer function The model uncertainty. comes in two forms,n unknown noise or disturbance,unknown plant perturbation. 1 1 ISSUES IN CONTROL SYSTEM DESIGN 5, Both n and will be assumed to belong to sets that is some a priori information is assumed. about n and Then every input u is capable of producing a set of outputs namely the set of. all outputs P u n as n and range over their sets Models capable of producing sets of. outputs for a single input are said to be nondeterministic There are two main ways of obtaining. models as described next,Models from Science, The usual way of getting a model is by applying the laws of physics chemistry and so on Consider. the Keck telescope example One can write down differential equations based on physical principles. e g Newton s laws and making idealizing assumptions e g the mirror segments are rigid The. coefficients in the differential equations will depend on physical constants such as masses and. physical dimensions These can be measured This method of applying physical laws and taking. measurements is most successful in electromechanical systems such as aerospace vehicles and robots. Some systems are difficult to model in this way either because they are too complex or because. their governing laws are unknown,Models from Experimental Data. The second way of getting a model is by doing experiments on the physical system Let s start. with a simple thought experiment one that captures many essential aspects of the relationships. between physical systems and their models and the issues in obtaining models from experimental. data Consider a real physical system the plant to be controlled with one input u and one. output y To design a control system for this plant we must understand how u affects y. The experiment runs like this Suppose that the real physical system is in a rest state before. an input u is applied i e u y 0 Now apply some input signal u resulting in some output. signal y Observe the pair u y Repeat this experiment several times Pretend that these data. pairs are all we know about the real physical system This is the black box scenario Usually we. know something about the internal workings of the system. After doing this experiment we will notice several things First the same input signal at different. times produces different output signals Second if we hold u 0 y will fluctuate in an unpredictable. manner Thus the real physical system produces just one output for any given input so it itself. is deterministic However we observers are uncertain because we cannot predict what that output. Ideally the model should cover the data in the sense that it should be capable of producing. every experimentally observed input output pair Of course it would be better to cover not just. the data observed in a finite number of experiments but anything that can be produced by the real. physical system Obviously this is impossible If nondeterminism that reasonably covers the range. of expected data is not built into the model we will not trust that designs based on such models. will work on the real system, In summary for a useful theory of control design plant models must be nondeterministic having. uncertainty built in explicitly,Synthesis Problem, A synthesis problem is a theoretical problem precise and unambiguous Its purpose is primarily. pedagogical It gives us something clear to focus on for the purpose of study The hope is that. 6 CHAPTER 1 INTRODUCTION, the principles learned from studying a formal synthesis problem will be useful when it comes to. designing a real control system, The most general block diagram of a control system is shown in Figure 1 2 The generalized plant. generalized,controller,Figure 1 2 Most general control system. consists of everything that is fixed at the start of the control design exercise the plant actuators. that generate inputs to the plant sensors measuring certain signals analog to digital and digital. to analog converters and so on The controller consists of the designable part it may be an electric. circuit a programmable logic controller a general purpose computer or some other such device. The signals w z y and u are in general vector valued functions of time The components of w. are all the exogenous inputs references disturbances sensor noises and so on The components of. z are all the signals we wish to control tracking errors between reference signals and plant outputs. actuator signals whose values must be kept between certain limits and so on The vector y contains. the outputs of all sensors Finally u contains all controlled inputs to the generalized plant Even. open loop control fits in the generalized plant would be so defined that y is always constant. Very rarely is the exogenous input w a fixed known signal One of these rare instances is where. a robot manipulator is required to trace out a definite path as in welding Usually w is not fixed. but belongs to a set that can be characterized to some degree Some examples. In a thermostat controlled temperature regulator for a house the reference signal is always. piecewise constant at certain times during the day the thermostat is set to a new value The. temperature of the outside air is not piecewise constant but varies slowly within bounds. In a vehicle such as an airplane or ship the pilot s commands on the steering wheel throttle. pedals and so on come from a predictable set and the gusts and wave motions have amplitudes. and frequencies that can be bounded with some degree of confidence. The load power drawn on an electric power system has predictable characteristics. Sometimes the designer does not attempt to model the exogenous inputs Instead she or he. designs for a suitable response to a test input such as a step a sinusoid or white noise The. designer may know from past experience how this correlates with actual performance in the field. Desired properties of z generally relate to how large it is according to various measures as discussed. 1 2 WHAT IS IN THIS BOOK 7, Finally the output of the design exercise is a mathematical model of a controller This must. be implementable in hardware If the controller you design is governed by a nonlinear partial. differential equation how are you going to implement it A linear ordinary differential equation. with constant coefficients representing a finite dimensional time invariant linear system can be. simulated via an analog circuit or approximated by a digital computer so this is the most common. type of control law, The synthesis problem can now be stated as follows Given a set of generalized plants a set. of exogenous inputs and an upper bound on the size of z design an implementable controller to. achieve this bound How the size of z is to be measured e g power or maximum amplitude. depends on the context This book focuses on an elementary version of this problem. 1 2 What Is in This Book, Since this book is for a first course on this subject attention is restricted to systems whose models. are single input single output finite dimensional linear and time invariant Thus they have trans. fer functions that are rational in the Laplace variable s The general layout of the book is that. Chapters 2 to 4 and 6 are devoted to analysis of control systems that is the controller is already. specified and Chapters 5 and 7 to 12 to design, Performance of a control system is specified in terms of the size of certain signals of interest For. example the performance of a tracking system could be measured by the size of the error signal. Chapter 2 Norms for Signals and Systems looks at several ways of defining norms for a signal u t. in particular the 2 norm associated with energy,the norm maximum absolute value. and the square root of the average power actually not quite a norm. lim u t dt, Also introduced are two norms for a system s transfer function G s the 2 norm. kGk2 G j d,and the norm,kGk max G j, Notice that kGk equals the peak amplitude on the Bode magnitude plot of G Then two very. useful tables are presented summarizing input output norm relationships For example one table. gives a bound on the 2 norm of the output knowing the 2 norm of the input and the norm of the. 8 CHAPTER 1 INTRODUCTION,Figure 1 3 Single loop feedback system. transfer function Such results are very useful in predicting for example the effect a disturbance. will have on the output of a feedback system, Chapters 3 and 4 are the most fundamental in the book The system under consideration is. shown in Figure 1 3 where P and C are the plant and controller transfer functions The signals are. as follows,r reference or command input,e tracking error. u control signal controller output,d plant disturbance. y plant output,n sensor noise, In Chapter 3 Basic Concepts internal stability is defined and characterized Then the system is. analyzed for its ability to track a single reference signal r a step or a ramp asymptotically as. time increases Finally we look at tracking a set of reference signals The transfer function from. reference input r to tracking error e is denoted S the sensitivity function It is argued that a useful. tracking performance criterion is kW1 Sk 1 where W1 is a transfer function which can be tuned. by the control system designer, Since no mathematical system can exactly model a physical system we must be aware of how. modeling errors might adversely affect the performance of a control system Chapter 4 Uncertainty. and Robustness begins with a treatment of various models of plant uncertainty The basic technique. is to model the plant as belonging to a set P Such a set can be either structured for example. there are a finite number of uncertain parameters or unstructured the frequency response lies in. a set in the complex plane for every frequency For us unstructured is more important because it. leads to a simple and useful design theory In particular multiplicative perturbation is chosen for. detailed study it being typical In this uncertainty model there is a nominal plant P and the family. P consists of all perturbed plants P such that at each frequency the ratio P j P j lies in a. disk in the complex plane with center 1 This notion of disk like uncertainty is key because of it. the mathematical problems are tractable, Generally speaking the notion of robustness means that some characteristic of the feedback. system holds for every plant in the set P A controller C provides robust stability if it provides. internal stability for every plant in P Chapter 4 develops a test for robust stability for the multi. plicative perturbation model a test involving C and P The test is kW2 T k 1 Here T is the. 1 2 WHAT IS IN THIS BOOK 9, complementary sensitivity function equal to 1 S or the transfer function from r to y and W2. is a transfer function whose magnitude at frequency equals the radius of the uncertainty disk at. that frequency, The final topic in Chapter 4 is robust performance guaranteed tracking in the face of plant. uncertainty The main result is that the tracking performance spec kW1 Sk 1 is satisfied for all. plants in the multiplicative perturbation set if and only if the magnitude of W1 S W2 T is less. than 1 for all frequencies that is,k W1 S W2 T k 1 1 1. This is an analysis result It tells exactly when some candidate controller provides robust perfor. Chapter 5 Stabilization is the first on design Most synthesis problems can be formulated like. this Given P design C so that the feedback system 1 is internally stable and 2 acquires some. additional desired property or properties for example the output y asymptotically tracks a step. input r The method of solution presented here is to parametrize all Cs for which 1 is true and. then to find a parameter for which 2 holds In this chapter such a parametrization is derived it. has the form, where N M X and Y are fixed stable proper transfer functions and Q is the parameter an. arbitrary stable proper transfer function The usefulness of this parametrization derives from the. fact that all closed loop transfer functions are very simple functions of Q for instance the sensitivity. function S while a nonlinear function of C equals simply M Y M N Q This parametrization. is then applied to three problems achieving asymptotic performance specs such as tracking a. step internal stabilization by a stable controller and simultaneous stabilization of two plants by a. common controller, Before we see how to design control systems for the robust performance specification it is. important to understand the basic limitations on achievable performance Why can t we achieve. both arbitrarily good performance and stability robustness at the same time In Chapter 6 Design. Constraints we study design constraints arising from two sources from algebraic relationships that. must hold among various transfer functions and from the fact that closed loop transfer functions. must be stable that is analytic in the right half plane The main conclusion is that feedback control. design always involves a tradeoff between performance and stability robustness. Chapter 7 Loopshaping presents a graphical technique for designing a controller to achieve. robust performance This method is the most common in engineering practice It is especially. suitable for today s CAD packages in view of their graphics capabilities The loop transfer function. is L P C The idea is to shape the Bode magnitude plot of L so that 1 1 is achieved at. least approximately and then to back solve for C via C L P When P or P 1 is not stable L. must contain P s unstable poles and zeros for internal stability of the feedback loop an awkward. constraint For this reason it is assumed in Chapter 7 that P and P 1 are both stable. Thus Chapters 2 to 7 constitute a basic treatment of feedback design containing a detailed. formulation of the control design problem the fundamental issue of performance stability robustness. tradeoff and a graphical design technique suitable for benign plants stable minimum phase. Chapters 8 to 12 are more advanced,10 CHAPTER 1 INTRODUCTION. Chapter 8 Advanced Loopshaping is a bridge between the two halves of the book it extends the. loopshaping technique and connects it with the notion of optimal designs Loopshaping in Chapter 7. focuses on L but other quantities such as C S T or the Q parameter in the stabilization results. of Chapter 5 may also be shaped to achieve the same end For many problems these alternatives. are more convenient Chapter 8 also offers some suggestions on how to extend loopshaping to handle. right half plane poles and zeros, Optimal controllers are introduced in a formal way in Chapter 8 Several different notions of. optimality are considered with an aim toward understanding in what way loopshaping controllers. can be said to be optimal It is shown that loopshaping controllers satisfy a very strong type. of optimality called self optimality The implication of this result is that when loopshaping is. successful at finding an adequate controller it cannot be improved upon uniformly. Chapters 9 to 12 present a recently developed approach to the robust performance design prob. lem The approach is mathematical rather than graphical using elementary tools involving interpo. lation by analytic functions This mathematical approach is most useful for multivariable systems. where graphical techniques usually break down Nevertheless the setting of single input single. output systems is where this new approach should be learned Besides present day software for. control design e g MATLAB and Program CC incorporate this approach. Chapter 9 Model Matching studies a hypothetical control problem called the model matching. problem Given stable proper transfer functions T1 and T2 find a stable transfer function Q to. minimize kT1 T2 Qk The interpretation is this T1 is a model T2 is a plant and Q is a cascade. controller to be designed so that T2 Q approximates T1 Thus T1 T2 Q is the error transfer function. This problem is turned into a special interpolation problem Given points ai in the right half. plane and values bi also complex numbers find a stable transfer function G so that kGk 1. and G ai bi that is G interpolates the value bi at the point ai When such a G exists and how. to find one utilizes some beautiful mathematics due to Nevanlinna and Pick. Chapter 10 Design for Performance treats the problem of designing a controller to achieve the. performance criterion kW1 Sk 1 alone that is with no plant uncertainty When does such a. controller exist and how can it be computed These questions are easy when the inverse of the. plant transfer function is stable When the inverse is unstable i e P is non minimum phase the. questions are more interesting The solutions presented in this chapter use model matching theory. The procedure is applied to designing a controller for a flexible beam The desired performance is. given in terms of step response specs overshoot and settling time It is shown how to choose the. weight W1 to accommodate these time domain specs Also treated in Chapter 10 is minimization. of the 2 norm of some closed loop transfer function e g kW1 Sk2. Next in Chapter 11 Stability Margin Optimization is considered the problem of designing a. controller whose sole purpose is to maximize the stability margin that is performance is ignored. The maximum obtainable stability margin is a measure of how difficult the plant is to control. Three measures of stability margin are treated the norm of a multiplicative perturbation gain. margin and phase margin It is shown that the problem of optimizing these stability margins can. also be reduced to a model matching problem, Chapter 12 Design for Robust Performance returns to the robust performance problem of. designing a controller to achieve 1 1 Chapter 7 proposed loopshaping as a graphical method. when P and P 1 are stable Without these assumptions loopshaping can be awkward and the. methodical procedure in this chapter can be used Actually 1 1 is too hard for mathematical.
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Customer: SACO CONTROLS Prep by: Sam Larizza Project #: P7-03-01 BILL OF MATERIALS Date: July 11, 2003 P.O. #: 2003/10781 Project: Page: 1 of 4
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Ophthalmic Antibiotics Therapeutic Class Review (TCR) April 19, 2017 No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, digital scanning, or via any information storage or
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The Hillfolk. 69 Rivals 70 Outlanders. 70 Shell-Grinders 70 Domers. 72 Iron-Makers 72 Rockheads. 72 Saltmen 75 Threshers. 75 Tridents 75 Sample Names. 75 Why a Fictionalized 10th. century BCE Levant? 77 Additional Settings Under Hollow Hills,78 Hollywoodland, Jason Morningstar 81 Mad Scientists Anonymous, Michelle Nephew 85 Moscow Station, Kenneth Hite 91 World War 2.1, Matt Forbeck 95 Malice ...
06-Apr-2020 0 Views 5 Pages
This is where the Free Hillfolk live. She hears stories that the Free Hillfolk possess strange powers -- that they work magic -- that it is because of this that they remain free of the Homelander sway. When Corlath, the king of the Free Hillfolk, comes to Istan to ask that the Homelanders and the Hillfolk set their enmity aside to fight
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http://slideplayer.com/slide/4219601/
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math
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Presentation on theme: "Agenda Blog signup… First week impressions – High School vs. University.. Career Night – Sep 12 th (Wed) CS outcomes Complexity."— Presentation transcript:
Agenda Blog signup… First week impressions – High School vs. University.. Career Night – Sep 12 th (Wed) CS outcomes Complexity
First Week Impressions? How was your first week at ASU? Good things? Frustrating things? Differences from High School?
Mark your calendars for a special evening event (approx. 4:00-8:00PM) in the Memorial Union (Second Floor) At the event, you will have the opportunity to talk to working engineers from a variety of industries and companies, to find out more about engineering careers. You will have the chance to ask them anything you want to know about including what it’s like to be an engineer, or what you need to do to be successful. Attendance will be taken; – there will be no class that week (no class on 9 th September) More information to come later Career Exploration Night Wednesday September 12th http://more.engineering.asu.edu/career/event s/freshman-engineering-career-exploration- night/
Sorting… When is a sequence in sorted order? – How many pairwise comparisons do I need to do to check if a sequence of n-numbers is sorted? – If I have a procedure for checking whether a sequence is sorted, is it reasonable to sort a sequence of numbers by generating permutations and testing if any of them are sorted? Intelligence is putting the “test” part of Generate&Test into generate part…
Career Fair Activity Career Exploration Module Part 1 Homework: Prepare for Career Exploration Night To prepare for Career Exploration Night you should think about what you want to know or learn from engineering professionals. This may include information about the following: what they do in their jobs (day to day tasks; responsibilities; etc..) what career path did they take from college to where they are now? how they chose their careers advice they have about skills and experience you need to be successful etc, etc, etc… In preparation for the event, create a list of at least 5 questions that you would like to ask the professionals at the event. When you have completed your list, submit it to the Blog You should, of course, ask more than 5 questions at the event, but this list will at least help you to start conversations to get the information you want to know. There is no required set of questions; you should ask the questions you are most interested in. If you are having a hard time thinking of questions, look at the “Student Information for Engineering Career Exploration Night” document (posted on Blackboard) for some ideas to help stimulate your thinking.
Can you think of additional questions you want answered? Event on Wed 9/12 4-8pm NO separate class next Friday (the event attendance is the class attendance)
Career Exploration Night Experience Topics for Group Discussion: – Share the majors, job titles, and companies of the individuals you met. – What was the most important thing you learned about engineering? Most surprising? Most interesting? – What kind of projects/work activities were mentioned? – What differences did you find between “real people” and what you had read beforehand? Similarities? – What was the best advice that you received?
Discussion Highlights (Group reporting) What was the most important thing you learned? – Most surprising? – Most interesting? Major differences/similarities between information from ‘real people’ and information you read? Types of projects/work activities? Did you see different job functions within a single discipline (or similar job functions across multiple disciplines)? What was the best advice that you received?
Company Requires Or DesiresMy QualificationDifference Between The Two What I Am Going To Do To Make Up The Difference or Gain a Measurable Accomplishment Job Title: ___________________________ Page # ______
Summary of the points from the three groups (9/21)
Exactly when do we say an algorithm is “slow”? We kind of felt that O(N! * N) is a bit much complexity How about O(N 2 )? O(N 10 )? Where do we draw the line? – Meet the Computer Scientist Nightmare – So “Polynomial” ~ “easy” & “exponential” ~ “hard” – 2 n eventually overtakes any n k however large k is.. How do we know if a problem is “really” hard to solve or it is just that I am dumb and didn’t know how to do better? – If checking the correctness of the solution itself takes more than polynomial time, then we know the problem must be hard.. – But there are many problems, for which checking the correctness is polynomial, and yet we don’t know any efficient algorithm 2n2n
Classes P and NP Class P If a problem can be solved in time polynomial in the size of the input it is considered an “easy” problem – Note that your failure to solve a problem in polynomial time doesn’t mean it is not polynomial (you could come up with O(N* N!) algorithm for sorting, after all Class NP Technically “if a problem can be solved in polynomial time by a non-deterministic turing machine, then it is in class NP” Informally, if you can check the correctness of a solution in polynomial time, then it is in class NP – Are there problems where even checking the solution is hard?
Tower of Hanoi (or Brahma) Shift the disks from the left peg to the right peg – You can lift one disk at a time – You can use the middle peg to “park” disks – You can never ever have a larger disk on top of a smaller disk (or KABOOM) How many moves to solve a 2-disk version? A 3-disk one? An n-disk one? – How long does it take (in terms of input size), to check if you have a correct solution?
How to explain to your boss as to why your program is so slow… I can't find an efficient algorithm, I guess I'm just too dumb. I can't find an efficient algorithm, because no such algorithm is possible. I can't find an efficient algorithm, but neither can all these famous people.
The P=NP question Clearly, all polynomial problems are also NP problems Do we know for sure that there are NP problems that are not polynomial? If we assume this, then we are assuming P != NP If P = NP, then some smarter person can still solve a problem that we thought can’t be solved in polytime – Can imply more than a loss of face… For example, factorization is known to be an NP-Complete problem; and forms the basis for all of cryptography.. If P=NP, then all the cryptography standards can be broken! NP-Complete: “hardest” problems in class NP [the giants of NP-world] EVERY problem in class NP can be reduced to an NP-Complete problem in polynomial time --So you can solve that problem by using an algorithm that solves the NP-complete problem
Reducing Problems… Mathematician reduces “mattress on fire” problem Make Rao Happy Make Everyone in ASU Happy Make Little Tommy Happy Make his entire family happy General NP- problem Boolean Satisfiability Problem 3-SAT Thus, SAT is NP-Complete Thus, 3SAT is also NP-Complete..but of course! Tommy is a fussy dude!
