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# Intensity (physics)

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### Intensity (physics)

In physics, intensity is the power transferred per unit area. In the SI system, it has units watts per metre squared (W/m2). It is used most frequently with waves (e.g. sound or light), in which case the average power transfer over one period of the wave is used. Intensity can be applied to other circumstances where energy is transferred. For example, one could calculate the intensity of the kinetic energy carried by drops of water from a garden sprinkler.

The word "intensity" as used here is not synonymous with "strength", "amplitude", "magnitude", or "level", as it sometimes is in colloquial speech.

Intensity can be found by taking the energy density (energy per unit volume) at a point in space and multiplying it by the velocity at which the energy is moving. The resulting vector has the units of power divided by area.

## Mathematical description

If a point source is radiating energy in all directions (producing a spherical wave), and no energy is absorbed or scattered by the medium, then the intensity decreases in proportion to distance from the object squared. This is an example of the inverse-square law.

Applying the law of conservation of energy, if the net power emanating is constant,

P = \int \bold I\, \cdot \mathrm{d}\bold A,

where P is the net power radiated, I is the intensity as a function of position, and dA is a differential element of a closed surface that contains the source.

If one integrates over a surface of uniform intensity I, for instance over a sphere centered around the point source, the equation becomes

P = |I| \cdot A_\mathrm{surf} = |I| \cdot 4\pi r^2 \,,

where I is the intensity at the surface of the sphere, and r is the radius of the sphere. (A_\mathrm{surf} = 4\pi r^2 is the expression for the surface area of a sphere).

Solving for I gives

|I| = \frac{P}{A_\mathrm{surf}} = \frac{P}{4\pi r^2}.

If the medium is damped, then the intensity drops off more quickly than the above equation suggests.

Anything that can transmit energy can have an intensity associated with it. For an electromagnetic wave, if E is the complex amplitude of the electric field, then the time-averaged energy density of the wave is given by

\left\langle U \right \rangle = \frac{n^2 \epsilon_0}{2} |E|^2 ,

and the intensity is obtained by multiplying this expression by the velocity of the wave, c/n:

I = \frac{c n \epsilon_0}{2} |E|^2,

where n is the refractive index, c is the speed of light in vacuum and \epsilon_0 is the vacuum permittivity.

The treatment above does not hold for electromagnetic fields that are not radiating, such as for an evanescent wave. In these cases, the intensity can be defined as the magnitude of the Poynting vector.[1]

## Alternative definitions of "intensity"

In photometry and radiometry intensity has a different meaning: it is the luminous or radiant power per unit solid angle. This can cause confusion in optics, where intensity can mean any of radiant intensity, luminous intensity or irradiance, depending on the background of the person using the term. Radiance is also sometimes called intensity, especially by astronomers and astrophysicists, and in heat transfer.

Table 1. SI photometry units
Quantity Unit Dimension Notes
Name Symbol[nb 1] Name Symbol Symbol
Luminous energy Qv [nb 2] lumen second lm⋅s TJ [nb 3] units are sometimes called talbots
Luminous flux Φv [nb 2] lumen (= cd⋅sr) lm J [nb 3] also called luminous power
Luminous intensity Iv candela (= lm/sr) cd J [nb 3] an SI base unit, luminous flux per unit solid angle
Luminance Lv candela per square metre cd/m2 L−2J units are sometimes called nits
Illuminance Ev lux (= lm/m2) lx L−2J used for light incident on a surface
Luminous emittance Mv lux (= lm/m2) lx L−2J used for light emitted from a surface
Luminous exposure Hv lux second lx⋅s L−2TJ
Luminous energy density ωv lumen second per metre3 lm⋅sm−3 L−3TJ
Luminous efficacy η [nb 2] lumen per watt lm/W M−1L−2T3J ratio of luminous flux to radiant flux
Luminous efficiency V 1 also called luminous coefficient
1. ^ photon quantities. For example: USA Standard Letter Symbols for Illuminating Engineering USAS Z7.1-1967, Y10.18-1967
2. ^ a b c Alternative symbols sometimes seen: W for luminous energy, P or F for luminous flux, and ρ or K for luminous efficacy.
3. ^ a b c "J" here is the symbol for the dimension of luminous intensity, not the symbol for the unit joules.
Quantity Unit Dimension Notes
Name Symbol[nb 1] Name Symbol Symbol
Radiant energy Qe[nb 2] joule J ML2T−2 energy
Radiant flux Φe[nb 2] watt W or J/s ML2T−3 radiant energy per unit time, also called radiant power.
Spectral power Φ[nb 2][nb 3] watt per metre W⋅m−1 MLT−3 radiant power per wavelength.
Radiant intensity Ie watt per steradian W⋅sr−1 ML2T−3 power per unit solid angle.
Spectral intensity I[nb 3] watt per steradian per metre W⋅sr−1⋅m−1 MLT−3 radiant intensity per wavelength.
Radiance Le watt per steradian per square metre W⋅sr−1m−2 MT−3 power per unit solid angle per unit projected source area.