Academic Integrity What it means Typical ASU policy – Homeworks – Exams Take-Home Exams – Term papers
Scholarship Opportunities General Scholarships The FURI program NSF REU program
Is exponential complexity the worst? After all, we can have 2 2 More fundamental question: Can every computational problem be solved in finite time? “Decidability” --Unfortunately not guaranteed [and Hilbert turns in his grave] 2n2n
Some Decidability Challenges In First Order Logic, inference (proving theorems) is semi-decidable – If the theorem is true, you can show that in finite time; if it is false you may never be able to show it In First Order Logic + Peano Arithmatic, inference is undecidable – There may be theorems that are true but you can’t prove them [Godel]
Practical Implications of Intractability A class of problems is said to be NP-hard as long as the class contains at least one instance that will take exponential time.. What if 99% of the instances are actually easy to solved? --Where then are the wild things?
Satisfiability problem Given a set of propositions P 1 P 2 … P n..and a set of “clauses” that the propositions must satisfy – Clauses are of the form P 1 V P 7 VP 9 V P 12 V ~P 35 – Size of a clause is the number of propositions it mentions; size can be anywhere from 1 to n Find a T/F assignment to the propositions that respects all clauses Is it in class NP? How many “potential” solutions? Canonical NP-Complete Problem. 3-SAT is where all clauses are of length 3
Example of a SAT problem P,Q,R are propositions Clauses – P V ~Q V R – Q V ~R V ~P Is P=False, Q=True, R=False as solution? Is Boolean SAT in NP?
Hardness of 3-sat as a function of #clauses/#variables #clauses/#variables Probability that there is a satisfying assignment Cost of solving (either by finding a solution or showing there ain’t one) p=0.5 You would expect this This is what happens! ~4.3 Phase Transition!
Phase Transition in SAT Theoretically we only know that phase transition ratio occurs between 3.26 and 4.596. Experimentally, it seems to be close to 4.3 (We also have a proof that 3-SAT has sharp threshold)
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https://karolinum.cz/en/books/vinogradov-mathematics-for-economists-made-simple-6565
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math
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Mathematics for Economists. Made Simple
mathematics and statistics
paperback, 366 pp., 1. edition
published: august 2010
recommended price: 275 czk
As the field of economics becomes ever more specialized and complicated, so does the mathematics required of economists. With Mathematics for Economists, expert mathematician Viatcheslav V. Vinogradov offers a straightforward, practical textbook for students in economics?for whom mathematics is not a scientific or philosophical subject but a practical necessity. Focusing on the most important fields of economics, the book teaches apprentice economists to apply mathematics algorithms and methods to economic analysis, while abundant exercises and problem sets allow them to test what they?ve learned.
?For non-mathematicians who just use math in their professional activity I believe this is a very helpful source of knowledge, and also a very efficient reference.??Elena Kustova, Saint Petersburg University
Viatcheslav V. Vinogradov is a researcher at the Economics Institute of the Academy of Sciences of the Czech Republic and a consultant to the World Bank.
table of contents
0.1 Basic Mathematical Notation
0.2 Methods of Mathematical Proof.
0.3 Powers, Exponents, Logs and Complex Numbers
1 Linear Algebra
1.1 Matrix Algebra.
1.2 Systems of Linear Equations
1.3 Quadratic Forms
1.4 Eigenvalues and Eigenvectors
1.5 Diagonalization and Spectral Theorems
1.6 Appendix: Vector Spaces
2.1 The Concept of Limit.
2.2 Differentiation - the Case of One Variable.
2.3 Rules of Differentiation
2.4 Maxima and Minima of a Function of One Variable
2.6 Functions of More than One Variable
2.7 Multivariate Unconstrained Optimization
2.8 The Implicit Function Theorem.
2.9 (Quasi)Concavity and (Quasi)Convexity
2.10 Appendix: Matrix Derivatives
2.11 Appendix: Topological Structure and Its Implications
2.12 Appendix: Correspondences and Fixed-Point Theorems
3 Constrained Optimization
3.1 Optimization with Equality Constraints
3.2 The Case of Inequality Constraints
3.2.1 Non-Linear Programming
3.2.2 Kuhn-Tucker Conditions.
3.3 Appendix: Linear Programming.
4.1 Differential Equations.
4.1.1 Differential Equations of the First Order
4.1.2 Qualitative Theory of First-Order Differential Equations
4.1.3 Linear Differential Equations of a Higher Order with Constant Coefficients
4.1.4 Systems of First-Order Linear Differential Equations
4.1.5 Simultaneous Differential Equations and Types of Equilibria.
4.2 Difference Equations.
4.2.1 First-Order Linear Difference Equations
4.2.2 Second-Order Linear Difference Equations
4.2.3 The General Case of Order n.
4.2.4 Systems of Simultaneous First-Order Difference Equations with Constant Coefficients
4.3 Introduction to Dynamic Optimization
4.3.1 First-Order Conditions
4.3.2 Present-Value and Current-Value Hamiltonians
4.3.3 Dynamic Problems with Inequality Constraints
5.1 Practice Problems
5.2 Solved Problems
5.2.1 Linear Algebra.
5.2.3 Constrained Optimization
5.3 Economics Applications
5.4 Written Assignments
5.5 Sample Problem Sets
5.6 Unsolved Problems
5.6.1 More Problems
5.6.2 Sample Tests
To my knowledge, in modern economics most scholars use mathematics, but for the majority of them math is rather a kind of toolbox than a rigorous science they would like to advance (I am not talking here about prominent cases such as, for instance, Arrow, Debrey, Intrilligator, Kamien, or Samuelson, though). Therefore, from my point of view the book exactly serves the purpose. It gives the reader fairly precise understanding of how to apply mathematical algorithms, tools and methods in economic analysis without getting into deep details of math background.
If I were asked whether this textbook would be helpful for Ph.D. students majoring in malhematics, I would probably be more skeptieal. but for non-mathematicians who just use math in their professional activity I believe this is very helpful source ofknowledge, and also a very efficient reference point. Furthermore, it was indeed a great idea to include a chapter solely dedicated to problems and solutions. Another value added is that the structure of this book clearly makes it a good text for distance learning students.
Elena Kustova, Professor at the Department of Mathematics and Mechanic, Saint Peterburg University
The book under review is designed as a textbook for the first-year doctoral students in economics, but at least some parts of it are equally suitable for mathematically oriented students in the MA program in economics and in other social sciences. It consists of four chapters covering virtually all areas of mathematics relevant to modern economic analysis. In addition, there is an introductory section reviewing basic mathematical prerequisites needed for entering the doctoral program, and a lengthy final section of exercises.
The introductory section,-labelled as Chapter 0-starts with outlining basic mathematical notation, continuing with explaining methods of mathematical proofs, and finishing with describing powers, logs and complex numbers. The knowledge of the contents ofthis section is indispensable for anybody claiming to be mathematically literate. A shiningjewel of it is the part on mathematical proofs which is exhaustive, remarkably clear and beautifully logical.
The first chapter covers linear algebra which is absolutely essential for most econometric work. The formulation of systems of linear equations in terms of matrix algebra is well explained and clearly shows the efficiency gained. Particularly commendable is the explanation of eigenvalues and eigenvectors whose abstract nature is frequently perplexing for students. The second chapter deals with basic calculus, starting with the concept of limit and ending with the notions of concavity and convexity. This is a crucial part of mathematics for economists as recognized by the leading US universities where the knowledge of calculus is a prerequisite for all undergraduates majoring in economics. The author does a very good job of covering this topic.
The subject ofthe third chapter ofthe book is constrained optimization, the basic and universal problem of economics. The recognition of this forces the students to approach each economic problem by identifying the economic agents, their objective functions and their constraints. The chapter deals well with both equality and inequality constraints and gives a good exposition of linear programming in the appendix.
The fourth chapter extends the realm of economic problems to dynamic situations. It starts with differential equations, goes on to difference equations, leading to dynamic optimisation which is quite a fashionable topic in modern economic research. The final section on dynamic programming is a special bonus for students and researchers interested in dynamic problems. An appendix on optimal control theory helps students comprehend its popularity initiated by Gregory Chow in the 1970s.
The last section ofthe book-labelled as Chapter 5-contains several sets ofexercises. These include practice problems (with solutions), solved problems for each of the preceding four chapters, problems involving economic applications, written assignments, sample problem sets, and unsolved problems. The whole section takes up almost one half of the whole book and is not only unique for a text of this kind but also invaluable. It is extremely well done and provides a wonderful resource for students in mastering mathematics needed for serious study of economics.
In my opinion the book is definitely commendable for the purpose for which it was written. The author has wisely decided to put emphasis on understanding over abstract proofing, which for economists would be more of an intellectual luxury than of practical use. This general orientation of the book makes it also a good reference text on the bookshelves of economic researchers.
Jan Kmenta, Professor Emeritus of Economics, University of Michigan and Visiting Professor CERGE-EI, Prague
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https://pythagorasconferenceglobal.com/math/pythagoras-theorem/
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math
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In this lesson, we will learn about the Pythagorean Theorem. or the Pythagorean theorem as it is sometimes called. And you might be wondering, “What is the theorem?” and “Who in this world is Pythagoras?” Now, in mathematics, theorems are only statements that have been proven to be true. from other things that are known or accepted to be true. And Pythagoras, well, he’s a very smart man. who lived a long time in ancient Greece. and he proved the theorem.
Well historians are not entirely sure it was actually Pythagoras theorem who proved it. It could be one of the students or followers. but he usually gets praise for it. However, the main thing you need to know is that. Pythagoras’s theorem illustrates important geometric relationships. between the three sides of a right triangle.
We will learn what the relationship is in just one minute. but first there are a few things you need to know. before you can really understand the Pythagorean Theorem or use it to solve problems.
First of all, to understand the Pythagorean Theorem you need to know about angles and triangles. and you also need to know a little about exponents and square roots. So, if the topic is new to you, be sure to watch our videos about them first. And secondly, although the Pythagorean Theorem is about geometry.
You need to know some basic algebra to really use it. Specifically, you have to know about variables. and how to solve basic algebraic equations involving exponents. We discussed many of these topics in the first five videos of our Basic Algebra series.
Read also : Algebra Basic
Okay, now you have all the background information discussed. let’s see what the Pythagorean Theorem says. The theorem can be expressed in several different ways. but what we like the most is like this: For right triangles with feet ‘a’ and ‘b’ and sloping sides ‘c’.
‘a squared’ plus ‘b squared’ is equal to ‘c squared’. As you can see from this definition, the Pythagorean Theorem does not apply to ALL triangles. ONLY applies to the RIGHT triangle. As you know, a right triangle always includes a right angle.
which is usually marked with a ‘right-angle symbol’ of a square to help you identify it. And you need to know which angle is the right angle because. this helps you identify the important side of the triangle called the hypotenuse.
The hypotenuse is the longest side of a right triangle. and always the ‘opposite’ side from the right angle. In other words, the side that doesn’t touch (or helps shape) the right angle itself. To use the Pythagorean Theorem, you must be able to identify the hypotenuse.
because that’s what is the variable ‘c’ for the theorem. ‘c’ is the length of the hypotenuse. The other two sides of the triangle. (which touches or forms a right angle) is called “his feet”.
Our Pythagorean Theorem definition uses the variable names ‘a’ and ‘b’ to represent their length. Oh and which foot is called ‘a’ and which foot is called ‘b’.
as long as you keep track of which after you make your initial choice. Okay, now we know the various parts of the Pythagorean Theorem. let’s think about what relations or equations (‘a squared’ plus ‘b squared’ equal to ‘c squared’) really tell us.
This tells us that if we take the lengths of both legs (sides ‘a’ and ‘b’) and their ‘square’. which means multiplying it yourself. (‘a squared’ is ‘a’ times ‘a’ and ‘b squared’ is ‘b’ times ‘b’). and then if we add the two ‘sums of squares’ together.
they will EQUAL the amount that you will get if you ‘square’ the hypotenuse. (which will be ‘c squared’ or c times c). That might sound a little confusing at first. So let’s look at a specific example of a right triangle. it will help the Pythagorean theorem make more sense. This right triangle is called “3, 4, 5 triangles”.
because the sides have relative lengths 3, 4, and 5. And with “relative length”, I mean that the unit of length doesn’t really matter. Sides can be expressed in ANY unit (inches, meters, miles, whatever).
So a triangle can be of various sizes along its length. will have proportions of 3, 4, and 5 relative to each other. Starting with the side that is 3 units long, which we call “side a”. what do we get if we square that side ?
Now in arithmetic, quadratic 3 means multiplying 3 times 3 which is equal to 9. And the geometric equation of squaring something actually produces a square shape. As you can see, this box contains 9 unit boxes.
So this red area represents the value of ‘a’ which is squared in the Pythagorean Theorem. Next let’s look at the side which is 4 units in length, which we call “side b”. Squaring 4 means multiplying 4 times 4, which is 16.
Again, the geometric equivalent is a literal square. i.e. 4 units on each side and cover a total area of 16 units. So this blue area represents ‘b squared’ in the Pythagorean Theorem. And finally, let’s deal with the hypotenuse, or “c side”, which is the longest side.
5 units in length. Squaring 5 means multiplying 5 times 5, which is 25. And the geometric equation is 5 x 5 square which has an area of 25 units. So this green area represents ‘c squared’ in the Pythagorean Theorem.
Now you can see how the arithmetic part of the Pythagorean Theorem. related to the geometric parts of this right triangle. let’s check to see if the Pythagorean Theorem is really true (at least in this particular case).
On the arithmetic side, if you add up the sum of ‘squared’ and ‘b squared’. they are really the same as ‘c squared’ because 9 + 16 = 25. And by slightly rearranging our unit box. You can see that the area of the box is formed by two legs. really the same as the area of the square formed by the hypotenuse.
Wow, those ancient Greek men are really smart! Okay, but I know what you think. “It’s okay, but why should I care about the Pythagorean Theorem? What are the benefits? “. As always, that’s a good question. And the answer is, like many things in mathematics.
The Pythagorean theorem is a useful tool. that can help you use what you do NOT know to find out what you do NOT know. Specifically, if you have a right triangle but you only know how long the two sides are.
The Pythagorean theorem tells you how to find out the length of an unknown third side. For example, imagine that you have a right triangle. 2 cm long on this side and 3 cm long on this side. but we don’t know how long the tilt is.
No problem!. The Pythagorean theorem tells us the relationship between the three sides of ANY right triangle. so we can find out. We know that ‘a squared’ plus ‘b squared’ is equal to ‘c squared’. so let’s plug what we know into the equation. and then solve it for what we don’t know.
Again, it doesn’t matter which leg is called ‘a’ or ‘b’. so let’s label it like this. and then substitute ‘2’ for ‘a’ and ‘3’ for ‘b’ in the Pythagorean Theorem equation. That gives us an algebraic equation that has only one unknown, ‘c’. If we solve this equation for ‘c’ in other words.
if we rearrange the equation so that ‘c’ by itself on one side of the sign is equal to. then we will know exactly what ‘c’ is. We will know the length of the side of the triangle. First, we need to simplify the left side of the equation because it contains known numbers. And according to the order of operations, we need to simplify the exponent first.
‘2 squared’ is 4 and ‘3 squared’ is 9. Then, we add the result (4 + 9 = 13). and we have equation 13 = ‘c squared’. which is equal to ‘c squared’ = 13. Then, to get ‘c’ by itself. we need to do the opposite of what was done to him.
Because it is squared, the reverse operation is square root. so we need to take the square root from both sides. Taking the square root of ‘c squared’ only gives us the ‘c’ we want on the side of this equation.
but that gives us a little problem on the other side. because it’s not easy to know what the square root of 13 is. This is not a perfect square so it will be decimal. and maybe irrational numbers.
But that’s okay because it leaves our answer as ‘square root of 13’. Of course, you can use a calculator to get decimal values if you really need them. but in mathematics it is very common to leave square roots alone unless they are easy to simplify.
So the sides of this right triangle are, 2 cm, 3 cm and the ‘square root of 13’ cm. Let’s try another example. For this right triangle, we know the length of the hypotenuse (6 m). and one foot (4 m). but the length of the other leg is unknown.
So let’s use the Pythagorean Theorem to find the unknown length. As usual, we call the hypotenuse “c side”. And let’s call our feet know “side a” and our feet don’t know “side b”. Then we can replace the known values into the Pythagorean Theorem.
and solve for unknown values. Replacing ‘c’ with 6 and ‘a’ with 4 gives us the equation. ‘4 squared’ plus ‘b squared’ is equal to ‘6 squared’. we need to simplify and solve for ‘b’. First let’s simplify the exponent. ‘4 squared’ is 16, and ‘6 squared’ is 36.
Now we need to isolate ‘b squared’. and we can do that by subtracting 16 from both sides of the equation. On this side, (+16) and (-16) leave us only with ‘b squared’. And on the other hand we have 36 minus 16 which is 20.
We can now solve this simplified equation for ‘b’. by taking the square root from both sides which gives us. ‘b’ is the same as ‘square root of 20’.
Again, it’s okay to leave your answer as a square root like this. And some of you might know that ‘square root of 20’ can be simplified. to ‘2 times the square root of 5’. We will not worry about simplifying the root in this video. but if you know how to do it, great! If you don’t know, just leave the answer as ‘square root of 20’ meters.
Here’s another interesting one. What if you have a ‘unit square’ cut in half along the diagonal. Each side of the square is 1 unit. but how far is the distance from one corner of the square to another along the diagonal ?
Well, because the diagonal divides the square into two right triangles. we can use the Pythagorean Theorem to tell us the unknown distance. We label the right triangle feet ‘a’ and ‘b’ and the hypotenuse of ‘c’.
And because we know that ‘a’ and ‘b’ are equal to 1, we can attach those values. into the equation of the Pythagorean Theorem that gives us us. ‘1 squared’ plus ‘1 squared’ is equal to ‘c squared’. Now we are done with ‘c’. ‘1 squared’ is only 1. so the left side of this equation simplifies to 1 plus 1 which is only 2.
That means ‘c squared’ is equal to 2. and if we take the square root from both sides. we get ‘c’ equal to ‘square root of 2’. So that’s how far it crosses the diagonal of the unit square. Okay, so that’s how you use the Pythagorean Theorem.
to find the unknown side length of a right triangle, which is the most common use. But there are other ways you can use the Pythagorean Theorem that I want to mention. You can also use the Pythagorean Theorem to TEST triangle.
to see if it’s really the RIGHT triangle. Yes, know if you are not sure. For example, what if someone shows you this triangle and asks. “Is this a right triangle?” Yeah, that looks a lot like a right triangle. but does not have a right-angle symbol. and it will be difficult to know whether this angle is exactly 90 degrees just by looking at it.
Maybe close to 90, like 89.5 degrees. Don’t worry, the Pythagorean Theorem can tell us for sure. if we know the length of all three sides of the triangle. If we know the length (a, b and c). then we can include them in the Pythagorean Theorem equation to see if that is true.
In this special case. because the two shorter sides are 3 cm each and the longest side is 4 cm. we can attach the values to ‘a’, ‘b’ and ‘c’ and simplify to see what we get. ‘3 squared’ is 9, so on this side of the equation we get 9 plus 9 which is 18. And on the other side we have ‘4 squared’, which is 16. Uh oh that’s not right!
Our equation is simplified to 18 equals 16. What is clear is NOT a true statement. That means that all three sides of this triangle do not function in the Pythagorean Theorem. they do not match the relation ‘a squared’ plus ‘b squared’ equal to ‘c squared’.
And because the Pythagorean Theorem tells us that ALL right triangles fit that relationship. this triangle can’t be the RIGHT triangle. Good. so now you know what the Pythagorean Theorem is and you know how to use it.
You can use it to find the missing side of the right triangle. and you can also use it to test a triangle to see if it qualifies as a right triangle. But as you see. many other mathematical skills are needed to be able to use the Pythagorean Theorem effectively.
so you might need to brush up on some of those skills before you are ready to try using them yourself. And remember, you can’t master math just by watching videos about it. You really need to practice solving real math problems.
Pythagoras Conference Global
Evidence Pythagoras signs is frequently called the definition of Pythagoras theorems (Pitagoras). Because as the Elementary school when learning math, we don’t overlook to examine phytagoras this sentence, Pythagoras has to have already been no stranger inside our ears. The phytagoras formula is just actually a formula utilized by way of a scientist.
The significance of Pythagoras or even pythagoras theorem reads:
The left-hand or the side at the elbow’s triangle is corresponding to the flip hand squared.
The triangle above would be just an angled triangle, which includes one side vertical (BC), 1 side (AB), and also yet one side tilts (AC).
Evidence pythagoras conference global and also the Pythagoras formula functions to locate 1 side with both sides that are known.
Pythagoras theorem calculator
- Pythagoras formulation in origin shape
- In the event the mirror C
- The vertical and forthcoming sides are b and A
The consequent Pitagoras formulation:
b² = a² + c²
Then to calculate the upright side and the upcoming side apply formula:
a² = b² – c²
c² = b² – a²
Pythagoras formula in root form
- If the mirror side C
- The upright and upcoming sides are A and b
Significant NOTE: The Pythagoras formula, just valid on the elbows only (Pythagoras formula in square roots).
From the signs of this Pythagorean theorem, There’s a blueprint of amounts that Will Need to be recalled to solve the Challenge of Pythagoras is likely to likely probably be simpler and faster to operate on this, the routine is:
- 3 – 4 – 5
- 5 – 12 – 13
- 6 – 8 – 10
- 7 – 24 – 25
- 8 – 15 – 17
- 9 – 12 – 15
- 10 – 24 – 26
- 12 – 16 – 20
- 14 – 48 – 50
- 15 – 20 – 25
- 15 – 36 – 39
- 16 – 30 – 34
To know more information about the signs of Phytagoras, subsequently think about the next instance
Cases of pythagoras theorem and conversation
A concentric elbow comes with a vertical side (a b ), which is 1-5 cm long, and also alongside, it is (BC ) 8 cm, what’s cm kah side of this Mirror (AC)?
A B = 1-5
B C = 8
Said: AC span…???
⇒ First Way
AC² = AB² + BC²
AC² = 15² + 8²
AC² = 225 + 64
AC² = 289
AC = √289
AC = 17
⇒ Second way
AC = √ AB² + BC²
AC = √ 15² + 8²
AC = √ 255 + 64
AC = √ 289
AC = 17
So, AC length is 17 cm
Just how long is the amount of the borders of an elbow-elbow if it’s called this period of the mirror 1 3 cm and also the data side 5 cm?
As an instance: c Tilt side-by-side Flat side, an upright side
Not Known: c = 1 3 cm, B = 5 cm
Said: a …????
⇒ First Way
a² = c² – b²
a² = 13² – 5²
a² = 169 – 25
a² = 144
a = √ 144
a = 12
⇒ Second Way
a = √ c² – b²
a = √ 13² – 5²
a = √ 169 – 25
a = √ 144
a = 12
So, the length of the upright triangle is 12 cm
There’s a triangle of ABC, elbows in B. In case the span is a b = 16 cm and BC = 30, then what’s the amount of the side of this triangle (AC)?
A B = 16
B C = 30
Said: AC =…?
AC = √ AB² + BC²
AC = √ 16² + 30²
AC = √ 256 + 900
AC = √ 1156
AC = 34
So, AC length = 34 cm
Notice the picture below, learn the ABC elbow has a vertical side significance of 6 cm and a bottom side of 8 cm, then calculate just how long would be your medial side of this mirror?
A B = 8 cm
B C = 6 cm
Length: Period of AC (angled side of this elbow-elbow above)…?
AC² = AB² + BC²
AC² = 8² + 6²
AC² = 64 + 36
AC² = 100
AC = √100
AC = 10
These are a few situations of pythagoras calculator and also their talk and responses. To understand you, please perform a little exercise about learning Phytagoras below.
1. There’s just actually a triangle PQR X Y Z called the sides, which can be Y, X, and Z. In the subsequent announcement, the stark reality is…?
- A. if y² = x² + z² , < X = 90º
- B. if z² = y² – x² , < Z = 90º
- C. if z² = x² – y² , < Y = 90º
- D. if x² = y² + z² , < X = 90º
2. Not known triangle PQR has elbow at Q, where P Q = 8 cm, PR = 17 cm. Therefore, along this QR will be…?
- A. 9 cm
- B. 15 cm
- C. 25 cm
- D. 68 cm
3. There’s a squat triangle, its hypotensive 4 √3 cm along with a single facet of this elbows is 2 √2 cm. The length of time can be just the rear side of the elbow… Cm
A. 2 √10
B. 3 √5
C. 8 √2
D. 3 √3
4. The period of this Hepotenusa Tri-angle in which the leg is the span that is elbow and also 16 cm is x 5. Figure out the price of X …. Cm
A. 4 √2
C. 8 √2
D. 8 √3
Therefore the reason for this sign pythagoras conference global, ideally helpful and certainly will assist in learning math, which frequently makes us all around. Once the initial when we study, then all of the problematic things will probably be more comfortable.
The gist of this Pythagoras formula could be that your angled side adds up to the vertical side on both sides and a horizontal border (however, remember to get acquainted).
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http://www.jiskha.com/members/profile/posts.cgi?name=CAL
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math
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Solve n + 1 = -4
what if i have 6 1/2 ft of lumber and i only need 3/5 how much is itZ?
subtract 31 m-31=r
Andrew factored the expression 28x©ø-6x©÷-10x as 2x(14x©ø-3x©÷-5x) . But when Melissa applied the distributive law and multiplied out 2x(14x©ø-3x©÷-5x), she got 28x©ù-6x©ø-10x©...
The area of a rectangular athletic field is represented by the expression 16y²-49z² square meters. Write an algebraic expression to represent one possible set of dimensions (in the sense length times width) of the athletic field. Include correct units wit...
If g(x)=3x-5, then g inverse(x)=
Im in third grade and i dont understand colons.i have to proofread a paragraph and combine them using colons.
A piece of wood discovered in an archaeological dig was found to have lost 62% of it's carbon-14. Carbon-14 has a half-life of 5630 years. Determine it's age.
What is the energy of a photon that has the same wavelength as a 12-eV electron? (h = 6.63 × 10-34 J×s)
If three unequal capacitors, initially uncharged, are connected in series across a battery, which of the following statements is true? 1 The equivalent capacitance is greater than any of the individual capacitances. The capacitor with the smallest capacitance has the smallest ...
For Further Reading
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https://www.coursehero.com/tutors-problems/Statistics-and-Probability/8425339-It-is-reported-that-27-percent-of-American-households-use-a-cell-phone/
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math
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A. None use a cell phone as their exclusive service. (Round your answer to 4 decimal places.)
B. At least one uses the cell exclusively. (Round your answer to 4 decimal places.)
C. At least eight use the cell phone. (Round your answer to 4 decimal places.)
This question was asked on Jan 28, 2013 and answered on Jan 28, 2013.
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https://www.physicsforums.com/threads/effective-voltage-in-series-rlc-circuit.552318/
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math
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Given a series RLC circuit with a sinusoidal voltage input, find the effective voltage across each element.
1) If the effective value of the source voltage is 1 V, the effective value of the current is 1 amp.
2) i(t) lags v(t) by 45 degrees
4) w=2 rads/sec
Veff = [1/T * ∫ v^2(t) dt] ^ (1/2)
Ieff = Im/√2
Veff = Vm/√2
The Attempt at a Solution
Based on the information I know that:
v(t) = Vmsin(2t)
i(t) = Imsin(2t-45)
Not exactly sure where to go from here especially since R and C aren't given, but I'm assuming you don't need these values or can find out based on the information already given.
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https://softmath.com/algebra7.htm
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math
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Try our Free Online Math Solver!
Review of Intermediate Algebra
Text/workbook for low level and English as a second language students. Uses applications of algebra to the real world throughout. Annotation copyright Book News, Inc. Portland, Or. --This text refers to an out of print or unavailable edition of this title.
Review of Imtermediate Algebra
Reviewed by a reader, from Milpitas,
This book is recommended for any guy looking to be on top of the world of math. The book clearly and completely shows how to go about solving problems. Every problem in the book is solved in the back, step-by-step, not just giving the answers.also, it also covers a wide array of topics.
Review of Interactive Math for Introductory Algebra
Key Benefit: Interactive Mathematics is an innovative new learning system that covers the full series of developmental mathematics in an interactive, multimedia environment. Interactive Math uses animation, video, audio, graphics, and math tools to support multiple learning styles. It is a program complete with instruction, practice, applications, and assessment. Key Topics: Introduction — A brief teaching statement directs the reader's attention toward mastering a particular skill. A visual representation of the skill is also presented. Read — Book with accompanying audio (which may be disabled) addresses the needs of those who feel more comfortable reading about the concepts and skills before exploring or working problems. Watch — Visual learners can watch and listen as example problems are worked out clearly and completely by the author in a brief on-screen video. Explore — This feature offers the most interactive learning experience because one can master the skills and learn the concept through discovery.
Reviewed by nancyeve, from Orange County,
CA United States
First, just to clarify, access to the on-line portion of this workbook/CD is through the systems at Prentice Hall, via the educational institution.The only reason I did not give this 5 stars is because they are still working out some of the software bugs. A number of my classmates had problems running this program on their computers at home, though I had virtually none. The few problems I did have were just the sometimes slow response times moving from the problem sets to the syllabus.Basically, I loved using this program! The many options for learning on the computer alone helped me to fly though this class. (As of 11/01 I am still in class but well on my way to receiving an "A"). If I get stuck on a concept, there are many options for working through it from being shown a brief video, reading about it, or just being taken step by step through a problem on which I am working. One finds out immediately if their answer to a problem is right or wrong. If wrong, there are several different ways of finding out why, and actually being taken through THAT PROBLEM step by step in order to assist in understanding the concept so that the next problem is done with greater understandng and ease. All in all, I found the learning process enhanced using this program. It was and is an extremely valuable educational tool for me. We will, I am told, be using a different program next year (Algebra II), I think I will miss this one!
Reviewed by Joi Cardinal, from northern
I've never done well at math in high school or college, but now that I'm re-entering college in my 40s, I really have to learn it in order to succeed in biology and chemistry courses. Thank heavens my local community college has adopted K. Elayn Martin-Gay's phenomenal Interactive Math program as an online course. The package consists of easy to install and very easy to use software on a CD-ROM which communicates with Prentice Hall's computer, a paperback textbook which contains all the teaching material that is in the software as well as additional problem sets and chapter tests for away-from-computer use, and a detailed student handbook explaining the program and its use as well as offering many valuable study skill tips. The software is broken down by the chapter subheadings with each discrete topic covered having its own section. Each section consists of an introduction screen, then three different options for learning that suit different learning styles. If one is most comfortable with reading a traditional textbook, then the concept can be learned that way. People who learn best by watching and listening to an instructor can watch short video clips of Martin-Gay explaining each concept. Those who are most comfortable with experimenting with numbers will enjoy the explore option which provides tools for playing with numbers and deducing the concepts through the patterns of responses that emerge. Finally, each section ends with a practice set of problems to check understanding, then an assessment set of problems, the results of which are then posted to the grade book which is accessed by the professor for the class. Each chapter ends with a more lengthy test which is also posted to the gradebook. I never thought I'd enjoy math so much that I'd look forward to studying it, but this program has made all the difference. Instead feeling totally lost and only able to solve problems that are like the examples given in the textbook, I'm now perceiving math to be fun puzzles that are satisfying to work out. I sincerely hope the author goes on to create additional programs for more advanced math work in time for me to use them!
Review of Algebra: Tools for a Changing World
Reviewed by titasusan, from Fort Washington,
Maryland United States
This book is great for practice but practice only. The methods on how to solve the problems are not explained.This book is for practice and not to be confused as the textbook.
Review of Introductory Algebra
The second volume of a three-book series designed for students with introductory algebra as a prerequisite of their course. This edition emphasizes real-world applications of algebra, and includes geometric applications and exercise and problem sets.
Review of Experiencing Intermediate Algebra
A text for a one-semester course in intermediate algebra, designed to help students model real-world situations, reason mathematically, choose appropriate problem-solving methods, connect algebra to other disciplines, and communicate mathematics. Concepts are developed using numeric, graphic, algebraic, and verbal approaches. Numeric presentation emphasizes tables of values, either constructed manually or by using a calculator. Assumes students have a TI-83 graphic calculator available. The authors are affiliated with Pellissippi State Technical Community College. -- Copyright © 2000 Book News, Inc., Portland, OR All rights reserved
Review of Intermediate Algebra for College Students (5th Edition)
Angel's text is one that students can read, understand, and enjoy. With short sentences, clear explanations, many detailed worked examples, and outstanding pedagogy. Practical applications of algebra throughout make the subject more appealing and relevant for students. Key pedagogical features include: Preview and Perspective at the beginning of each chapter; Helpful Hints; Group Activities/Challenge Problems, Writing, exercises, Real-Life Application Problems; and Calculator and Graphing Calculator Corners. --This text refers to the Hardcover edition.
Reviewed by a reader, from NC United
I used this book to challenge my Intermediate Algebra course, and I passed the exams. This book explain clearly the steps to the questions.
Review of Intermediate Algebra Concepts and Applications with Algebra for College Students Sticker Package
Preface For the past half century many introductory differential equations courses for science and engineering students have emphasized the formal solution of standard types of differential equations using a (seeming) grab-bag of mechanical solution techniques. The evolution of the present text is based on experience teaching a new course with a greater emphasis on conceptual ideas and the use of computer lab projects to involve students in more intense and sustained problem-solving experiences. Both the conceptual and the computational aspects of such a course depend heavily on the perspective and techniques of linear algebra. Consequently, the study of differential equations and linear algebra in tandem reinforces the learning of both subjects. In this book we have therefore combined core topics in elementary differential equations with those concepts and methods of elementary linear algebra that are needed for a contemporary introduction to differential equations. The availability of technical computing environments like Maple, Mathematica, and MATLAB is reshaping the current role and applications of differential equations in science and engineering, and has shaped our approach in this text. New technology motivates a shift in emphasis from traditional manual methods to both qualitative and computer-based methods thatrender accessible a wider range of more realistic applications; permit the use of both numerical computation and graphical visualization to develop greater conceptual understanding; and encourage empirical investigations that involve deeper thought and analysis than standard textbook problems. Major Features The following features of this text are intended to support a contemporary differential equations course with linear algebra that augments traditional core skills with conceptual perspectives:The organization of the book emphasizes linear systems of algebraic and differential equations. Chapter 3 introduces matrices and determinants as needed for concrete computational purposes. Chapter 4 introduces vector spaces in preparation for understanding (in Chapter 5) the solution set of an nth order homogeneous linear differential equation as an n-dimensional vector space of functions, and for realizing that finding a general solution of the equation amounts to finding a basis for its solution space. (Students who proceed to a subsequent course in abstract linear algebra may benefit especially from this concrete prior experience with vector spaces.) Chapter 6 introduces eigenvalues and eigenvectors in preparation for solving linear systems of differential equations in Chapters 7 and 8. In Chapter 8 we may go a bit further than usual with the computation of matrix exponentials. These linear tools are applied to the analysis of nonlinear systems and phenomena in Chapter 9. We have trimmed the coverage of certain seldom-used topics and added new topics in order to place throughout a greater emphasis on core techniques as well as qualitative aspects of the subject associated with direction fields, solution curves, phase plane portraits, and dynamical systems. To this end we combine symbolic, graphic, and numeric solution methods wherever it seems advantageous. A healthy computational flavor should be evident in figures, examples, problems, and projects throughout the text. Discussions and examples of the mathematical modeling of real-world phenomena appear throughout the book. Students learn through modeling and empirical investigation to balance the questions of what equation to formulate, how to solve it, and whether a solution will yield useful information. Students also need to understand the role of existence and uniqueness theorems in the subject. While it may not be feasible to include proofs of these fundamental theorems along the way in a elementary course, students need to see precise and clear-cut statements of these theorems. We include appropriate existence and uniqueness proofs in the appendices, and occasionally refer to them in the main body of the text. Computer methods for the solution of differential equations and linear systems of equations are now common, but we continue to believe that students need to learn certain analytical methods of solution (as in Chapters 1 and 5). One reason is that effective and reliable use of numerical methods often requires preliminary analysis using standard elementary techniques; the construction of a realistic numerical model often is based on the study of a simpler analytical model. We therefore continue to stress the mastery of traditional solution techniques (especially through the inclusion of extensive problem sets). Computational Flavor The following features highlight the computational flavor that distinguishes much of our exposition. About 250 computer-generated graphics—over half of them new for this version of the text, and most constructed using MATLAB—show students vivid pictures of direction fields, solution curves, and phase plane portraits that bring symbolic solutions of differential equations to life. Over 30 computing projects follow key sections throughout the text. These "technology neutral" project sections illustrate the use of computer algebra systems like Maple, Mathematica, and MATLAB, and seek to actively engage students in the application of new technology. A fresh numerical emphasis that is afforded by the early introduction of numerical solution techniques in Chapter 2 (on mathematical models and numerical methods). Here and in Section 7.6, where numerical techniques for systems are treated, a concrete and tangible flavor is achieved by the inclusion of numerical algorithms presented in parallel fashion for systems ranging from graphing calculators to MATLAB. A conceptual perspective shaped by the availability of computational aids, which permits a leaner and more streamlined coverage of certain traditional manual topics (like exact equations and variation of parameters) in Chapters 1 and 5. Applications To sample the range of applications in this text, take a look at the following questions:What explains the commonly observed time lag between indoor and outdoor daily temperature oscillations? (Section 1.5) What makes the difference between doomsday and extinction in alligator populations? (Section 2.1) How do a unicycle and a two-axle car react differently to road bumps? (Sections 5.6 and 7.4) Why might an earthquake demolish one building and leave standing the one next door? (Section 7.4) Why might an eartquake demolish one building and leave standing the one next door? (Section 7.4) How can you predict the time of next perihelion passage of a newly observed comet? (Section 7.6) What determines whether two species will live harmoniously together, or whether competition will result in the extinction of one of them and the survival of the other? (Section 9.3) Organization and Content The organization and content of the book may be outlined as follows:After a precis of first-order equations in Chapter 1—with a somewhat stream-lined coverage of certain traditional symbolic methods—Chapter 2 offers an early introduction to mathematical modeling, stability and qualitative properties of differential equations, and numerical methods. This is a combination of topics that ordinarily are dispersed later in an introductory course. Chapters 3 (Linear Systems and Matrices), 4 (Vector Spaces), and 6 (Eigenvalues and Eigenvectors) provide concrete and self-contained coverage of the elementary linear algebra concepts and techniques that are needed for the solution of linear differential equations and systems. Chapter 6 concludes with applications of diagonizable matrices and a proof of the Cayley-Hamilton theorem for such matrices. Chapter 5 exploits the linear algebra of Chapters 3 and 4 to present efficiently the theory and solution of single linear differential equations. Chapter 7 is based on the eigenvalue approach to linear systems, and includes (in Section 7.5) the Jordan normal form for matrices and its application to the general Cayley-Hamilton theorem. This chapter includes an unusual number of applications (ranging from railway cars to earthquakes) of the various cases of the eigenvalue method, and concludes in Section 7.6 with numerical methods for systems. Chapter 8 is devoted to matrix exponentials with applications to linear systems of differential equations. The spectral decomposition method of Section 8.3 offers students an especially concrete approach to the computation of matrix exponentials. Our treatment of this material owes much to advice and course notes provided by Professor Dar-Veig Ho of the Georgia Institute of Technology. Chapter 9 exploits linear methods for the investigation of nonlinear systems and phenomena, and ranges from phase plane analysis to applications involving ecological and mechanical systems. Chapters 10 treats Laplace transform methods for the solution of constant-coefficient linear differential equations with a goal of handling the piecewise continuous and periodic forcing functions that are common in engineering applica
Review of HBJ Algebra 1
Reviewed by Tom, from Boston
Excellent no nonsense book BUT I did find a couple errors that will drive students nuts...page 303 top, 3 not right.page 150 and 151, numbers 22 and 38 can not be solved. I actually got the author on the phone who said "the answer is the empty set" which in my opinion just means that the author goofed and made problems that couldn't be solved.This far exceeds all other algebra books I've seen. Old but still excellent.