confusingly called "intensity" in some other fields of study.

or
L[nb 4]
or

metre per hertz

W⋅sr−1m−3
or
W⋅sr−1⋅m−2Hz−1
ML−1T−3
or
MT−2
commonly measured in W⋅sr−1⋅m−2⋅nm−1 with surface area and either wavelength or frequency.

Irradiance Ee[nb 2] watt per square metre W⋅m−2 MT−3 power incident on a surface, also called radiant flux density.

sometimes confusingly called "intensity" as well.

or
E[nb 4]
watt per metre3
or
watt per square metre per hertz
W⋅m−3
or
W⋅m−2⋅Hz−1
ML−1T−3
or
MT−2
commonly measured in W⋅m−2nm−1
or 10−22 W⋅m−2⋅Hz−1, known as solar flux unit.[nb 5]

Me[nb 2] watt per square metre W⋅m−2 MT−3 power emitted from a surface.
M[nb 3]
or
M[nb 4]
watt per metre3
or

watt per square
metre per hertz

W⋅m−3
or
W⋅m−2⋅Hz−1
ML−1T−3
or
MT−2
power emitted from a surface per unit wavelength or frequency.

Radiosity Je watt per square metre W⋅m−2 MT−3 emitted plus reflected power leaving a surface.
Spectral radiosity J[nb 3] watt per metre3 W⋅m−3 ML−1T−3 emitted plus reflected power leaving a surface per unit wavelength
Radiant exposure He joule per square metre J⋅m−2 MT−2 also referred to as fluence
Radiant energy density ωe joule per metre3 J⋅m−3 ML−1T−2
1. ^ quantities should be denoted with a suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.
2. Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant emittance.
3. Spectral quantities given per unit wavelength are denoted with suffix "λ" (Greek) to indicate a spectral concentration. Spectral functions of wavelength are indicated by "(λ)" in parentheses instead, for example in spectral transmittance, reflectance and responsivity.
4. ^ a b c Spectral quantities given per unit frequency are denoted with suffix "ν" (Greek)—not to be confused with the suffix "v" (for "visual") indicating a photometric quantity.
5. ^ NOAA / Space Weather Prediction Center includes a definition of the solar flux unit (SFU).

## References

1. ^ Paschotta, Rüdiger. "Optical Intensity". Encyclopedia of Laser Physics and Technology. RP Photonics.
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### Home > CALC > Chapter 10 > Lesson 10.1.7 > Problem10-71

10-71.

Use the arclength formula to find the length of the curve $y = \frac { 1 } { 2 } x + 1$ from $x = 0$ to $x = 5$. Then compare your answer with the one found using the Pythagorean theorem.

format: plain


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Address 490 Park St, Hartford, CT 06106 (860) 519-1138

# expansion error East Windsor Hill, Connecticut

The system returned: (22) Invalid argument The remote host or network may be down. Firstly, we prove that the errors (YN−Y,ZN−Z)(YN−Y,ZN−Z) measured in the strong LpLp-sense (p≥1p≥1) are of order N−1/2N−1/2 (this generalizes the results by Zhang [J. Why would a password requirement prohibit a number in the last character? IDL: provides both erf and erfc for real and complex arguments.

Ronin-Life Enlisted: 2011-10-26 2015-09-01 18:43 , edited 2015-09-01 18:46 by Ronin-Life StarscreamUK said:if you have done the install log out then log back in I did. Privacy policy About Wikipedia Disclaimers Contact Wikipedia Developers Cookie statement Mobile view current community blog chat Mathematics Mathematics Meta your communities Sign up or log in to customize your list. The communication between module and controller was interrupted for more than 200 milliseconds. The forward component XX is the solution of a Brownian stochastic differential equation and is approximated by a Euler scheme XNXN with NN time steps.