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https://www.rcsb.org/structure/3T60
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math
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Design, synthesis, and evaluation of 5'-diphenyl nucleoside analogues as inhibitors of the Plasmodium falciparum dUTPase.Hampton, S.E., Baragana, B., Schipani, A., Bosch-Navarrete, C., Musso-Buendia, J.A., Recio, E., Kaiser, M., Whittingham, J.L., Roberts, S.M., Shevtsov, M., Brannigan, J.A., Kahnberg, P., Brun, R., Wilson, K.S., Gonzalez-Pacanowska, D., Johansson, N.G., Gilbert, I.H.
(2011) ChemMedChem 6: 1816-1831
- PubMed: 22049550
- DOI: 10.1002/cmdc.201100255
- Primary Citation of Related Structures:
3T60, 3T64, 3T70, 3T6Y
- PubMed Abstract:
Deoxyuridine 5'-triphosphate nucleotidohydrolase (dUTPase) is a potential drug target for malaria. We previously reported some 5'-tritylated deoxyuridine analogues (both cyclic and acyclic) as selective inhibitors of the Plasmodium falciparum dUTPase ...
Deoxyuridine 5'-triphosphate nucleotidohydrolase (dUTPase) is a potential drug target for malaria. We previously reported some 5'-tritylated deoxyuridine analogues (both cyclic and acyclic) as selective inhibitors of the Plasmodium falciparum dUTPase. Modelling studies indicated that it might be possible to replace the trityl group with a diphenyl moiety, as two of the phenyl groups are buried, whereas the third is exposed to solvent. Herein we report the synthesis and evaluation of some diphenyl analogues that have lower lipophilicity and molecular weight than the trityl lead compound. Co-crystal structures show that the diphenyl inhibitors bind in a similar manner to the corresponding trityl derivatives, with the two phenyl moieties occupying the predicted buried phenyl binding sites. The diphenyl compounds prepared show similar or slightly lower inhibition of PfdUTPase, and similar or weaker inhibition of parasite growth than the trityl compounds.
Division of Biological Chemistry and Drug Discovery, College of Life Science, University of Dundee, Sir James Black Centre, Dundee DD1 5EH, UK.
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https://www.slideserve.com/urania/identify-name-and-draw-points-lines-segments-rays-and-planes
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math
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Objectives. Identify, name, and draw points, lines, segments, rays, and planes. Apply basic facts about points, lines, and planes. Vocabulary. undefined term point line plane collinear coplanar segment endpoint ray opposite rays postulate.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Identify, name, and draw points, lines, segments, rays, and planes.
Apply basic facts about points, lines, and planes.
undefined term point
ray opposite rays
The most basic figures in geometry are undefined terms, which cannot be defined by using other figures. The undefined terms point, line, and plane are the building blocks of geometry.
Points that lie on the same line are collinear. K, L, and M are collinear. K, L, and N are noncollinear. Points that lie on the same plane are coplanar. Otherwise they are noncoplanar.
Example 1: Naming Points, Lines, and Planes
A. Name four coplanar points.
A, B, C, D
B. Name three lines.
Check It Out! Example 1
Use the diagram to name two planes.
PlaneRand plane ABC.
Example 2: Drawing Segments and Rays
Draw and label each of the following.
A. a segment with endpoints M and N.
B. opposite rays with a common endpoint T.
Check It Out! Example 2
Draw and label a ray with endpoint M that contains N.
A postulate, or axiom, is a statement that is accepted as true without proof. Postulates about points, lines, and planes help describe geometric properties.
Example 3: Identifying Points and Lines in a Plane
Name a line that passes through two points.
Check It Out! Example 3
Name a plane that contains three noncollinear points.
Possible answer: plane GHF
Recall that a system of equations is a set of two or more equations containing two or more of the same variables. The coordinates of the solution of the system satisfy all equations in the system. These coordinates also locate the point where all the graphs of the equations in the system intersect.
An intersection is the set of all points that two or more figures have in common. The next two postulates describe intersections involving lines and planes.
Use a dashed line to show the hidden parts of any figure that you are drawing. A dashed line will indicate the part of the figure that is not seen.
Example 4: Representing Intersections that you are drawing. A dashed line will indicate the part of the figure that is not seen.
A. Sketch two lines intersecting in exactly one point.
B. Sketch a figure that shows a line that lies in a plane.
Check It Out! that you are drawing. A dashed line will indicate the part of the figure that is not seen. Example 4
Sketch a figure that shows two lines intersect in one point in a plane, but only one of the lines lies in the plane.
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CC-MAIN-2017-51
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https://algosim.org/doc/arccoth.html
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math
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The inverse hyperbolic cotangent function.
xis a real or complex number
arccoth is the inverse of the hyperbolic cotangent function. For real numbers, the domain is ℝ ∖ [−1, 1]. It is defined by
arccoth(z) = ln((z + 1)/(z − 1)) / 2
for all complex
z. This formula is also used for real numbers in (−1, 1).
This function is also called
arcoth (area hyperbolic cotangent) in the literature. Some authors claim that the name
arccoth is a misnomer, but this depends crucially on how you view the connections between the trigonometric and the hyperbolic functions and their (restriction) inverses. One can argue that the name
arccoth makes perfect sense.
0.385968416453 − 1.57079632679⋅i
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https://www.mathworks.com/matlabcentral/answers/44853-i-have-simulink-model-with-many-parameters-and-i-want-to-set-thes-parameters-in-m-file-and-then-cont
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math
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I have simulink model with many parameters and I want to set thes parameters in M-file and then control them from the simulink model, for example by editing or clearing these parameters via block has link directly with the Mfile
2 views (last 30 days)
Ilham Hardy on 31 Jul 2012
If the blocks you tried to explain are initialize, clear, and edit blocks (green, red, and blue), they are not entirely empty.
It is basically masked subsystems with callbacks; To check what callback each block has, do the following:
1. Right-click the subsystems.
2. Select "Block Properties"
3. select "callbacks" tab
In this case, each subsystem has a callback "OpenFcn" which will be executed when one tries to open the subsystems (double-click).
More Answers (1)
Sumit Tandon on 30 Jul 2012
Edited: Sumit Tandon on 30 Jul 2012
What is your requirement?
If you want to control model parameters, you could do that by declaring model parameters as variables in MATLAB base workspace and then control their values. See: http://www.mathworks.com/help/releases/R2012a/toolbox/simulink/ug/f13-82509.html
If you want to write signal values or some text to a MATLAB file, you could look at ways to create text file from Simulink model. See: http://www.mathworks.com/support/search_results.html?q=simulink+text+file
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CC-MAIN-2022-27
| 1,289
| 15
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https://www.theguardian.com/science/2020/dec/28/can-you-solve-it-the-count-reaches-twenty-twenty-one
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math
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Count von Count will be fizzing with excitement. For the first time since 1920, the coming year, 2021, consists of two ascending, consecutive numbers. Enjoy this ‘counting date’ while it lasts, people! It ain’t going to happen again for another hundred and one years.
Today’s puzzles reveal more arithmetical patterns concerning 2021.
1. Countdown conundrum
The first question is an annual ritual. Fill in the blanks in the following equation so it makes arithmetical sense:
10 9 8 7 6 5 4 3 2 1 = 2021
You are allowed to use any of the basic mathematical operations, +, –, x, ÷, and as many brackets as you like. An answer might look something like (10 – 9 + 8) x (7 – 6 – 5)/(4 + 3 + 2 + 1) = 2021, but not this one since the equation is incorrect.
There are many correct answers – try to find the most elegant one.
2. Inder’s enigmas
Inder J Taneja, a retired maths professor from Brazil, likes to find ways to describe the new date using combinations of the same digit. For example, here’s how he does it with 1.
(1+1)11 −(1+1+1)(1+1+1) = 2021
Can you find combinations of 2’s, 3’s, 4’s 5’s, 6’s, 7s, 8’s and 9’s that also equal 2021? You are only allowed to use at most ten digits per equation. (Try at least one of them.) But you can concatenate, i.e, place two or more digits together in the same number, as above with 11.
3. Marek’s mindbender
The Polish puzzle creator Marek Penszko sent in the grid puzzle below, which you can print out here.
You must fill in each of the nine empty cells so that all the equations are correct. Each cell requires a single digit. Since 0, 1 and 2 are already visible, the only digits that can appear in the empty cells are the digits from 3 to 9, some of which appear more than once. The calculations are to be done strictly from left to right, or from top to bottom (ie. ignore operator precedence). [note: the ‘:’ is the symbol for division.]
I’ll be back at 5pm UK with a selection of my favourite 2021 equations and answers to the puzzles. Please fill the comments below the line with as many numerical curiosities about 2021 as you can!
Finally, I’d like to wish the readers of this column a Happy New Year (in four days time) and say thank you for your continued support. The column totalled almost 3 million views in 2020. If you want to browse through the archive, the top five columns in order were:
I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
I’m the author of several books of puzzles, most recently the Language Lover’s Puzzle Book.
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CC-MAIN-2022-40
| 2,637
| 18
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https://writingservice.top/2021/06/10/how-to-solve-physics-problem_53/
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math
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Math / physics problem solver this program solves simple math and physics problems stated in english. 18x24collection: so that good conclusion for essay is my three-step energy solution to solve oscillation problem in physics: then, the snack bar business plan application of the kinematic equations and the problem-solving page 2/10. transfer examples of a thesis all important data and information the fast food essay systematically onto the diagram. each of these modes supports students' efforts to solve physics how to solve physics problem problems. how to write a persuasive speech outline if the string not bend, it's possible if only the string stuck problem solving matrix at nail how to solve physics problem on c point then goes around to d, it means the height of d is a-b. the first step sample research paper on bullying is to how to solve physics problem identify the physical principles, the knowns, and the unknowns involved in the problem. the above cause and effect thesis example method, called solving systems word problems worksheet a fully coupled approach, assumes that all of the couplings between the physics must be considered at the same time how to solve physics problem mark saroufim. the main points in this problem are the psychology critical thinking detailed vector diagram and the choice of the wall as the pivot point in calculating the torques. draw a clear and large diagram. determine what type of problem it is. learn how to solve problems that have free body diagrams! how to solve physics problems.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487582767.0/warc/CC-MAIN-20210612103920-20210612133920-00354.warc.gz
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CC-MAIN-2021-25
| 1,541
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https://poca.pw/problem-contract-answer-law/71064-vsntwb.php
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math
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For that only existing contract is recognised throughout example of question answer contract law problem and comparative negligence? Your membership is on hold because of a problem with your last payment. This sum up for compensation, either bilateral offer or python programming is contract law problem question model answer uk.
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https://ecommons.cornell.edu/handle/1813/67816
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math
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Network Models and Information Diffusion
The study of networks in such diverse areas as biology, technology, and social sciences has given rise to the interdisciplinary field of network science. Many real-world networks exhibit strongly connected communities and a degree distribution that follows a power law. This thesis explores these two topics - community structure and power law distributions - as they relate to network models and the diffusion of information on networks. We first consider the generation of heavy-tailed distributions in stochastic processes. We give a system of stochastic differential equations in which processes grow at an exponential rate, but are reset at exponentially distributed times. We show that this system has a stationary solution which is regularly varying. It is known that networks with a power law degree distribution are produced under the preferential attachment model, where edges are attached with preference to nodes of high degree. We analyze the effect of community structure on the degree distribution of a community-aware preferential attachment model. We also consider a generative network model where the metric for edge formation is not degree but the number of common neighbors. We further study the effect of community structure on information diffusion in networks. Under the Susceptible-Infected-Susceptible model, we show that the epidemic threshold of a network is closely related to the epidemic threshold of its strongest community. We consider the lifetime of an infection on a growing preferential attachment network and show that the lifetime distribution has heavier tails on the growing network than on static networks.
Statistics; Applied mathematics; Information diffusion; networks; Operations research; preferential attachment; Communities; Epidemics; Stochastic Processes
Saloff-Coste, Laurent Pascal; Chen, Yudong; Ghosh, Souvik
Operations Research and Information Engineering
Ph.D., Operations Research and Information Engineering
Doctor of Philosophy
dissertation or thesis
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CC-MAIN-2021-31
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https://www.lessonplanet.com/teachers/addition-practice-7-adding-4-numbers
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math
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Saxon Math Intermediate 5 - Student Edition
Expand your resource library with this collection of Saxon math materials. Covering a wide range of topics from basic arithmetic and place value, to converting between fractions, decimals, and percents, these example problems and skills...
4th - 6th Math CCSS: Adaptable
Practical Problems Involving Decimals
After discussing decimals and "going shopping" in the classroom, young mathematicians are given four practical word problems that require them to estimate their answers, given specific information. The highlight of the lesson is having...
5th - 7th Math CCSS: Adaptable
Performance-Based Assessment Practice Test (Grade 3 Math)
Put the knowledge of your third grade mathematicians to the test with this practice Common Core assessment. Offering a change from typical standardized math tests, 3rd graders are asked to answer not only multiple choice questions but...
3rd Math CCSS: Designed
Deciphering Word Problems in Order to Write Equations
Help young mathematicians crack the code of word problems with this three-lesson series on problem solving. Walking students step-by-step through the process of identifying key information, creating algebraic equations, and finally...
5th - 8th Math CCSS: Adaptable
Solve Real World Problems by Finding the Area of a Rectangle
Young mathematicians learn to apply their understanding of area in real-world contexts with the final video of this series. Multiple examples are presented that demonstrate different situations that involve calculating the area of a...
8 mins 2nd - 4th Math CCSS: Designed
Solve Multiplication Problems: Using Repeated Addition
While young mathematicians are still working to memorize their multiplication facts, teach them how to use repeated addition when solving multiplication problems. The second video in a series models this skill with multiple examples,...
5 mins 2nd - 4th Math CCSS: Designed
What Members Say
- Viola H., Teacher
- Lafe, AR
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s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988721606.94/warc/CC-MAIN-20161020183841-00222-ip-10-171-6-4.ec2.internal.warc.gz
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http://quatr.us/math/geometry/rhombus.htm
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math
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What is a Rhombus?
A rhombus is a kind of quadrilateral that has two sides that are parallel to each other, and another two sides that are parallel to each other. A rhombus is a special kind of parallelogram, and squares and rectangles are special kinds of rhombus.
To figure out the perimeter of the rhombus, you can add the lengths of all the sides together. To figure out the area of a rhombus, you have to cut it into shapes that are easier to figure out. You want to cut it into a rectangle and two right triangles. Draw a line from one angle so that it is perpendicular to the opposite side, and another line from the opposite angle that is parallel to your first line, and also perpendicular to the opposite side. This will make a rectangle and two identical right triangles (one of them upside-down).
The area of the rectangle is the height multiplied by the width. The areas of the right triangles are the height multiplied by the width, divided by two. Add the areas of the triangles and the rectangle together, and you've got the area of your rhombus. (Because the two triangles are the same, you can just multiply the height by the width once and then add that to the area of the rectangle).
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https://noraagreene.com/2019/04/25/to-write-is-right-a-follow-up/
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math
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In the beginning of this school year, I wrote a post called: In Math Class: To Write is Right. It discusses some thoughts on how we use writing to express ourselves, and how we use the written word in today’s world. I also promised to follow-up with some strategies that I have tried, and want to try, in order to help my students practice writing. Here is that follow-up:
In class, I have incorporated writing in a few small activities. In the beginning of the school year, I asked each student to write down goals for math class for the upcoming year.
Some responses included:
“To get better at math.”
“I want to not fail and work harder.”
“Have fun and enjoy math! 🙂 ”
Responses tended to be shorter, and more phrase-like, especially from my Freshmen classes. Students wrote these responses on Post-It notes, and we displayed them on large posters in the room. This way, students are always able to refer back to their original goals. It holds a certain accountability when they can see their own words written in their own handwriting.
Phrases, however, aren’t enough. I want students to gain a level of sophistication in how they express themselves in math class (appropriate for each individual, of course). So, I have begun to ask more thought-provoking questions about our work throughout the year, asking students to write down their answers using complete sentences. Furthermore, I have tried to make my questions more specific, rather than vague. I have come to realize that specific questions elicit more specific answers, while vaguer questions elicit more vague answers.
Most recently, I asked my Algebra students: “If you check your solution to a system of linear equations, why does the solution work in both equations?” Students know to substitute their coordinate point in each equation to see if it “works,” but I really wanted them to understand why. It also helps bridge the gap between the graphical representation and the algebraic representation of a system of linear equations.
Here are some responses:
“The x value and the y value work in both equations because they are the same in both equations.”
“Because there are three different methods of doing this type of question, and you need to check your work to see if you get this equation/problem right.”
“The solution is the point of intersection of the two lines.”
“It is the same equation written differently.”
“It’s linear, so they have the same slope.”
“Both equations share the same x value and y value.”
“They both have a point in which they cross.”
While some responses are a bit more reasonable than others, I was pleased to see students using decent vocabulary. They were also writing slightly more complex sentences than their phrases from the beginning of the year. It’s clear they have some sense of what the answer means to my question, even if their answers need more fine-tuning.
In my Algebra 2 class, I asked the following question: “Which should always have a higher value: sine or cosecant of the same angle? Why?”
Here are some responses:
“Cosecant, because the hypotenuse is the longest side of the triangle and for cosecant the hypotenuse is on the top.”
“The cosecant should be higher because it is the flipped of sine.”
“Cosecant has to be higher, because the hypotenuse is the longest side of the triangle.”
As we can see, they were trying to express the concept that cosecant is the reciprocal of sine, which brings the hypotenuse, the longest side of the right triangle, to the numerator. They used some good vocabulary, while other vocabulary could be expanded upon (i.e. use “reciprocal” instead of “flipped,” or “numerator” instead of “the top”), but they were definitely trying to describe the differences between sine and cosecant.
As the Math Research director at our school, I advise students throughout the year in researching a topic in advanced mathematics. These students also write a 10-15 page research paper and prepare a presentation for a local competition involving dozens of school districts and over 400 students. This is no easy task. These students struggle to begin their papers, because they have found that they have never written an essay about math before. It also takes some practice interweaving equations and mathematical concepts throughout the paper, without sounding like a textbook. I have worked, and continue to work, to help my students use detailed and clear explanations, while using proper vocabulary to describe the mathematics that they are researching.
The trend between my classes and my math research students is that students feel more comfortable, and are more adept at, writing about math in a straight-forward, fact generating way, rather than truly analyzing the concepts. We could all use a little more practice in this area. Students can definitely learn to write more analytically about mathematics, and teachers can also learn to assign specific writing prompts in order to elicit detailed, more complex responses. I hope to continue to practice helping students become better, more analytical writers in the field of mathematics for years to come.
One thought on “To Write Is Right: A Follow-Up”
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https://www.topperlearning.com/cbse-class-7-mathematics/fractions-and-decimals/addition-and-subtraction-of-fractions
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math
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CBSE Class 7 Maths Addition And Subtraction Of Fractions
- subtract the sum of 11 and 5 from 20.
- Hi 1)Please answerthe following question 2)please explain the cocept,logic and the thought process to solve this question 3)please tell how much time a 7th class student should take to solve this in any competitive exam?
- Add -3/17 and -6/51
- Shobhit spent ₹153 and 75 paise on Monday, ₹250 and 50 paise on Tuesday and ₹ 85 and 9 paise on Wednesday. If he had a total amount equal to ₹ 500, find tha amount left with him?
- Find the sum of the following fractions : (a) (b)
- Simplify the following: (a) ++ (b)
- Ram ate kg apples and kg grapes in a day. What is the total weight of fruits consumed by him?
- Add the following: (a) (b)
- Solve : (a) + (b)
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s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670601.75/warc/CC-MAIN-20191120185646-20191120213646-00273.warc.gz
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https://books.google.de/books?id=iwNRAAAAMAAJ&dq=editions:ISBN0262032937&hl=de&output=html_text&source=gbs_book_other_versions_r&cad=5
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math
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Multi-objective optimization using evolutionary algorithms
John Wiley & Sons, 12.07.2001 - 497 Seiten
Evolutionary algorithms are relatively new, but very powerful techniques used to find solutions to many real-world search and optimization problems. Many of these problems have multiple objectives, which leads to the need to obtain a set of optimal solutions, known as effective solutions. It has been found that using evolutionary algorithms is a highly effective way of finding multiple effective solutions in a single simulation run.
* Comprehensive coverage of this growing area of research
* Carefully introduces each algorithm with examples and in-depth discussion
* Includes many applications to real-world problems, including engineering design and scheduling
* Includes discussion of advanced topics and future research
* Can be used as a course text or for self-study
* Accessible to those with limited knowledge of classical multi-objective optimization and evolutionary algorithms
The integrated presentation of theory, algorithms and examples will benefit those working and researching in the areas of optimization, optimal design and evolutionary computing. This text provides an excellent introduction to the use of evolutionary algorithms in multi-objective optimization, allowing use as a graduate course text or for self-study.
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Multi-Objective Optimization using Evolutionary Algorithms
Eingeschränkte Leseprobe - 2001
MULTI-OBJECTIVE OPTIMIZATION USING EVOLUTIONARY ALGORITHMS
Keine Leseprobe verfügbar - 2010
assigned fitness best non-dominated better calculated choose chosen clusters computational complexity constraint violation convergence convex corresponding created crossover operator decision variable space discussed distribution dominated solutions elitist equation Euclidean distance evaluated evolution strategy evolutionary algorithms Evolutionary Computation external population feasible solution find multiple genetic algorithm genetic operations global goal programming hypercube infeasible solutions mating pool maximum method metric Minimize minimum MOEAs multi-objective evolutionary algorithms multi-objective optimization problem mutation operator mutation strength niche count non-dominated front non-dominated set non-dominated solutions nonconvex NPGA NSGA NSGA-II number of solutions o"Share objective function values objective space obtained solutions offspring population optimum parent solutions Pareto Pareto-optimal region Pareto-optimal set Pareto-optimal solutions performed population members random real-parameter schema search space selection operator set of solutions shown in Figure shows solving SPEA Step strategy string studies subpopulation suggested technique test problems tournament selection trade-off solutions true Pareto-optimal front VEGA WBGA weight vector
Alle Ergebnisse von Google Books »
Data Mining and Knowledge Discovery with Evolutionary Algorithms
Alex A. Freitas
Eingeschränkte Leseprobe - 2002
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s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251778168.77/warc/CC-MAIN-20200128091916-20200128121916-00463.warc.gz
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CC-MAIN-2020-05
| 3,139
| 23
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http://www.wyzant.com/33129_algebra_tutors.aspx
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math
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Miami, FL 33129
Science and Math expertise! (College & High School)
...If you haven't figured it out already, I enjoy learning (and teaching). I have been tutoring for over 5 years now in subjects that include: SAT, SAT II [Chemistry, Math I , Math II), Algebra
I and II, Pre-calculus, Calculus I, Chemistry, Biology, Organic Chemistry,...
including algebra 1 and algebra 2
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s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1409535919886.18/warc/CC-MAIN-20140909054759-00432-ip-10-180-136-8.ec2.internal.warc.gz
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CC-MAIN-2014-35
| 373
| 5
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https://forums.macrumors.com/threads/jailbreak-2g-no-sim-how.1032024/
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math
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I have a first gen. iphone that I got from someone. He restored it and now I have to jailbreak it but I have no sim. He had one from atnt, but doesn't have it anymore, so I need to jailbreak (and maybe also unlock?) it without a sim card. I'm very new at this, so I very appreciate your help!
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s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583657097.39/warc/CC-MAIN-20190116073323-20190116095323-00356.warc.gz
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CC-MAIN-2019-04
| 292
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http://www.usnpl.com/addr/aacountyresult.php?countyid=3059
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math
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Huntington Herald-Dispatch (A)
Huntington HuntingtonNews.Net (A)
Wayne Wayne County News (A)
Huntington Marshall Univ - College
Charleston WOWK - TV
Huntington WSAZ - TV
WVHU 800 AM News Talk
USNPL has address downloads for US Newspapers and TV Stations.
USNPL - Facebook
USNPL - Google+
USNPL - Twitter
USNPL - Linkedin
Did you know you can check the Facebook or Twitter page for a listing by just clicking on the bold (F) or (T)?
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http://bullythebear.blogspot.com/2010_04_01_archive.html
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math
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Since in the real world, there are no teachers to check for you and no answers behind the textbook to assure that you're right, we always have to try solving the problem using different methods. If all the methods arrive at the same conclusion, then chances are, you're right until someone proves you wrong.
I tried using numbers to have a feel of how it works:
Let's say I have 10 lots of ARA shares @ $1.00 average price. Since the dividend is declared at $0.025 per share, or $25 per lot, I'll have $250 dividend for my 10 shares. The closing price a day before XA was $1.15, so I can calculate what's my profits so far.
My inventory before XA: 10 lots of ARA shares bought at $1.00
Sell price : 1.15
Profit from shares : (1.15 - 1) x 10,000 = $1,500
Dividend : $250
Total profit before XA: $1,750 (1500+250)
Now, what happens after XA? The price of ARA drops because there are more shares floating around due to the 1 for 5 bonus issue. This means that for every 5 lots of ARA shares you own, you will now have 1 lot of bonus ARA shares. The price drops accordingly to reflect the fact that the market value of ARA remains the same. Do note that only the ordinary shares are entitled to dividend; Bonus shares are not entitled to this round of dividend but they are eligible for future dividends.
Let y be the price of ARA after XA.
My Inventory after XA: 10 lots of ARA bought at $1.00 PLUS 2 lots of bonus shares
Sell price : y
Dividend : $250
Profit from the original 10 lots of shares : (y - 1.00) x 10,000
Profit from the bonus share : y x 2,000
Total profit : 10,000y + 2,000y -10,000+ 250 = 12,000y - 9,750
Since y should represent the theoretical price such that my profit/loss before and after XA is to be the same, I equate the two profits,
12,000y - 9,750 = 1,750
Solving, y = 0.95833
Hence $0.958 is the price such that my profits before XA and after XA is the same.
I noticed that several terms can be removed without changing the answer. First of all, dividends doesn't matter as both sides of the equation contain the $250 divy term. Next, even if I tried different no. of shares bought at different price, it doesn't change the answer. I changed all the variables to algebra, and confirmed that the calculation remains the same. Without bothering you with the details, here's the much simplified formula:
Since the closing price is 1.15,
Price = 5 x 1.15/6 = $0.958
Not really a calculation. It's more like to show you that chartnexus had worked out what I had worked out in the morning. The chart clearly shows that the price before XA, on 28th Apr, had a closing of $0.958 whereas it was 1.15 just the day before the software updated the changes.
|The closing price a day before XA clearly shows $0.958 instead of $1.15|
The theoretical price is definitely different from the closing price. I cannot predict how the price will close and I know that the theoretical price will only be there for a fleeting moment. So, isn't it a waste of time trying to calculate something that only exists for a moment?
Not to me. I take great pleasure in such intellectual masturbation. It's like an unreachable itch behind the back, irritating me until I can solve it :)
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https://philosophynews.com/algebraic-propositional-logic/
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math
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[Revised entry by Ramon Jansana on May 20, 2022.
Changes to: Main text, Bibliography]
George Boole was the first to present logic as a mathematical theory in algebraic style. In his work, and in that of the other algebraists of the algebraic tradition of logic of the nineteenth century, the distinction between a formal language and a mathematically rigorous semantics for it was still not drawn. What the algebraists in this tradition did was to build algebraic theories (of Boolean algebras, and relation algebras) with among other interpretations a logical one….
Originally appeared on Stanford Encyclopedia of Philosophy Read More
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https://nz.erf-est.org/4591-l-mites-matem-ticos.html
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math
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The term that we are going to analyze now is interesting to emphasize that it is formed by the union of two words that have their etymological origin in ancient languages. Thus, limits comes from the Latin word limes, which is the genitive of limit which can be translated as border or border of something.
On the other hand, mathematicians is a word that has its origin cited in the Greek and specifically in the term mathema. This can be defined as the study of a particular topic or issue.
The division which marks a separation between two regions is known as limit . This term is also used to name a restriction or limitation, to the extent that can be reached from the physical aspect and to the point at which a time period arrives.
For the math , a limit is a magnitude to which the terms of an infinite sequence of magnitudes progressively approach. A mathematical limit , therefore, it expresses the tendency of a function or a sequence as its parameters approach a certain value.
An informal definition of the mathematical limit indicates that the limit of a function f (x) is T when x tends to s , provided that you can find for each occasion a x near s so that the value of f (x) be so close to T as intended.
However, in addition to the quoted limit, we cannot ignore that there are others that are very important in the field of Mathematics. Thus, we can also talk about the limit of a sequence that can be existing or unique and divergent, in the event that the terms of that sequence do not converge at any point.
In the same way, we must also talk about another series of mathematical limits such as the limit of a succession of sets or that of topological spaces. Among the latter are those that refer to filters or networks.
Finally, we cannot ignore the existence of what is known as the Banach Limit. The latter, which is called the Polish mathematician Stefan Banach, is the one that revolves around what is known as Banach space. This is a fundamental piece of what functional analysis is and can be defined as the space where there are functions that have an infinite dimension.
Like other mathematical concepts, the limits meet various general properties that help simplify the calculations . However, it can be very difficult to understand this idea since it is an abstract concept.
In mathematics, the notion is linked to the variation of values that take the functions or sequences and with the idea of approximation between numbers . This tool helps to study the behavior of the function or succession when they approach a given point.
The formal definition of the mathematical limit was developed by various theorists around the world over the years, with works that formed the basis of the Infinitesimal calculation .
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http://www.ipadforums.net/threads/uses-in-education.16512/
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math
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Hello from the Twin Cities, I'm mainly interested in using the iPad as a tool while teaching college mathematics courses: - displaying PDF lecture slides through the VGA out. GoodReader seems to work well for this. - displaying Mathematica through the VGA out. Expedition is a browser that has VGA support, and I can run Mathematica via Wolfram|Alpha. - My laptop would become completely unemployed (except for syncing) if I could compile LaTeX on the iPad. Have read about LatexLab for Google Docs and some remote TeX compilers, but would enjoy hearing about other solutions. Also, would enjoy hearing folks' experiences with ssh and Dropbox (of course, I'll search the forum for these things). Aside from all that, I'm interested in seeing what this thing can do, especially in conjunction with our iPod touch, iPhones, Mac laptops, etc. I've been a steady user of Apple products since my parents' chugging Apple //c, and the Apple IIGS they got me instead of a Macintosh, because it had a color screen.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583792338.50/warc/CC-MAIN-20190121111139-20190121133139-00205.warc.gz
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CC-MAIN-2019-04
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https://journals.tubitak.gov.tr/math/vol42/iss3/40/
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math
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In this paper, we introduce the concepts of order-congruences and strong order-congruences on an ordered semihypergroup $S,$ and obtain the relationship between strong order-congruences and pseudoorders on $S.$ Furthermore, we characterize the (strong) order-congruences by the $\rho$-chains, where $\rho$ is a (strong) congruence on $S.$ Moreover, we give a method of constructing order-congruences, and prove that every hyperideal $I$ of an ordered semihypergroup $S$ is congruence class of one order-congruence on $S$ if and only if $I$ is convex. Finally, we define and study the strong order-congruence generated by a strong congruence. As an application of the results of this paper, we solve an open problem on ordered semihypergroups given by Davvaz et al.
Ordered semihypergroup, pseudoorder, (strong) order-congruence, $\rho$-chain
TANG, JIAN; LUO, YANFENG; and XIE, XIANGYUN
"A study on (strong) order-congruences in ordered semihypergroups,"
Turkish Journal of Mathematics: Vol. 42:
3, Article 40.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/40
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CC-MAIN-2023-50
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http://mogenalirico.blogspot.com/2008/08/mistake.html
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math
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Meet me here!!
Saturday, August 2, 2008
Yes..it's a mistake.I know it's a mistake but there's certain thing in life, when u know its a mistake but you not really know it's a mistake because the only way to really know it's a mistake its to make a mistake and look back and say yes that was a mistake.So really the bigger mistake would be they not made a mistake because they not really knows something are mistake or not.And damn it.. i made no mistake. I've done all of all this, my life, my career, my relationship mistake free.Does any of this make sense to you!!!!!!.
har har harr..i don't know how many word mistake i write.Can u spot that for me..:)
Morale of the story...Here the things about mistake.Sometimes even you know it was a mistake but u got to make it anyway..Believe me, dont afraid to make a mistake but keep improving yourself and learn from the mistake but please don't make a same mistake twice because that was a real mistake. Bluekkk!!!!...penin kalo baca balik..bluekkkkk!!!
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218193284.93/warc/CC-MAIN-20170322212953-00464-ip-10-233-31-227.ec2.internal.warc.gz
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CC-MAIN-2017-13
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https://suvivaarla.com/cash-drawer-count-sheet-template/
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math
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Cash Drawer Count Sheet Template. We tried to get some amazing references about free daily cash register balance sheet template and cash drawer reconciliation sheet for you. Cash drawer balance sheet template.
30 money drawer count sheet. Cash count sheet template counting worksheets bookkeeping templates cash enter your organization name and logo to get started. This free inventory count sheet can be used by a business to produce sheets for recording the results of a physical inventory count.
4 free math worksheets second grade 2 counting money counting money canadian nickels dimes qu … 30 money drawer count sheet. It was coming from reputable online resource which we like it.
Statistically, Only About 15% Of People Earn Money On Their Hobbies.
You don’t have to spend too much time or dime in doing so because our cash drawer tally sheet has everything you need. The template is specially made by our professionals to set things up from tables to its contents. Feel free to use 3 available options;
Cash In Cash Out Sheet.
But it is never too late to create. The cash count sheet provides a summary of. The cashier balance sheet template contains the name of the cashier and the signature, date, drawer total, counted total, cash total, and over/short amount.
We Tried To Get Some Amazing References About Free Daily Cash Register Balance Sheet Template And Cash Drawer Reconciliation Sheet For You.
When autocomplete results are available use up and down arrows to review and enter to select. Simple cash drawer count sheet. Beginning of shift cash count time:end of shift cash count time:amountamount$ 0.01 $$ 0.01 $$ 0.05 $$ 0.05 $$ 0.10 $$ 0.10 $$ 0.25 $$ 0.25 $$ 0.50.
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https://quizlet.com/6509824/chapter-16-flash-cards/
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math
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How can we help?
You can also find more resources in our
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What is 1 + 3?
Reflect graph about x-axis
Reflect graph about y-axis
Keep all of graph above or on x-axis reflect all of graph below x-axis about the x-axis
Reflect the right side of graph to left keep right side but toss the old left side
Inverse/ f(x)=(x−3)³ + 1 → f⁻¹(x)=y=³√x-1+3
symmetric about y=x
exchange x+y values, x+y variables, domain + range
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http://books.google.com/books?id=POG-LSUgYckC&source=gbs_similarbooks_r&cad=3
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math
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The Theory of Homogeneous Turbulence
Cambridge University Press, 1953 - Mathematics - 197 pages
This is a reissue of Professor Batchelor's text on the theory of turbulent motion, which was first published by Cambridge Unviersity Press in 1953. It continues to be widely referred to in the professional literature of fluid mechanics, but has not been available for several years. This classic account includes an introduction to the study of homogeneous turbulence, including its mathematic representation and kinematics. Linear problems, such as the randomly-perturbed harmonic oscillator and turbulent flow through a wire gauze, are then treated. The author also presents the general dynamics of decay, universal equilibrium theory, and the decay of energy-containing eddies. There is a renewed interest in turbulent motion, which finds applications in atmospheric physics, fluid mechanics, astrophysics, and planetary science.
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anemometer approximately asymptotic average Batchelor and Townsend Central Limit Theorem correlation functions curves described determined different Reynolds numbers dynamical equation effect energy spectrum energy transfer energy-containing eddies energy-containing range equilibrium range exist experimental field of turbulence final period flatness factor fluid Fourier analysis Fourier components Fourier transform function E(K G. I. Taylor gauze homogeneous turbulence hypothesis inertia forces inertial subrange initial conditions integral isotropic turbulence joint-probability distribution kinetic energy large Reynolds numbers large wave-numbers linear measurements motion associated Navier-Stokes equation normal distribution obtained parameters period of decay points pressure probability density function probability distribution problem Proc product mean values quantities quasi-equilibrium range of wave-numbers relation scalar function solution spectrum function spectrum tensor statistically independent Stewart and Townsend stream theoretical theory transfer of energy turbulent motion universal equilibrium variation vector velocity components velocity correlation velocity field velocity-product mean values viscous forces vorticity wave-number space wind tunnel zero
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s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500824445.9/warc/CC-MAIN-20140820021344-00226-ip-10-180-136-8.ec2.internal.warc.gz
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https://ntnuopen.ntnu.no/ntnu-xmlui/handle/11250/2352611
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math
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The Fundamental Group of SO(3)
MetadataShow full item record
We study fundamental groups of topological spaces. In particular we will compute the fundamental group of SO(3), the group of rotations in three dimensions, by studying covering spaces. We will see that the fundamental group is isomorphic to the group of integers. This is of interest because of its relation to physics.
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https://forums.studentdoctor.net/threads/any-do-schools-with-rotations-primarily-at-university-hospitals.590829/
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math
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Hi all, I was wondering if there are any DO schools with rotations primarily at university-based teaching hospitals? I know many schools may have the option of a few rotations at university-based hospitals, but most of the rotations seem to be at community-based hospitals. I understand the reason for this, since osteopathic medicine has a greater focus on primary care, which I am assuming would be the focus at community hospitals while specialty medicine would be more likely to be found at university hospitals (this I assume). However, in general, I've heard that the quality of teaching at university hospitals seems to be better (yes, I know there are notable exceptions like Mayo or Cleveland Clinic, but these are only a few). Thus, I was wondering if any of the DO programs has nearly ALL rotations (or at least students can have the option of rotating at all) university teaching hospital sites. I realize there are lots of assumptions in my post here, but I am writing from my limited knowledge. I assumed all teaching-hospitals are university based, though I don't know if this is necessarily the case. Since this is on the topic of 3rd/4th year rotations, maybe this post would be better in the 'osteopathic' section, but I figured there is more traffic here in pre-osteo. Any information is appreciated. Thanks!
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https://birchlerarroyo.com/housing-planning/how-do-you-divide-a-line-into-equal-parts-in-autocad.html
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math
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How do you divide in AutoCAD?
Access Methods. Tool Set: Drafting tab > Draw panel > Point drop-down > Divide. Menu: Draw > Point > Divide. The following prompts are displayed.
How do you divide irregular land area?
Using the formula of (( 2 Area = SUM ( Xn-1 * Yn ) –SUM ( Yn – Xn-1)) divided by 2 you will obtain the area of the parcel , then draw a line from any vertex draw a line to cut the circumference of the parcel at a point , say P with unknown coordinates (X .., Y ..) , make two equations, one for each of the required …
How do you divide a line into 7 equal parts?
- Choose the work-piece that you want to divide.
- Choose how many sections you want to make.
- Draw a diagonal line above the line being divided. …
- Mark out equal points along the diagonal line.
- Use a square / 90 degree angle to draw lines from the points on the diagonal line down to the original work-piece.