Let r>0 such that the closed disk B(z,r)∪S(z,r) is contained in U. Similarly, R k ( x ) = f ( k + 1 ) ( ξ C ) k ! ( x − ξ C ) k ( x − a ) Namely, f ( x ) = ∑ | α | ≤ k D α f ( a ) α ! ( x − a ) α + ∑ | β | The zero function is analytic and every coefficient in its Taylor series is zero.

See [2]. ^ http://hackage.haskell.org/package/erf ^ Commons Math: The Apache Commons Mathematics Library ^ a b c Cody, William J. (1969). "Rational Chebyshev Approximations for the Error Function" (PDF). CmdrNeidermeyer Enlisted: 2011-10-24 2015-09-01 22:34 Can you check your Origin version? Using the alternate value a≈0.147 reduces the maximum error to about 0.00012.[12] This approximation can also be inverted to calculate the inverse error function: erf − 1  ( x ) The Taylor polynomials of the real analytic function f at a are simply the finite truncations P k ( x ) = ∑ j = 0 k c j ( x

Remedy signal interference. Let f: R → R be k+1 times differentiable on the open interval with f(k) continuous on the closed interval between a and x. Generated in 0.034 seconds (88% PHP - 12% DB) with 9 queries ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: Part of a series of articles about Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Rolle's theorem Differential Definitions Derivative(generalizations) Differential infinitesimal of a function total Concepts Differentiation notation

Note that here the numerator F(x) − F(a) = Rk(x) is exactly the remainder of the Taylor polynomial for f(x). Something is messed up. I then rebooted a second time and Origin had another update. The function f is infinitely many times differentiable, but not analytic.

Mar 28 '12 at 17:38 Sure, the error function is analytic... –J. Hence the k-th order Taylor polynomial of f at 0 and its remainder term in the Lagrange form are given by P k ( x ) = 1 + x + more stack exchange communities company blog Stack Exchange Inbox Reputation and Badges sign up log in tour help Tour Start here for a quick overview of the site Help Center Detailed Our open-source software package Cluster Expansion Version 1.0 allows users to expand their own energy function of interest and thereby apply cluster expansion to custom problems in protein design.© 2010 Wiley

more... Negative integer values of Im(ƒ) are shown with thick red lines. The graph of y = P1(x) is the tangent line to the graph of f at x = a. In general, the error in approximating a function by a polynomial of degree k will go to zero a little bit faster than (x − a)k as x tends toa.

However, its usefulness is dwarfed by other general theorems in complex analysis. Assuming that [a − r, a + r] ⊂ I and r

All that is said for real analytic functions here holds also for complex analytic functions with the open interval I replaced by an open subset U∈C and a-centered intervals (a−r,a+r) replaced Such an error may also result from a hardware malfunction. For complex, the Faddeeva package provides a C++ complex implementation. I'm now also getting the following issue: The Blue JOINING SERVER indicator at the bottom of the screen just keeps blinking Then after a long while the following error comes up:

Java: Apache commons-math[19] provides implementations of erf and erfc for real arguments. Since 1 j ! ( j α ) = 1 α ! {\displaystyle {\frac {1}{j!}}\left({\begin{matrix}j\\\alpha \end{matrix}}\right)={\frac {1}{\alpha !}}} , we get f ( x ) = f ( a ) + IEEE Transactions on Communications. 59 (11): 2939–2944. After multiplying by $2/\sqrt{\pi}$, this integrates to $$\operatorname{erf}(z) =\frac{2}{\sqrt{\pi}} \left(z-\frac{z^3}{3}+\frac{z^5}{10}-\frac{z^7}{42}+\frac{z^9}{216}-\ \cdots\right) .$$ EDIT: Since $\displaystyle \frac{d^n}{dx^n}e^{-x^2}= (-1)^n e^{-x^2} H_n(x),$ one can do a Taylor Series for every $a$:

Like Show 0 Likes (0) Actions Go to original post Follow Share Like Show 0 Likes 0 More Like This Retrieving data ... Click the View full text link to bypass dynamically loaded article content. National Library of Medicine 8600 Rockville Pike, Bethesda MD, 20894 USA Policies and Guidelines | Contact Screen reader users, click here to load entire articleThis page uses JavaScript to progressively load In particular, if | f ( k + 1 ) ( x ) | ≤ M {\displaystyle |f^{(k+1)}(x)|\leq M} on an interval I = (a − r,a + r) with some

Like Show 0 Likes (0) Actions 7. As a trade-off for evaluation speed, the cluster-expansion approximation causes prediction errors, which can be reduced by including more training sequences, including higher order terms in the expansion, and/or reducing the Taylor's theorem in complex analysis Taylor's theorem generalizes to functions f: C → C which are complex differentiable in an open subset U⊂C of the complex plane. PARI/GP: provides erfc for real and complex arguments, via tanh-sinh quadrature plus special cases.

Find its Taylor expansion. Like Show 0 Likes (0) Actions 9. Am I supposed to see it in the Expansions list, next to Final Stand? dfrnz Enlisted: 2013-10-06 2015-09-01 22:14 I've installed the new patch, I've purchased the new expansion for $0 and installed it, Origin launches as admin. This means that for every a∈I there exists some r>0 and a sequence of coefficients ck∈R such that (a − r, a + r) ⊂ I and f ( x ) For example, using Cauchy's integral formula for any positively oriented Jordan curve γ which parametrizes the boundary ∂W⊂U of a region W⊂U, one obtains expressions for the derivatives f(j)(c) as above, Secondly, an error expansion is derived: surprisingly, the first term is proportional to XN−XXN−X while residual terms are of order N−1N−1.MSC60H07; 60F05; 60H10; 65G99KeywordsBackward stochastic differential equation; Discretization scheme; Malliavin calculus; The error function and its approximations can be used to estimate results that hold with high probability. The fundamental theorem of calculus states that f ( x ) = f ( a ) + ∫ a x f ′ ( t ) d t . {\displaystyle f(x)=f(a)+\int _{a}^{x}\,f'(t)\,dt.} Not the answer you're looking for? It's free dbag! An example of this behavior is given below, and it is related to the fact that unlike analytic functions, more general functions are not (locally) determined by the values of their evandro_n Enlisted: 2013-11-08 2015-09-01 22:52 Same problem here, a pop up appears saying that I need to download the expansion to play the night shift. However, mapping parameters are introduced with two dollar signs$$whereas session parameters are always introduced with only one dollar sign$. Approximation of f(x)=1/(1+x2) by its Taylor polynomials Pk of order k=1,...,16 centered at x=0 (red) and x=1 (green).


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grobCoords {grid} R Documentation

## Calculate Points on the Perimeter of a Grob

### Description

These functions calculate points along the perimeter (or length) of a grob.

### Usage

grobCoords(x, closed, ...)
grobPoints(x, closed, ...)

### Arguments

 x A grob object. closed Whether we are asking for points along the perimeter of a closed object or points along the length of an open object. Some grobs (e.g., X-splines) can do both. ... Arguments to be used by methods.

### Details

The difference between grobCoords and grobPoints is that grobCoords performs all pre- and post-drawing operations on the grob that would normally occur if the grob was being drawn, then calls grobPoints. So the former takes into account any vp and gp settings on the grob. This means that users should usually only want to call grobCoords; only (expert) developers may have a need to call grobPoints.

Custom grobs can write their own methods for grobPoints (see gridCoords).

### Value

Either a "GridGrobCoords" object (a list of lists with components x and y) or a "GridGTreeCoords" object (a list of "GridGrobCoords" and/or "GridGTreeCoords" objects).

All locations are in inches relative to the current grid viewport.