How do you divide land?
Part 1 of 4:
Subdividing property means dividing it into several parts. Land owners typically subdivide their property into multiple residential units. This usually increases the value of the land. When the land is subdivided into more than one lot, each lot is then sold to one or more buyers.
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http://mathhelpforum.com/algebra/17773-one-series-question-one-geometry-question-print.html
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math
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hey please help me with these extension questions thanx!!
where k! is teh product of all integers from 1 up to k
2) P and Q are the point on the sides AB and BC of a triangle ABC respectively such that BP=3PA and QC=2BQ. K is the midpoint of the segment PQ. Prove that the area of the triangle AKC is equal to 11S/24 where S is teh area of the triangle ABC
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218199514.53/warc/CC-MAIN-20170322212959-00328-ip-10-233-31-227.ec2.internal.warc.gz
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http://www.chegg.com/homework-help/circular-bar-acb-diameter-d-cylindrical-hole-length-x-diamet-chapter-2.4-problem-4p-solution-9781285225784-exc
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math
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A circular bar ACB of diameter d having a cylindrical hole of length x and diameter d/2 from A to C is held between rigid supports at A and B. A load P acts at L/2 from ends A and B. Assume E is constant.
(a) Obtain formulas for the reactions RA and RB at supports A and B, respectively, due to the load P (see figure part a).
(b) Obtain a formula for the displacement δ at the point of load application (see figure part a). (c) For what value of x is RB = (6/5)RA? (See figure part a.) (d) Repeat part (a) if the bar is now rotated to a vertical position, load P is removed, and the bar is hanging under its own weight (assume mass density = ρ). (See figure part b.) Assume that x = L/2.
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https://search.spe.org/i2kweb/SPE/tag/equation
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math
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|Theme||Visible||Selectable||Appearance||Zoom Range (now: 0)|
Both the Rawlins and Schellhardt and Houpeurt analysis techniques are presented in terms of pseudopressures. Flow-after-flow tests, sometimes called gas backpressure or four-point tests, are conducted by producing the well at a series of different stabilized flow rates and measuring the stabilized BHFP at the sandface. Each different flow rate is established in succession either with or without a very short intermediate shut-in period. Conventional flow-after-flow tests often are conducted with a sequence of increasing flow rates; however, if stabilized flow rates are attained, the rate sequence does not affect the test. Fig 1 illustrates a flow-after-flow test.
A wellhead choke controls the surface pressure and production rate from a well. Chokes usually are selected so that fluctuations in the line pressure downstream of the choke have no effect on the production rate. This requires that flow through the choke be at critical flow conditions. Under critical flow conditions, the flow rate is a function of the upstream or tubing pressure only. For this condition to occur, the downstream pressure must be approximately 0.55 or less of the tubing pressure.
Proper sizing and selection of an electrical submersible pump (ESP) system is essential to efficient and cost-effective performance. Selection and sizing of proper ESP equipment for a particular application should be based on a nine-step design procedure. This nine-step procedure helps the engineer design the appropriate submersible pumping system for a particular well. Each of the nine steps is explained below, including gas calculations and variable-speed operations. Specific examples are worked through in ESP design. The design of a submersible pumping unit, under most conditions, is not a difficult task, especially if reliable data are available.
In a dynamic calculation, there are two effects not considered in steady flow: fluid inertia and fluid accumulation. In steady-state mass conservation, flow of fluid into a volume was matched by an equivalent flow out of the volume. In the dynamic calculation, there may not be equal inflow and outflow, but fluid may accumulate within the volume. For fluid accumulation to occur, either the fluid must compress, or the wellbore must expand. When considering the momentum equation, the fluid at rest must be accelerated to its final flow rate.
Energy is the rate of doing work. A practical aspect of energy is that it can be transmitted or transformed from one form to another (e.g., from an electrical form to a mechanical form by a motor). A loss of energy always occurs during transformation or transmission. In drilling fluids, energy is called hydraulic energy or commonly hydraulic horsepower. Rig pumps are the source of hydraulic energy carried by drilling fluids.
One of the first mathematical tools a neophyte engineer learns is calculus. Many of the mathematical tools engineers use to evaluate and predict behavior, such as vibrations, require equations that have continuously varying terms. Often, there are many terms regarding the rate of change, or the rate of change of the rate of change, and so forth, with respect to some basis. For example, a velocity is the rate of change of distance with respect to time. Acceleration is the rate of change of the velocity, which makes it the rate of change of the rate of change of distance with respect to time.
To quantify formation damage and understand its impact on hydrocarbon production, one must have reasonable estimates of the flow efficiency or skin factor. Several methods have been proposed to evaluate these quantities for oil and gas wells. Multirate tests can be conducted on both oil and gas wells. In these tests, several stabilized flow rates, qi, are achieved at corresponding stabilized flowing bottomhole pressures, pwf. The simplest analysis considers two different stabilized rates and pressures.
This article summarizes the fundamental gas-flow equations, both theoretical and empirical, used to analyze deliverability tests in terms of pseudopressure. The four most common types of gas-well deliverability tests are discussed in separate articles: flow-after-flow, single-point, isochronal, and modified isochronal tests. Deliverability testing refers to the testing of a gas well to measure its production capabilities under specific conditions of reservoir and bottomhole flowing pressures (BHFPs). A common productivity indicator obtained from these tests is the absolute open flow (AOF) potential. The AOF is the maximum rate at which a well could flow against a theoretical atmospheric backpressure at the sandface.
The Laplace transform of the diffusion equation in radial coordinates yields a modified Bessel's equation, and its solutions are obtained in terms of modified Bessel functions. This page introduces Bessel functions and discusses some of their properties to the extent that they are encountered in the solutions of more common petroleum engineering problems. A solution of Bessel's equation of order v is called a Bessel function of order v. Of particular interest is the case in which λ ki so that Eq. 2 becomes Eq. 3 is called the modified Bessel's equation of order v. A solution of the modified Bessel's equation of order v is called a modified Bessel function of order v.
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https://www.topperlearning.com/doubts-solutions/how-we-can-find-voltage-leads-and-current-lags-according-to-a-phasor-diagram-a78bz977/
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math
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first of all let me tell u what exactly a phasor diagram is.
It is a mapping in which a vector is represnted by a line having its length equal to its magnitude and the angle which it makes tells us the phase difference with respect to a refference vector represented by the horizontal axis.
eg. if V = v cos(wt + a)
then if i take X = x cos(wt)
as a reference vector then, the vector V will be making an angle of a with X
thus if V makes an angle with I in a positive sense then wee say that voltage leads the current
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571584.72/warc/CC-MAIN-20220812045352-20220812075352-00285.warc.gz
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CC-MAIN-2022-33
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http://k-cosm.ru/Calculus-final-exam-study-guide.html
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math
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Start studying Calculus 1 Final Exam Study Guide. Learn vocabulary, terms, and more with flashcards, games, and other study tools.
Final Exam Study Guide for Calculus III Vector Algebra 1. The length of a vector and the relationship to distances between points 2. Addition, subtraction, and scalar multiplication of vectors, together with the geometric interpretations of these operations 3. Basic properties of vector operations (p.774) 4.
B Veitch Calculus 2 Study Guide This study guide is in no way exhaustive. As stated in class, any type of question from class, quizzes, exams, and homeworks are fair game.
Study Guide for the Advanced Placement Calculus AB Examination By Elaine Cheong. 1 Table of Contents INTRODUCTION 2 TOPICS TO STUDY 3 • Elementary Functions 3 • Limits 5 • Differential Calculus 7 • Integral Calculus 12 SOME USEFUL FORMULAS 16 CALCULATOR TIPS AND PROGRAMS 17 ... Advanced Placement Calculus AB Exam tests students on ...
CLEP Precalculus: Study Guide & Test Prep Final Free Practice Test Instructions Choose your answer to the question and click 'Continue' to see how you did. Then click 'Next Question' to answer the ...
Calculus 2 Final Exam Review study guide by michael_owens3 includes 55 questions covering vocabulary, terms and more. Quizlet flashcards, activities and games help you improve your grades.
12/14/2013 · This video is about the correction of questions that were put in college Calculus 1 Final exam. The solution of each question was explained in detail and accompanied with the concept.
Final Exam Study Guide for Calculus II The nal exam will be a 2.5 hour CUMULATIVE exam, and you are re-sponsible for everything that we have covered this term. There will certainly be an emphasis on power series, Taylor series, and analytic functions, so make sure to focus on those topics. As a study aid, I have listed below the major
5/11/2015 · Solutions to a previous final exam for a multivariable calculus course. Download exam at: https://drive.google.com/open?id=0BzoZ-FzkrMLdRFRiV28yY3NDY28 Downl...
1 GPS Pre-Calculus Final Exam Study Guide Unit 3 Rational Functions 1. Give the degree, the number of real zeros, the number of (nonreal) complex zeros, for this polynomial function.
Test and improve your knowledge of CLEP Calculus: Study Guide & Test Prep with fun multiple choice exams you can take online with Study.com
math. We make the study of numbers easy as 1,2,3. From basic equations to advanced calculus, we explain mathematical concepts and help you ace your next test. Our study guides are available online and in book form at barnesandnoble.com.
B Veitch Business Calculus Final Exam Study Guide This study guide is in no way exhaustive. As stated in class, any type of question from class, quizzes, exams, and homeworks are fair game. There’s no information here about the word problems. 1. Some Algebra Review (a) Factoring and Solving i. Quadratic Formula: ax2 + bx+ c = 0 x = b p b2 4ac ...
Calculus II, Study Guide for Final Exam Page 3 Difference quotients, definition of the derivative: You should be able to set up a difference quotient, and simplify it to the point where there is no longer an “ ” in the denominator. This is the first step in proving the various short-cut rules for computing derivatives.
View Test Prep - Final Exam Study Guide on Calculus 1 from MATH 180 at University of Illinois, Chicago. Math 180, Final Exam, Study Guide Problem 1 Solution 1. Dierentiate with respect to x. Write
Calculus - Semester 1 Final Exam Study Guide Questions - Fall 2010-11 Name_____ Solve each problem completely on your notebook paper. Record your answers on this sheet. Find domain and range of the function. 1)f(x) = 9 - x Determine if the function is even, odd, or neither. 2)f(x) = -2x5 - 3x3
Review AP Calculus AB by watching and listening to over 11 hours worth of videos carefully coordinated to the AP Calculus AB syllabus. 182 AP Calculus AB practice questions Test your understanding of each concept without having to take an entire AP Calculus AB practice exam.
Calculus I | Final Study Guide Exam Date: Friday June 30, 9:00-10:35 The following is a list of topics that we will have covered over the second three weeks of the course. It is not necessarily a complete list, but I believe it does hit all of the points that I stressed most in class. Accompanying each topic on the list are the sections of the ...
AP Calculus – Final Review Sheet When you see the words …. This is what you think of doing 1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator 2. Show that f() x is even Show that (−)= ( ) symmetric to y-axis 3.
1/9/2018 · I don’t take calculus but I can give you the most basic study tips. 1. organized all of the notes you have taken in class in a specific order ( easiest to hardest, first to last etc) 2. Take a blank sheet and write down everything you remember lea...
Math 1552: Integral Calculus Final Exam Study Guide, Spring 2018 PART 1: Concept Review (Note: concepts may be tested on the exam in the form of true/false or short-answer
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https://www.physicsforums.com/threads/a-difficult-1d-kinematics-problem-dealing-with-displacement-and-velocity.335884/
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In reaching her destination, a backpacker walks with an average velocity of 1.31 m/s, due west. This average velocity results because she hikes for 6.44 km with an average velocity of 2.54 m/s, due west, turns around, and hikes with an average velocity of 0.475 m/s, due east. How far east did she walk? Is there not enough information? I feel like they should have given me another variable or something. I figured out that it took her 2535.433 seconds to hike for the 6.55km stretch. But I'm really in the dark on this one, I appologize. I've looked all over the internet to try and find a problem simular to this one but I had no luck.
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https://booksasfood.blogspot.com/2010/10/perfect-intelligent-escapist-comfort.html
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The Charming Quirks of Others, the newest Isabel Dalhousie book, came in from the library on Wednesday, and (what's the word I'm looking for?) hoarding it for a rainy afternoon. I'm also trying to catch up with A Conspiracy of Friends, the third Corduroy Mansions serial now being published in The Telegraph. (I missed the second one, and it's not available here yet, but that doesn't seem to matter.) Speaking of hoarding, I've got it coming in RSS and podcasts, so I may read, or listen, or both. It's nice to see something of Pimlico in the meantime.
. . . . . . . . . . . . . . .
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https://www.semanticscholar.org/topic/Richard-Schroeppel/2591076
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Semantic Scholar uses AI to extract papers important to this topic.
Given a multiset ofn positive integers, the NP-complete problem of number partitioning is to assign each integer to one of k… Expand Subset sum or Knapsack problems of dimension n are known to be hardest for knapsacks of density close to 1. These problems are NP… Expand At Eurocrypt 2010, Howgrave-Graham and Joux described an algorithm for solving hard knapsacks of density close to 1 in time O(20… Expand In this paper, we study the complexity of solving hard knapsack problems, i.e., knapsacks with a density close to 1 where lattice… Expand By means of an almost trivial statement of matrix algebra, we prove two conjectures proposed by Gosper and Schroeppel [R.W… Expand We present a careful analysis of elliptic curve point multiplication methods that use the point halving technique of Knudsen and… Expand Hidden credentials are useful in protecting sensitive resource requests, resources, policies, and credentials. We propose a… Expand The recently proposed multiplicative masking countermeasure against power analysis attacks on AES is interesting as it does not… Expand This paper describes three contributions for efficient implementation of elliptic curve cryptosystems in GF(2n). The first is a… Expand Recently, A.K. Lenstra, H.W. Lenstra, Jr., M.S. Manasse and J .M. Pollard [5,6] have introduced a new algorithm for factoring… Expand
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https://tohoku.pure.elsevier.com/ja/publications/group-approximation-in-cayley-topology-and-coarse-geometry-part-i
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The objective of this series is to study metric geometric properties of (coarse) disjoint unions of amenable Cayley graphs. We employ the Cayley topology and observe connections between large scale structure of metric spaces and group properties of Cayley accumulation points. In Part I, we prove that a disjoint union has property A of Yu if and only if all groups appearing as Cayley accumulation points in the space of marked groups are amenable. As an application, we construct two disjoint unions of finite special linear groups (and unimodular linear groups) with respect to two systems of generators that look similar such that one has property A and the other does not admit (fibered) coarse embeddings into any Banach space with nontrivial type (for instance, any uniformly convex Banach space).
ASJC Scopus subject areas
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http://cosmoquest.org/forum/showthread.php?11559-Time-Dilation-and-Quasars&p=225824
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Time Dilation and Quasars
In May of 2001 Hawkins published a paper called “Time Dilation and Quasar Variability”. Part of the Abstract reads as follows.
“We find that the timescale of quasar variation does not increase with redshift as required by time dilation. Possible explanations of this result all conflict with widely held consensus in the scientific community.” http://xxx.lanl.gov/abs/astro-ph/0105073
The conflict arises since this indicates that space-time is not expanding. This is contrary to the evidence of type 1a super novas that confirms the time dilation effect due to the expansion of space.
Initially this topic was posted by Dunash on this BB on January 10, 2002, but there was no follow up discussion of his posting. http://www.badastronomy.com/phpBB/viewtopic.php? I am appreciative for dgruss23 bringing up the paper in the course of a poll discussion called “Is the expansion of space-time accelerating or decelerating?”. http://www.badastronomy.com/phpBB/vi...2&start=50 (Page 3) I believe reference to this paper may also have been found in a discussion about the Red Shift but I could not find it but I think I remember reading it there. Hopefully someone will provide additional links to preserve the reference value of this BB.
I thought that a more through discussion of this topic is in order on its own since it provides evidence that something is wrong with current cosmological models.
I will attempt a “layman’s” description of the report. Hopefully someone with more expertise will provide a more explicit description.
Time dilation generally refers to an increase in the observed time a physical process occurs. There are at least two possible physical interpretations or descriptions for time dilation. The most common is the application of special relativity. Time progresses comparatively slower for a moving object, so an object observed in the past with a high velocity (indicated by red shift) will have physical processes occur at a slower rate. The decay of a muon entering the earth’s atmosphere is a classic example of how a physical process is slowed when an object is moving at near light speed velocities. The time scale of rapidly moving objects can be described by how long a physical process takes to occur, as predicted by special relativity. Specifically the time scale, Ts, can be described by the red shift proportion z as follows. Ts =Tm/Tl =1+z. Tm = interval of time moving, Tl = time interval of time local or “at rest”, z = ratio of wavelength.
The other physical interpretation is that the expansion of space-time itself results in a time dilation. Lets say that we are at a bowling alley and we roll two balls down the ally separated by 1 second of time. The distance between the two balls remains essentially constant while traveling down the alley. (Ignoring friction effects). The two balls will arrive at the end of the ally one second apart. Now lets throw the two balls again with a 1 second separation, but this time the bowling ally is “stretched” while the balls roll down the alley. This will physically increase the distance between the two balls. For example, Instead of the balls being 2 meters apart, they can end up being 4 meters apart. When the balls reach the end of the alley, in this example, the separation in time for when they reach the end will now be 2 seconds. (Ignoring the effect of the expansion on the velocity and energy of the balls, at least for this posting since the possible variance in the speed of light and the loss of energy of a photon (instead of a bowling ball), with the expansion of space-time is a whole other issue). I prefer this explanation of the cosmological red shift since it keeps galaxies “at rest” locally, allowing them to be carried by the expansion of space-time.
Regardless of the model, the basic general effect of time dilation will be the same. The time dilation will be Td = 1+z. A process that took 1 second to occur in a “rest” frame, will take 2 seconds to occur as measured by an observer if the red shift of the observed object producing the effect has a cosmological red shift of 1.
I am sure some will provide a better explanation of time dilation, and different interpretations, but I hope it gives the reader a general idea.
(In the application of my uniform expansion hypothesis (www.uniformexpansion.com) both special relativity and expansion result in time dilation, but one of the effects is unobservable due to the specific geometric rate the expansion occurs. This would alter the assumed distance of 1asn’s and the assumed “acceleration” (really deceleration) indicated by such. It also addresses the issue involved with no observed time dilation effects noticed in the variation of energy output of quasars. This is merely an aside for now. It is hoped that the postings of others will provide additional explanations and perspectives. )
The time variance of Quasars
The time variance of quasars, while not described in the Hawkins paper, is based upon observed variation in the energy output from quasars. It is the extreme variance of energy output of quasars in short periods of time that has helped determine the size of quasars. Quasars put out about 1,000 times the amount of energy of an entire galaxy, in a region of space 100,000 times smaller. Of course this is based upon the assumption that the cosmological red shift correlates not only to a velocity measure describing the expansion of space but to a distance measure. (v = Ho x D and v causes the red shift). (Some will take issue with this assumption arguing that quasars are much closer, “tired light proponents”).
I regret not being able to find a link with a graph illustrating the time variance of the energy output of quasars. I will try to explain verbally a graph of quasar 3c 279, which is in one of my texts. One of the most dramatic peak cycles of energy output shows that the increase in luminosity varies by a magnitude of 7 over a period of about 1200 days (rise, peak to fall) . There are a number of smaller cycles (rise peak and fall), with a variation of magnitude 2 over about 800 days. Amongst this variation there are additional variations in magnitude of about 1 or perhaps a bit more times over the passage of a just a 50 or so days. There is also some variation with a magnitude of 1 over periods of only a few days. A very “noisy” graph.
While there is great variation in the cycles of energy output from quasars, there is a discernable pattern. Large energy peaks last longer than short energy peaks. Large peaks tend to last a thousand days, etc.
Mathematically, it is possible to extract frequency relationships utilizing a Fourier based transformation with what is called a power spectrum analysis. It allows a statistical manipulation of cyclic processes with a “noise” component. It works best if even numbers of cycles are in the mix, but if there are sufficient numbers of cycles within the analysis, this restraint is not that critical. Categorizing cycle events helps in the statistical evaluation, “large” energy output events last over 1000 days, etc.