### Author(s)

Paul Murrell

[Package grid version 4.2.0 Index]


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## Latex Math Letters

They are organized into seven classes based on their role in a mathematical expression. The Wolfram Language by default interprets any sequence of letters or letter-like forms as the name of a symbol. The Comprehensive LATEX Symbol List Scott Pakin 9 November 2009 Abstract This document lists 5913 symbols and the corresponding LATEX commands that produce them. This is identical to the tabular environment described in essential LATEX except that the entries are typeset in math mode instead of LR mode. I also prepared a quick reference of math symbols. It is also a large topic due to the existence of so much mathematical notation. LaTeX Math Symbols Prepared by L. 6 Appendices. I have been using \epsilon. Math Mode Accents. This small website is a tool for looking up the LaTeX commands for mathematical symbols - because it often isn't obvious what the command is. LaTeX is a powerful tool to typeset math. LaTeX provides means to describe special characters like accents or umlauts using a special notation, which can be used just the same inside of BibTeX Entries. A list of accent marks that are available in math-mode in LaTeX. Finding it difficult to recollect the exact meaning of a notation while solving mathematical equations? Don't worry, ScienceStruck is here to help you out. pdf that you just can't memorize. To typeset math, LaTeX offers (among others) an environment called equation. To place something written in TeX in math mode, use $signs to enclose the math you want to display. The Comprehensive LATEX Symbol List Scott Pakin 3 January 2008 Abstract This document lists 4947 symbols and the corresponding LATEX commands that produce them. In this tutorial I discuss how to use math environment in Latex. Another thing to notice is the effect of the \displaystyle command. A list of LaTEX Math mode symbols. TeX (LaTeX math mode) symbols in legends and Learn more about figure, deep learning vs. The corresponding right delimiters are of course obtained by typing ), ] and \}. Math Symbols used as Relation Symbols. Some of these blocks are dedicated to, or. LaTeX Letter Template The files below contain an attempt to emulate the new University regulations for letters. com is a blog of Latex tutorials. How to write matrices in Latex ? matrix, pmatrix, bmatrix, vmatrix, Vmatrix. From the naming, I think \therefore and \implies are redundant, but I can't find a symbol for \suchthat and at university, we used$\therefore$as a shortcut for "such that". To place something written in TeX in math mode, use$ signs to enclose the math you want to display. You can also generate an image of a mathematical formula using the TeX language (pronounced "tek" or "tech"). LaTeX Mathematical Symbols - Free download as PDF File (. In mathematical mode as well as in text mode, you can change the typeface as needed. el --- display tables of (La)TeX symbols in XEmacs. Comment dire à LaTeX de couper mes formules. (In other. Click on the equation button in the toolbar and insert your symbol, and you can even insert advanced inline latex. Can someone tell me a command which can accomplish this? \mbox can't do math mode, I think. , braces { }. Even though commands follow a logical naming scheme, you will probably need a table for the most common math symbols at some point. The sybmol can be compressed to fit on one line (useful for small equations displayed within a text block), or enlarged to make it more readable. For interchange of math expressions between arbitrary math-aware programs,. The tables of symbols are ordered in a logical way (the document begins with a ‘frequently requested symbols’ list), the aim being to make the document a convenient way of looking up symbols. Inserting Images; Tables; Positioning Images and Tables; Lists of Tables and Figures; Drawing Diagrams Directly in LaTeX; TikZ package References and Citations. pdf that you just can't memorize. As well as these accents, some characters can not be put directly into a BibTeX-entry, as they would conflict with the format description, like {, " or $. LaTeX formats mathematics the way it's done in mathematics texts. This command forces LaTeX to give an equation the full height it needs to display as if it were on its own line. The Comprehensive LATEX Symbol List Scott Pakin ∗ 22 September 2005 Abstract This document lists 3300 symbols and the corresponding LATEX commands that produce them. Periods and commas in mathematical writing it should be punctuated as it would be if the symbols were expanded into words. Mathematical symbols Mathematical symbols. Several fonts require the addition of the line \usepackage{amssymb} to the preamble to work. A LaTeX letter class, oxmathletter. Only symbols of type \mathalpha will be affected by math alphabet commands: within the argument of a math alphabet command they will produce the character in slot of that math alphabet's font. Applied mathematics in partnership with computational science is essential in solving many real-world problems. Finding it difficult to recollect the exact meaning of a notation while solving mathematical equations? Don't worry, ScienceStruck is here to help you out. ca June 13, 2019 Abstract The package actuarialsymbol provides facilities to compose actuar-ial symbols of life contingencies and ﬁnancial mathematics charac-. The Comprehensive L a T e X Symbol List – Symbols accessible from L a T e X Over 14000 symbols are listed as a set of tables. When I asked my students for feedback on L a T e X the consensus was that it is pretty easy but they need a list of symbols. In this post, I’m not so much interested in the definition of these notations, but rather in how to correctly typeset them in LaTeX. the whole message has to be in Latex. LaTeX2e in 90 minutes , by Tobias Oetiker, Hubert Partl, Irene Hyna, and Elisabeth Schlegl. You can find them in Wikipedia's list of mathematical symbols. Here are some examples that show how to achieve this goal. Inserting Greek symbols, complicated technical. Also, one could observe the symbols being easy to reach when needed. LaTeX numbering One advantage of LaTeX over the other TeX-flavors is that it provides an automatic numbering of the sections, theorems, equations etc. Secondly, the words don't look quite right --- the letters are more spaced out than normal. I am looking for exactly the reverse of the vector symbol in \vec{x}. Typesetting journal articles, technical reports, books, and slide presentations. Board index LaTeX Text Formatting Ask a question LaTeX Community Announcements Community talk Comments & Wishes New Members LaTeX Text Formatting Graphics, Figures & Tables Math & Science Fonts & Character Sets Page Layout Document Classes General LaTeX's Friends. Set Subtraction. It turns out that a lot of the script styles in math mode are upper case only. Jump to: navigation, search. These range from accents and greek letters to exotic mathematical operators. Make math interesting. Comment dire à LaTeX de couper mes formules. MS-Word File with Mathematical Symbols First I give a list of symbols for both MS-Word and Powerpoint. If you want different spacing, LaTeX provides the following four commands for use in math mode: \; - a thick space \: - a medium space \, - a thin space. The format offers plenty of space for a longer cover letter and includes a description of the content that should be written in each paragraph. It contains a lot of keyboard shortcuts for rapid input almost all important math symbols. More complex operations? Get HTML symbols and ASCII characters for multiplication and division signs, greater than and less than signs, equals sign, not equal sign and more. Does anybody know if there is a way to make the math symbols work in latex in verbatim mode? If yes, then how?. Text Math Macro Category Requirements Comments 000A2 ¢ g \cent mathord wasysym = \mathcent (txfonts), cent 021BA ↺ " \circlearrowleft mathord amssymb = \leftturn (wasysym), ANTICLOCKWISE OPEN CIRCLE ARROW. Often, during a conversation or an email, or at a forum, I would like to type some math, but I don't need full equation support. Search results for MATH font, free downloads of MATH fonts at Fonts101. In certain cases it may be desirable to include "normal text" within an equation. Some Tips and Tricks for Using LaTeX in Math Theses by Rob Benedetto How to Use the les samplethesis. Let be an integer variable which tends to infinity and let be a continuous variable tending to some limit. A Mathematical symbols \alpha \beta \gamma \delta \epsilon \varepsilon \zeta \eta AMS miscellaneous symbols. Here is a definition of the grammar used to parse AsciiMath expressions. From our Help Center article, How do you use LaTeX mathematical notation for formulae on Quora?: > You can write LaTeX and have it styled correctly by using the Math formatting option in the Quora editor (see screenshot) or by using the keyboard s. 5 Table of symbols and notation It is sometimes useful to give the reader a table with the symbols and the notation used in the thesis (Fig. tex, and latextips. There are three commonly used environments in the math mode: the math environment: Used for formulas in running text the displaymath environment: Used to display longer formulas the equation environment: Used for displaying equations for numbering and cross reference math environment. which one is the best / recommended? how do i configure it? all i want is to be able to connect my desktop computer through my laptop. In my experience, the three biggest obstacles to learning are a student’s belief that math is boring, math is impossible, or math is irrelevant. Versions are available for a variety of computer operating systems, including Windows, linux, and MacOS. The Comprehensive LATEX Symbol List Scott Pakin ∗ 8 October 2002 Abstract This document lists 2590 symbols and the corresponding LATEX commands that produce them. In scilab, you can use Latex commands to add any symbols such as pi. The terminology from AMS-LaTeX documentation. ~\cite{latex}. The frequently used left delimiters include (, [ and {, which are obtained by typing (, [and \{respectively. Open an example in Overleaf [] Capital letters-only font typefaceThere are some font typefaces that support only a limited number of characters; these fonts usually denote some special