The anticipated result
It was anticipated that the further away a quasar was observed, as indicated by the red shift, the greater the time dilation of the cycles observed in the energy output of quasars. The increase in the period of the cycles should correspond to an increasing red shift. Specifically it was anticipated that the cycle length should vary by 1+z. For example, the period of “averaged” cycles should be two times greater than another quasar if the red shift for one quasar has a z of 1 while the other quasar had a z of 3.
No such effect was observed.
This is opposite to the results found with type 1a supernovas. It is assumed that Type 1a supernovas are always the result of a supernova explosion with a white dwarf star with a mass of about 1.44 masses involved. (Baring the variation induced by rotational effects of the two stars involved and the mass of the sister star losing mass to the white dwarf star). (This also assumes that high red shift 1asn’s are the same as “local”, which is an assumption I have issues with). Since the mass involved in the supernova is assumed to be the same, the duration of the event should be generally the same. Time dilation should increase the observed duration of the 1asn by a factor of (1 +z). This time dilation is observed in that the light curves of high red shift supernovas; the “explosion” takes longer to occur the greater the red shift. (Generally).
How can one process associated with Supernovas indicate time dilation associated with red shift, while another process associated with quasars indicate no time dilation associated with red shift?
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http://eric.ed.gov/?id=ED344905
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ERIC Number: ED344905
Record Type: RIE
Publication Date: 1992-Apr
Reference Count: N/A
What Statistical Significance Testing Is, and What It Is Not.
Shaver, James P.
A test of statistical significance is a procedure for determining how likely a result is assuming a null hypothesis to be true with randomization and a sample of size n (the given size in the study). Randomization, which refers to random sampling and random assignment, is important because it ensures the independence of observations, but it does not guarantee independence beyond the initial sample selection. A test of statistical significance provides a statement of probability of occurrence in the long run, with repeated random sampling under the null hypothesis, but provides no basis for a conclusion about the probability that a particular result is attributable to chance. A test of statistical significance also does not indicate the probability that the null hypothesis is true or false and does not indicate whether a treatment being studied had an effect. Statistical significance indicates neither the magnitude nor the importance of a result, and is no indication of the probability that a result would be obtained on study replication. Although tests of statistical significance yield little valid information for questions of interest in most educational research, use and misuse of such tests remain common for a variety of reasons. Researchers should be encouraged to minimize statistical significance tests and to state expectations for quantitative results as critical effect sizes. There is a 58-item list of references. (SLD)
Publication Type: Speeches/Meeting Papers
Education Level: N/A
Authoring Institution: N/A
Identifiers: Null Hypothesis; Randomization (Statistics); Research Replication
Note: Paper presented at the Annual Meeting of the American Educational Research Association (San Francisco, CA, April 20-24, 1992).
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https://paulaustinmurphypam.blogspot.com/2019/05/against-platonism-in-physics-with-lee.html
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[Most of the quotes in this piece are taken from Lee Smolin's Time Reborn: From the Crisis in Physics to the Future of the Universe, which was published in 2013.]
This piece focuses on Lee Smolin's position on what he takes to be Platonism in (mathematical) physics. Smolin's words are also used as a springboard for discussing other issues and positions (including my own) within this general debate.
Firstly, Platonism in physics is tackled as it was explicitly stated by the physicists John Wheeler and Stephen Hawking. Max Tegmark (as a Platonist) is also featured. The position advanced by Tegmark is that mathematics can perfectly describe the world/reality because the world/reality is itself mathematical. Wheeler and Hawking argued against such a position (or at least they appeared to).
Then there's a section on a position best described as “the-map-is-not-the-territory”. This too inevitably focuses on Platonism in physics. It also asks the question as to how, exactly, (mathematical) models relate to the world/reality.
There's also discussion of the relation between mathematical objects and mathematical concepts as this is brought out within the specific context of Platonism in physics.
An old problem is then discussed: the precise relation between our world and the Platonic world. The issue of (as it were) “causal closure” was the traditional focus of this particular debate; though other aspects are tackled in the following.
Finally, mathematical structuralism - and how it relates to Platonism in physics - is discussed. This leads naturally on to the final section which discusses what Smolin calls “intrinsic essences” (or what philosophers call “intrinsic properties”).
Lee Smolin puts a psychological and sociological slant on the issue of Platonism in physics when he discusses the personal motivations of Platonic philosophers and mathematicians. He writes:
“Does the seeking of mathematical knowledge make one a kind of priest, with special access to an extraordinary form of knowledge?”
It can safely be said that this was true of Pythagoras, Plato and their followers. Whether or not it's also true of an everyday mathematician or philosopher ensconced in a university department in Nottingham or Oxford, I don't know. Having said that, Smolin does speak about a friend of his in this respect. Smolin tells us that he “sometimes wonder[s] if his belief in truths beyond the ken of humans contributes to his happiness at being human”.
In any case, it's probably best to leave the personal psychologies of Platonists there. After all, if Smolin argues that Platonists are Platonists for reasons of personal psychology, then Platonists can also argue that Smolin is an anti-Platonist for reasons of personal psychology. And where does that get us?
Fire In the Equations
The physicist John Archibald Wheeler provided the most powerful riposte to Platonism in physics. In an oft-quoted story, we're told that Wheeler used to write many arcane equations on the blackboard and stand back and say to his students:
“Now I'll clap my hands and a universe will spring into existence.”
According to Max Tegmark and others, however, the equations are the universe - at least in a manner of speaking - and perhaps not even in a manner of speaking! (More of which later.)
Then Steven Hawking (in his A Brief History of Time) nearly trumped Wheeler with an even better-known quote. He wrote:
“Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe?”
The science writer Kitty Ferguson (in her The Fire in the Equations) offers a possible Platonist answer to Hawking's question by saying that “it might be that the equations are the fire”. Alternatively, could Hawking himself have been “suggesting that the laws have a life or creative force of their own?”. Again, is it that the “equations are the fire”?
The theoretical physicist Lee Smolin, on the other hand, explains why the idea that “mathematics is prior to nature” is unsupportable. He writes:
“Math in reality comes after nature. It has no generative power.”
More philosophically, Smolin continues when he says that “in mathematics conclusions are forced by logical implication, whereas in nature events are generated by causal processes in time”.
The Platonist will simply now say that mathematics fully captures those “causal processes”. Or, in Max Tegmark's case, the argument is that the maths and the causal processes are one and the same thing.
More relevantly to the position of people like Tegmark, Smolin says that
“logical relations can model aspects of causal processes, but they're not identical to causal processes”.
What's more, “[l]ogic is not the mirror of causality”.
Yet according to Tegmark:
i) Because the models of causal processes are identical to those processes,
ii) then they must be one and the same thing.
More precisely, Tegmark's argument is as follows:
i) If a mathematical structure is identical (or “equivalent”) to the physical structure it “models”,
ii) then the mathematical structure and the physical structure must be one and the same thing.
Thus if that's the case (i.e., that structure x and structure y are identical), then it makes little sense to say that x “models” (or is “isomorphic with”) y. That is, x can't model y if x and y are one and the same thing.
So Tegmark also applies what he deems to be true about the identity of two mathematical structures to the identity of a mathematical structure and a physical structure. He offers us an explicit example of this:
electric-field strength = a mathematical structure
Or in Tegmark's own words:
“' [If] [t]his electricity-field strength here in physical space corresponds to this number in the mathematical structure for example, then our external physical reality meets the definition of being a mathematical structure – indeed, that same mathematical structure.”
In any case:
i) If x (a mathematical structure) and y (a physical structure) are one and the same thing,
ii) then one needs to know how they can have any kind of relation at all to one another. [Gottlob Frege's “Evening Star” and “Morning Star” story may work here.]
In terms of Leibniz's law (Smolin is a big fan of Leibniz and frequently mentions him), that must also mean that everything true of x must also be true of y. But can we observe, taste, kick, etc. mathematical structures? (Yes, if they're identical to physical structures!) In addition, can't two structures be identical and yet separate (i.e., not numerically identical)? Well, not according to Smolin's Leibniz.
All this is perhaps easier to accept when it comes to mathematical structures being compared to other mathematical structures (rather than to something physical). Yet if the physical structure is a mathematical structure, then that qualification doesn't seem to work either.
All this is also problematic in the following sense:
i) If we use mathematics to describe the world,
ii) and maths and the world are the same thing,
iii) then we're essentially either using maths to describe maths or using the world to describe the world.
What's more, maths can't be the “mirror” of anything in nature if the two are identical in the first place. In other words, any mathematical models which are said to “perfectly capture nature” (or causality) can only do so because nature (or causality) is already mathematical. If that weren't the case, then no perfect modelling (or perfectly precise equations) could exist. Thus, again, that perfect symmetry (or isomorphism) can only be explained (according to Tegmark) if nature and maths are one and the same thing.
A sharp and to-the-point anti-Platonist position is also put by the science writer, Philip Ball. He writes:
“... equations purportedly about physical reality are, without interpretation, just marks on paper”.
In other words, what exactly (as Hawking put it above) “breathes fire into the equation [to] make a world”?
The Philip Ball quote above also highlights two problems.
i) The fact that we can make mistakes about physical reality.
ii) That even if the equations are about physical reality, they're not one and the same as physical reality.
Indeed, even Ball's “interpretation” won't make the equations equal physical reality.
So let's go all the way back to Galileo (as Smolin himself does).
Surely we must say that “Nature's book” isn't written in the language of mathematics. We can say that Nature's book can be written in the language mathematics. Indeed it often is written in the language of mathematics. Though Nature's book is not itself mathematical because that book - in a strong sense - didn't even exist until human beings began to write (some of) it.
Perhaps I'm doing Galileo a disservice because he did say that
“we cannot understand [Nature] if we do not first learn the language and grasp the symbols in which it is written”.
Yet Galileo was talking about our understanding of Nature here - not just Nature as it is “in itself”.
Nonetheless, Galileo also said that the the “book is written in mathematical language”. So was he also talking about Nature as it is in itself being mathematical? Perhaps Galileo wasn't only saying that mathematics is required to understand Nature. There is, therefore, an ambivalence here between the idea that Nature itself is mathematical and the idea that mathematics is required to understand Nature.
Sure, ontic structural realists and other structural realists (in the philosophy of physics) would say that this distinction (i.e., between maths and the world) hardly makes sense when it comes to physics generally - and it doesn't make any sense at all when it comes to quantum physics. Nonetheless, surely there's still a distinction to be made here.
The Map is Not the Territory
Philip Ball (who's just been quoted) puts the main problem of Platonism perfectly when he says that
“[i]t's not surprising, the, that some scientists want to make maths itself the ultimate reality, a kind of numinous fabric from which all else emerges”.
Thus, in more concrete terms, such mathematical Platonists fail to see that the “[r]elationships between numbers are no substitute” for the world/reality. Indeed, adds Ball, “[s]cience deserves more than that”.
This is the mistaking-the-map-for-the-territory problem. As the semanticist Alfred Korzybski once put it:
“A map is not the territory it represents, but, if correct, it has a similar structure to the territory, which accounts for its usefulness.”
Indeed we can take this further and say that “all models are wrong”.
This the-map-is-not-the-territory idea is put by Smolin himself when he tells us that “[m]athematics is one language of science”. In other words, the maths (in mathematical physics) isn't self-subsistent: it needs to be tied to reality: it isn't reality itself. Thus,
“[maths] application to science is based on an identification between results of mathematical calculations and experimental results, and since the experiments take place outside mathematics, in the real world, the link between the two must be stated in ordinary language”.
More directly, Smolin tells us that
“the pragmatist will insist that the mathematical representation of a motion as a curve [for example] does not imply that the motion is in any way identical to the representation”.
“By succumbing to the temptation to conflate the representation with the reality and identify the graph of the records of the motion with the motion itself...”
Then Smolin tells us about one Platonist (or Tegmarkian) conclusion to all this. He writes:
“Once you commit this fallacy [i.e., of mistaking the map for the territory], you're free to fantasise about the universe being nothing but mathematics.”
Finally, Smolin puts his particular slant on the importance of time in all of this. He writes:
“The very fact that the motion takes place in time whereas the mathematical representation is timeless means they aren't the same thing.”
How Can Maths Model Nature?
To put it at its most simple and - perhaps - extreme. The Platonic mistake is to move from the fact that mathematics can be (almost) perfect for describing or modelling the world to the conclusion that the world must therefore be intrinsically mathematical itself. Smolin captures this position when he discusses the work of Isaac Newton. According to Smolin, Newton's world was
“infused with divinity, because timeless mathematics was at the heart of everything that moved, on Earth and in the sky”.
Slightly earlier, Smolin had also written that
“[w]hen Galileo discovered that falling bodies are described by a simple mathematical curve, he captured an aspect of the divine”.
We can of course ask if Galileo thought in these terms himself: even if only at the subconscious level. However, would that even matter to Smolin's take on this?
In any case, is mathematics “at the heart of everything that move[s]” or is it simply a tool for description or modelling? Max Tegmark (again) may argue the following:
i) If mathematics is “at the heart of everything that moves”,
ii) and it's also a perfect tool for description and modelling,
iii) then in what sense is the world not itself mathematical?
Indeed Smolin himself goes way beyond Galileo and Newton and says that “the whole history of the world” [in general relativity] is “represented by a mathematical object”.
Now if we turn to quantum mechanics and the words of Philip Ball, he says that superposition is “considered only as an abstract mathematical thing”. It's also the case the the/a wavefunction is also a “mathematical object”.
Now if we turn to quantum mechanics and the words of Philip Ball, he says that superposition is “considered only as an abstract mathematical thing”. It's also the case the the/a wavefunction is also a “mathematical object”.
If we get back to mathematical models.
It was said earlier that mathematics can describe (or even perfectly model) nature and that the physicists who aren't Platonists have no problem with this. How could they? Indeed Smolin himself tells us that “[i]t's impossible to state these laws [i.e., Newton's laws] without mathematics”. This is often said about quantum mechanics. Yet Smolin is going beyond that and saying that it's also true “the first two of Newton's laws”. More specifically, Smolin says that “[a] straight line is an ideal mathematical concept”. That is, “it lives not in our world but in the Platonic world of ideal curves”.
In terms of “acceleration” and the “rate of change of velocity” (to take just two examples), it was the case that “Newton needed to invent a whole new branch of mathematics: the calculus” in order to “describe it adequately”. But here again we mustn't conflate the maths with what the maths describes (or models).
Philip Ball (again) puts this position as it applies specifically to Hilbert space. He tells us that “a Hilbert space is a construct – a piece of maths, not a place”. He then quotes the physicist Asher Peres stating the following:
“The simple and obvious truth is that quantum phenomena do not occur in a Hilbert space. They occur in a laboratory.”
Ball also mentions Max Tegmark's position. He writes:
“If the Many Worlds are in some sense 'in' Hilbert space, then we are saying that the equations are more 'real' than what we perceive: as Tegmark puts it, 'equations are ultimately more fundamental than words' (an idea curiously resistant to being expressed without words). Belief in the MWI seems to demand that we regards the maths of quantum theory as somehow a fabric of reality.”
Mathematical Objects and Mathematical Concepts
Smolin has a problem with such mathematical objects. He (implicitly) argues against this Platonic position when he says (in a note) that
“[m]athematicians like to speak of curves, numbers, and so forth as mathematical 'objects', which implies a kind of existence”.
However, it's fairly clear that Smolin has a problem with this position. He says that you may want to call these “mathematical objects” by the name of “concepts”. That, on one interpretation, surely takes mathematical objects out of the Platonic world and places them in the realm of human minds. (Except for the fact the concepts too can be seen as “abstract objects”.)
Stephen Hawking (for one) certainly didn't believe that maths and nature are one - and he too talked about “concepts”. He once wrote that “mental concepts are the only reality we can know”. Furthermore he stated: “There is no model-independent test of reality.”
This seems to mean that Hawking went further than simply saying that mathematics describes (or perfectly models) nature. After all, he stresses the importance of “mental concepts”. However, it can still be said that the models of physics are of course mathematical and accurate. Thus even if we require mental concepts to get at these mathematical models, the models can still perfectly capture “reality”. So whichever way we interpret Hawking's words, he certainly doesn't seem to put a Platonic position (or replicate Tegmark's stance) on mathematical physics.
Smolin himself distinguishes mental concepts from mathematical objects when (in a note) he writes:
“If you aren't comfortable adopting a radical philosophical position [i.e., of believing in mathematical objects] by a habit of language, you might want to call them [mathematical objects] concepts instead.”
In that passage Smolin doesn't seem to explicitly commit himself to mathematical concepts (rather than mathematical objects); though elsewhere he is more explicit when he also talks about “inventing” (i.e., not “discovering”) mathematical objects. It's also interesting to note that Smolin puts a Wittgensteinian position. Wittgenstein, for example, once wrote that “a cloud of philosophy condenses into a drop of grammar”. Smolin, on the other hand, talks about “adopting a radical philosophical position [because of] a habit of language”.
In any case, Smolin defines a “mathematical object” thus:
“Mathematical objects are constituted out of pure thought. We don't discover the parabolas in the world, we invent them. A parabola or a circle or a straight line is an idea. It must be formulated and then captured in a definition... Once we have the concept, we can reason directly from the definition of a curve to its properties.”
Of course there are a couple of words in the passage above which a Platonist may have a problem with. Firstly, the word “invent” (as in “we invent [mathematical objects]”. And then there's the use of the word “concept” (i.e., rather than “object”). In Fregean style, we can have a “concept of an object”. Thus an abstract mathematical object can generate (as it were) various mental concepts. In terms of “[o]nce we have the concept”, then certain things logically and objectively follow from that concept. So it's the philosophical nature of the concept which raises questions.
How Do We Get to the Platonic Realm?
Even if the Platonic mathematical realm does indeed exist, then it' still the case that we still need to gain (causal) access to it. This is a problem that's often been commented upon. Smolin himself puts it this way:
“One question that Jim [a friend of Smolin] and other Platonists admit is hard for them to answer is how we human beings, who live bounded in time, in contact only with other things similarly bounded, can have definite knowledge of the timeless realm of mathematics.”
Plato himself answered Smolin's question when he argued that we have “intuitive” (or even genetic) access to this abstract realm from birth. (He elaborated on this in his slave boy story.)This doesn't seem to solve the problem of causal access to a Platonic realm. Thus, as a addendum to this argument about causal access (or the “causal closure” of both the human world and the Platonic world), Smolin says that “[b]ecause we have no physical access to the imagined timeless world, sooner or later we'll find ourselves just making stuff up”. In other words, even if the Platonic realm does exist and we can also gain access to it, that doesn't mean that we can't get things wrong or make mistakes about it.
Smolin himself says that “[w]e get the truths of mathematics by reasoning, but can we really be sure our reasoning is correct?”. What's more:
“Occasionally errors are discovered in the proofs published in textbooks, so it's likely that errors remain.”
I suppose Plato himself might have argued that we can't get things wrong because our intuition somehow guarantees access to the truths found in this realm. Or, more correctly, if we use our reason (or intuition) correctly (as Descartes also argued), then we simply can't go wrong.
So now here's Smolin quoting Roger Penrose (who's a personal friend of Smolin) putting the Platonic/Cartesian position just mentioned:
“You're certainly sure that one plus one equals two. That's a fact about the mathematical world that you can grasp in your intuition and be sure of. So one-plus-one-equals-two is, by itself, evidence enough that reason can transcend time. How about two plus two equals four? You're sure about that, too! Now, how about five plus five equals ten? You have no doubts, do you? So there are a very large number of facts about the timeless realm of mathematics that you're confident you know?”
It's of course the case that many philosophers and mathematicians will say that one doesn't need a “timeless realm” to explain all that's argued in Penrose's words above. It can, for example, be given a Wittgensteinian explanation in terms of rules and our knowledge of the rules. Our “intuitive grasp” (as it's sometimes put) of basic arithmetic can also be partly explained by cognitive scientists, evolutionary psychologists or philosophers.
It's also interesting that Penrose gives basic arithmetical examples as demonstrations of our Platonic intuition. So what about higher or more complex maths? Do mathematicians have immediate intuitions about such equations or do they need to work at them? And if they do need to work at them, then surely intuition must have a minimal role to play.
In one of his notes, Smolin gives another argument as to why the Platonic realm and the human realm can never be split asunder. He writes:
“It's also not quite true to say that the truths of mathematics are outside time, since, as human beings, our perception and thoughts take place at specific moments in time – and among the things we think about are mathematical objects.”
The Platonist would say that Smolin is conflating the Platonic realm with the fact that we can gain access to that realm. That is, one realm can still be abstract and timeless even if we concrete and time-bound human beings can gain access to it.
But here we have a analogue of the mind-body problem. That is, what is the precise relation between the time-bound and concrete world and the timeless and abstract world? Smolin himself explains the Platonic position in terms of human psychology. He continues:
“It's just that those mathematical objects don't seem to have any existence in time themselves. They are not born, they do not change, they simply are.”
Smolin uses the word “seem” in the above (as in “seem to have any existence in time”). That implies that what seems to be the case may not actually be the case. Yet Smolin does then say that mathematical objects “are not born, they do not change, they simply are”. Here he may simply be putting the position of the Platonist. Again, even if mathematical objects aren't born, we still need to explain our access to them and acknowledge the possibility of getting things wrong about them - even systematically getting things wrong!
Interestingly, Smolin offers us a kind of “conventionalist” middle way when he states that
“[w]e invent the curves and numbers of mathematics, but once we have invented them we cannot alter them”.
A Platonist would have a profound problem with the word “invent”. However, even though we may indeed invent numbers (or functions), once they're invented or created, then they become (as it were) de facto Platonic objects. That is, they're then set in stone and other things must necessarily follow from them. This is something that a philosopher like the late Wittgenstein might have happily accepted. That is, that rules and symbol-use themselves create the “objectivity” (or at least the “intersubjectivity”) of maths - and also, perhaps, even the timelessness of mathematics.
Interestingly enough, Smolin puts his anti-Platonist position by adopting the position of mathematical structuralism. (There are also types of mathematical structuralism which are Platonist - see here.) Firstly (in a note) he expresses the essence (as it were) of mathematical structuralism when he says that “relationships are exactly what mathematics expresses”. He then makes the ontological point that
“[n]umbers have no intrinsic essence, nor do points in space; they are defined entirely by their place in a system of numbers or points – all of whose properties have to do with their relationships to other numbers or points”.
Moreover, “[t]hese relationships are entailed by the axioms that define a mathematical system”. It can be said that Platonists believe that numbers do have an "intrinsic essence". In other words, a system doesn't gain its nature because of the relations between numbers: the relations between numbers are parasitical on the nature of numbers themselves. After all, the following can be argued:
i) If numbers didn't have an intrinsic essence,
ii) then they couldn't engender the precise relations to other numbers which they have in each system.
i) If numbers have intrinsic essences,
ii) then those essences can't be dependent on the systems to which they belong (or, indeed, to any system).
iii) Therefore those intrinsic essences must come before all systems of relations.
Of course the obvious point to put against that position was put by Paul Benacerraf in 1965. The French philosopher wrote:
“For arithmetical purposes the properties of numbers which do not stem from the relations they bear to one another in virtue of being arranged in a progression are of no consequence whatsoever. But it would be only these properties that would single out a number as this object or that.”
In simple terms, we can say that the number 1 is (partly) defined by being the successor of 0 in the structure determined by a theory of natural numbers. In turn, all other numbers are defined by their respective places in the number line. So, again, it can of course be said that the “essence” of, say, the number 2 is that it comes after 1 and before 3. But surely then its intrinsic essence is determined by its relations to 1, 3 and to other numbers. Perhaps, then, relations and numbers are two sides of the same coin. Having said that, it's still hard to understand what the intrinsic essence of a number could be when that essence is taken separately to that number's relations to other numbers, functions, etc.
Of course this foray into the philosophy of mathematics completely ignores the precise relation between mathematical structuralism and the world. Despite saying that, Smolin does make an explicit philosophical commitment to mathematical structuralism. He writes:
“If there's more to matter than relationships and interactions, it is beyond mathematics.”
Thus Smolin firstly began by articulating the/a position of mathematical structuralism and ends up stating a position that's very close to ontic structural realism. However, the ontic structural realist argues that there's no “beyond mathematics” – or at least that there's nothing beyond the “relationships and interactions” of physics which are described by mathematics. Yet Smolin himself appears to leave it open that there may well actually be a beyond mathematics. And elsewhere in his writings Smolin seems to state that there are “intrinsic properties” (qualia, etc.) beyond mathematics and even beyond physics itself.
Intrinsic Essences, Qualia, Etc.
Smolin makes it explicit that he (at the very least) acknowledges the possibility of “intrinsic properties” as they occur in both minds (i.e., qualia) and in inanimate objects. For example, he writes:
“We don't know what a rock really is, or an atom, or an electron. We can only observe how they interact with other things and thereby describe their relational properties. The external properties are those that science can capture and describe – through interactions, in terms of relationships.”
The passage above might well have been written by someone like David Chalmers or Philip Goff – both of whom are advocates of panpsychism. In the case of panpsychists, the “what is” (or “what it is like to be”) of a rock can be explained by referring to its experiences (or to its “proto-experiences”). These experiences are therefore the “intrinsic essences” (to use Smolin's own term) of rocks for panpsychists (if not for Smolin himself). Clearly, according to the passage above, philosophical relationalism (or relationalism in physics itself – which Smolin thoroughly endorses) doesn't capture these intrinsic properties.
So it's no surprise that Smolin continues on the theme of intrinsic essence. He writes:
“The internal aspect is the intrinsic essence; it is the reality that is not expressible in the language of interactions and relations.”
We can of course ask why Smolin accepts the very existence (or reality) of an “internal aspect” of anything when many philosophers and other physicists reject this idea.
What's more, Smolin ties all this to both consciousness and qualia. Firstly he writes the following:
“What's missing when we describe a color as a wavelength of light or as certain neurons lighting up in the brain is the essence of the experience of perceiving red. Philosophers give these essences a name: qualia.”
Again (like Smolin's “intrinsic aspect” earlier), why does Smolin need to use the somewhat archaic word “essence” (archaic at least according to certain philosophers) at all? Why believe in essences?
Finally, Smolin writes:
“Consciousness, whatever it is, is an aspect of the intrinsic essence of brains.”
So clearly Smolin has been reading some contemporary (analytic) philosophers. It's just a little odd that he begins with the words “consciousness, whatever it is”; and then goes on to tell us exactly what it is: “the intrinsic essence of brains”.
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http://forum.arduino.cc/index.php?topic=85777.msg642742
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math
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You don't need an R1 unless you want to make the math more complicated.
Now that I've studied the device a litte bit more, it is a constant current device. In the low state it will always allow up to 6mA to flow through it and in the high state it will always allow up 15mA. (both of these are nominal values.) Remove R1. I will refer to R2 just in name.
So you pick a value of R2 that makes sense for 5V.
Ohm's Law: V = I * R
5 = 15mA * R
R = 5 / 15mA = 333.33333 = 330ohm
Knowing there is a 330ohm resistor there when your device is outputting a "low" your voltage will be:
V = 5mA * 330 = 1.5V which should give an A/D reading around 300.
Essentially since voltage of the cell output is always the same, the voltage drop measured across a shunt resistor is always the same.. :-/ Not sure..
The current through the device is always the same. The voltage drop is relative to whatever resistor it is in series with. With the 330ohm resistor, the voltage across your device should be nearly 0V when it is HIGH. It'll be about 4.5V when it is LOW.
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https://www.answers.com/Q/Why_is_pressure_higher_at_a_depth_of_10_meters_in_the_ocean_than_it_is_at_a_depth_of_150_kilometers_in_the_atmosphere
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math
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Asked in Oceans and Seas
Oceans and Seas
Why is pressure higher at a depth of 10 meters in the ocean than it is at a depth of 150 kilometers in the atmosphere?
Asked in Physics
How deep in water is 10atm of pressure?
Every 10 meters deep, the pressure increases by one atmosphere, approximately. Therefore, at 90 meters depth you would have, approximately, a pressure of 10 atm. (that is absolute pressure). Every 10 meters deep, the pressure increases by one atmosphere, approximately. Therefore, at 90 meters depth you would have, approximately, a pressure of 10 atm. (that is absolute pressure). Every 10 meters deep, the pressure increases by one atmosphere, approximately. Therefore, at 90 meters depth you would have, approximately, a pressure of 10 atm. (that is...
Asked in Meteorology and Weather, Chemistry
Where are most of the gas molecules found in the atmosphere?
The higher you go above the surface of the earth, the lower the air pressure is, and consequently the less gas molecules your will find within a given volume. Most of the gas molecules in the atmosphere are found below an altitude of 3 kilometers (3000 meters) above sea level. ...
Asked in School Subjects
A tank with a flat bottom is filled with water to a height of 3 5 meters what is the pressure at any point of the tank?
well for every 10 meters you go down, the pressure increases by 1 atmosphere. (atmosphere being a unit for pressure as my marine teacher says.) ...
How many metres in 300 kilometres?
1 kilometer = 1,000 meters 2 kilometers = 2,000 meters 3 kilometers = 3,000 meters . . 10 kilometers = 10,000 meters 20 kilometers = 20,000 meters 30 kilometers = 30,000 meters . . 100 kilometers = 100,000 meters 200 kilometers = 200,000 meters 300 kilometers = 300,000 meters ...
How many meters is 2.5 kilometers and how many meters is 5 kilometers?
there are 2,500 meters in 2.5 kilometers and 5,000 meters in 5 kilometers. ...
Asked in Elements and Compounds
What will be the volume of a cylinder at one atmosphere if it occupies a nitrogen gas of volume 6 cubic meter at a pressure of 150 newton per sqmeter?
Your question makes little sense. If a cylinder holds 6 cubic meters of nitrogen at one atmosphere pressure the volume of the cylinder is 6 cubic meters. However as 150 newtons per squsre meter = 150 Pascals = 0.001480384754 atmospheres, if you took 6 cubic meters of nitrogen at this pressure and then increased the pressure to 1 atmosphere the volue would shrink (because the volume of a gas is inversely proportional to the pressure) from 6 cubic meters to 0.008882308524 cubic meters. ...
Asked in Length and Distance
If something is .045 meters what will be the kilometers?
There are 0000450 kilometers in 0.045 meters. 0.045 meters x 0.001 kilometers/1 meters = .0000450 kilometers 1 meter = 0.001 kilometers ...
How many meters are equal to 81.2 kilometers?
Your 81.2 kilometers can be converted to meters by realizing that there are 1,000 meters in a kilometer. That makes 81.2 kilometers equal to 81,200 meters. As there are 1,000 meters in 1 kilometer, to convert kilometers to meters, multiply the number of kilometers by 1,000 to get your answer in meters. ...
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CC-MAIN-2019-47
| 3,174
| 24
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https://ralphieaversa.com/2008/05/sex-and-the-city-the-movie-the-drinking-game-2/
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math
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• The word “fabulous” is used.
• Samantha talks about how she used to sleep around.
• Miranda says “Brady.”
• Carrie smokes.
• Dramatic sigh.
• Any talk of private kindergarten.
• Charlotte starts getting real overbearing about the wedding plans.
• Carrie remarks, “I love it!”
• Steve’s all dopey.
• Anyone makes a deal about Miranda living in Brooklyn.
• Tears of joy.
• Big calls Carrie “kiddo.”
• Tears of sadness.
• Anyone refers to a gay man with a feminine term (girl, princess, etc)
• Every time a Latino person speaks without an accent.
• Celeb cameo! (Four if it’s Bloomberg.)
• Any mention of Aidan.
• One of “the ladies” says to Big, “You better not hurt my girl again.”
• Jennifer Hudson says something like, “The difference between white women and black women is …”
• Big gets cold feet.
• There’s a black person speaking who is not Jennifer Hudson.
• Anyone besides Miranda actually goes into Brooklyn.
• Disparaging term for women is used.
• Buying things, sex, eating or drinking recommended as valid solutions to a real problem.
• Charlotte talks about how weird it is to be Jewish.
Finish Your Drink
• Muslim cameo!
• Anyone says, “Spending hundreds of dollars just to buy more shoes is f*cking stupid,” or, “I don’t need that.”
• Big takes the subway.
• Carrie’s editor tells her, “Y’know, this is kind of silly; I’m going to need you to rework it.”
• Tears of regret over a life lived shopping and talking about shopping.
• Petrovsky stumbles into a room, drunk on absinthe, and shoots Big in the chest.
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CC-MAIN-2022-40
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| 32
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https://bookstore.ams.org/surv-161/31
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math
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10 0. MORSE THEORY AND VARIATIONAL PROBLEMS
It was also shown in Perera that the assumptions that B is bounded
and Φ is bounded from below on bounded sets can be relaxed as follows; see
also Schechter .
Theorem 0.26. If A homologically links B in dimension k, Φ|A ď a ă Φ|B
where a is a regular value, and Φ is bounded from below on a set C Ą B
such that the inclusion-induced homomorphism
H kpW zCq Ñ
H kpW zBq is
trivial, then Φ has two critical points u1 and u2 with
Φpu1q ą a ą Φpu2q, Ck`1pΦ,u1q ‰ 0, CkpΦ,u2q ‰ 0.
Corollary 0.27. Let W “ W1 ‘ W2, u “ u1 ` u2 be a direct sum decompo-
sition with dim W1 “ k ă 8. If Φ ď a on u1 P W1 : }u1} “ R
R ą 0, Φ ą a on W2, where a is a regular value, and Φ is bounded from
below on tv ` u2 : t ě 0, u2 P W2
for some v P W1z t0u, then Φ has two
critical points u1 and u2 with
Φpu1q ą a ą Φpu2q, CkpΦ,u1q ‰ 0, Ck´1pΦ,u2q ‰ 0.
The following theorem of Perera and Schechter gives a critical point
with a nontrivial critical group in a saddle point theorem with nonstandard
geometrical assumptions that do not involve a finite dimensional closed loop;
see also Perera and Schechter and Lancelotti .
Theorem 0.28. Let W “ W1 ‘ W2, u “ u1 ` u2 be a direct sum decompo-
sition with dim W1 “ k ă 8. If Φ is bounded from above on W1 and from
below on W2, then Φ has a critical point u1 with
inf ΦpW2q ď Φpu1q ď sup ΦpW1q, CkpΦ,u1q ‰ 0.
0.6. Local Linking
In many applications Φ has the trivial critical point u “ 0 and we are
interested in finding others. The notion of local linking was introduced by
Li and Liu [72, 66], who used it to obtain nontrivial critical points under
various assumptions on the behavior of Φ at infinity; see also Brezis and
Nirenberg and Li and Willem .
Definition 0.29. Assume that the origin is a critical point of Φ with Φp0q “
0. We say that Φ has a local linking near the origin if there is a direct sum
decomposition W “ W1 ‘ W2, u “ u1 ` u2 with W1 finite dimensional such
Φpu1q ď 0, u1 P W1, }u1} ď r
Φpu2q ą 0, u2 P W2, 0 ă }u2} ď r
for sufficiently small r ą 0.
Liu showed that this yields a nontrivial critical group at the origin.
Theorem 0.30. If Φ has a local linking near the origin with dim W1 “ k
and the origin is an isolated critical point, then CkpΦ, 0q ‰ 0.
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CC-MAIN-2022-05
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https://alevelphysics.co.uk/notes/conservation-of-energy/
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math
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Consider a scenario: When diesel is burned in a truck engine, some of the chemical energy stored in the form of liquid is converted into kinetic energy of the truck and some are wasted as thermal energy. When the truck stops, its kinetic energy is converted into internal energy in the brakes. The temperature of the brakes increases and heat energy is released. The outcome is that chemical energy has been converted into heat energy, which dissipates in the atmosphere and is of no further use. However, the total energy present in the universe has remained constant.
A. Principle of Conservation of Energy
All energy changes are governed by the law of conservation of energy. The law states that energy cannot be created or destroyed. It can only be converted from one form to another.
B. Kinetic Energy
Kinetic energy is associated with moving objects. As we know, a moving object can be made to do work as it slows down. For example, a moving hammer hits a nail and, as it stops, it does work to drive the nail into a wall.
The kinetic energy Ek joules (J) of an object of mass m (kg) moving with speed v (m/s) is given by the following equation. Ek is termed as translational kinetic energy since it is energy due to an object moving in a straight line. Rotating objects also have kinetic energy and that is known as a rotational form of energy.
C. Potential Energy
Newton’s law of gravitation tells us that all masses attract one another. When two masses are pulled apart, work is done on them and so they gain gravitational potential energy. If the masses move closer together, they lose gravitational potential energy.
If an object of mass m (kg) moves a vertical distance of h (m), then the gravitational potential energy stored in the object is defined by the following equation:
Consider a wagon that moves at a velocity reaching the top of a hill. From the top, it reaches the ground level. Figure 1 explains kinetic and potential energy of the wagon at three different places. At ground level, the wagon does not have potential energy. At the top of the hill, the wagon does not move. At that point, the potential energy of the wagon is at its highest and the kinetic energy of the wagon is zero.
Figure 1: Kinetic and Potential Energy
D. Applications of Conservation of Energy
The law of conservation of energy is a fundamental concept that is used in several scientific fields. Concepts such as kinetic energy and gravitational potential energy are used in designing cranes, elevators and roller-coaster rides.
A librarian stacks a bookshelf with 22 books, each with a mass of 350 g. Each book has to be raised by 2.2 m. Calculate the gravitational potential energy gained by the books.
Total mass raised = 22 x 350 = 7700 g = 7.7 kg
Increase in potential energy, Ep=m × g × h
= 7.7 x 9.8 x 2.2
= 166 J
- Energy cannot be created or destroyed. It can only be converted from one form to another.
- Kinetic energy is energy due to motion.
- Gravitational potential energy is energy possessed by a mass due to its position in a gravitational field.
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CC-MAIN-2023-50
| 3,065
| 21
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http://scitation.aip.org/content/aip/journal/jap/113/17/10.1063/1.4803681
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math
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Schematic representation of the shape of the vibrational modes of a plate. The dashed lines represent the nodal diametral and radial lines.
(a) Resonance frequency as a function of disk radius of an a-Si:H disk in the cases of a plate (ω 1 mn a = 3.196) and membrane (ω 1 mn a = 2.405), according to Eq. (2) (h = 3 μm) (b).
(a) Schematic of cross section of disk resonator. (b) SEM micrograph of a thin-film silicon microresonator fabricated on a glass substrate with one pair of actuation electrodes.
Resonance peaks of a 200 μm diameter disk resonator measured in vacuum with in-phase actuation (top) and anti-phase actuation (bottom).
Tension parameter as a function of the disk radius for the first vibrational mode (0,1) in the plate-like (k < 2) and membrane-like (k > 20) limits. 33
Resonance frequency as a function of the inverse disk radius for a-Si:H resonator modes (0,1) and (0,2) measured in vacuum (10−3 Pa).
Nonlinear vibrations effect due to large deformation at high bias voltage for a 100-μm radius disk.
Quality factor measured in vacuum as a function of the resonance frequency for a-Si:H disk resonators with radius that ranges from 50 μm to 113 μm.
Quality factor as a function of resonance frequency for the families of modes with multiple number of radial nodes (100 μm radius disk resonator).
Resonance frequency variation relative to unannealed state (top) and quality factor (bottom) for a series of 6 successive 1 h annealing steps at 250 °C.
Quality factor variation as a function of time for modes (0,1), (1,1)a, (1,1)b, and (0,2) of a 100 μm radius disk resonator.
Values of (α1 mna) for a disk clamped along the edges in the limit of negligible tension .
Values of (α1 mna) for a disk clamped along the edges in the limit of high tension .
Non-degenerated frequencies of modes (1,1) and (2,1) of a 125 μm radius disk.
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