sets. The nomenclpackage automatically generates such a list with the MakeIndex program. LaTeX also takes care of equation numbers for us:. Here are some examples that show how to achieve this goal. This is the standard for book margins. In math, certain blackboard (double-barred) letters Z, N, R, etc. The words are: minus, plus, times, equal, less than equal, less than, greater than, greater than or equal, percent, division symbol. It is especially useful for documents that contain mathematical symbols and related formulae. Learn about the people and activities that make UC Berkeley one of the best places in the world for advanced research, graduate and undergraduate study in mathematics. There's no sans serif upright Greek alphabet, but LaTeX can display this math style. Since I already know latex, it makes sense to use the latex symbol mnemonics to type the math symbols. Main article: Asymptote Asymptote is a powerful vector graphics language designed for creating mathematical diagrams and figures. Macro files for Plain TeX and LaTeX support; Bitmap (PK) files are no longer distributed or supported. Or, using Tools > Catalog, you can define symbols that use a specific font, so you still have all of Math's text categories available. In a math environment, LaTeX ignores the spaces you type and puts in the spacing that it thinks is best. The different font sizes are listed below. Found this handy List of LaTeX mathematical symbols! Close. The Comprehensive LATEX Symbol List Scott Pakin 9 November 2009 Abstract This document lists 5913 symbols and the corresponding LATEX commands that produce them. LaTeX: Changing the Font Size Latex provides 10 different font sizes. 2 Math symbols. This article provides the list of most commonly used symbols in LaTeX. Knows symbols and environments PDF synchronization extT folding. Open an example in Overleaf Further Reading. I have looked thru several documents re math in Latex, and have not found one which collects the common math symbols in one place. a=b \xleftarrow[H]{\xi+a\timesc} f=g; Using \overset. Setting mathematical styles. It turns out that a lot of the script styles in math mode are upper case only. Beautiful Math with LaTeX LaTeX is a powerful markup language for writing complex mathematical equations, formulas, and more. If these figures are e. Each letter consists of four parts. The$\rm\TeX $commands available in MathJax are listed alphabetically on this page, each with a brief description. Part of the problem is that the tilde is a reserved character in TeX, which means that it is very hard to display it (except through the \tilde command, which produces an accent above a letter). Start studying Math Symbols. Linting; Snippets. Mathematical Bold Fraktur. It is interesting to note that the whole of maths is completely based on numbers and symbols. math symbols latex | Documentine. Also mathematical documents often contain arrays of numbers or symbols (ma-trices) and other complicated expressions. I was wondering about the use of latex symbols \implies ($\implies$) and \therefore ($\therefore$). Inserting Greek symbols, complicated technical. Mathematical Alphanumeric Symbols In Unicode And LaTeX mathalpha -literal. Here is what your formula looks like with the Cambria font in MS Word: If you are considering a career as an academic, and you'll be publishing a lot of papers containing mathematics, then learning LaTeX is definitely worthwhile. For example, Edmodo will show the formula shown in the left column below if you send a note with the text shown in the right column. The layout is traditional and is best suited to single-page letters. It may happen that you need a more recent LaTeX than the one that your favourite TeX distribution carries, e. = mathrm{A}, LATIN CAPITAL LETTER A mathalpha -literal. Typesetting zodiac symbols in LaTeX is admittedly an unusual thing to do. It contains a lot of keyboard shortcuts for rapid input almost all important math symbols. The first mathematical symbols were signs for the depiction of numbers — ciphers, the appearance of which apparently preceded. Sometimes math uses a new font rather than a new alphabet, such as Fraktur. By typing standard text on a keyboard, one can represent all of the mathematical symbols from the most elementary to the most advanced. This is a list of symbols found within all branches of mathematics. tex) is NOTa good model to build a math thesis from. symbol name LATEXcode symbol leftarrow \leftarrow select \sigma ˙ project \Pi inner join \bowtie. Ahh, that's why I could get it to work. In fact, you can roundtrip RichEdit documents containing math zones through the plain-text editor Notepad and the math zones are preserved. Other than that, I think you are right, it’s a personal choice whether you prefer switching to math mode or using the textgreek package. If these figures are e. For example, A minus B can be written either A – B or A \ B. This what MathType does, a powerful equation editor that you can use with Office or on its own. I have listed them in this short tutorial. α \alpha κ \kappa ψ \psi Ϝ \digamma ∆ \Delta Θ \Theta. Selected LaTeX Math Symbols Note: there is another version of this document featuring HTML entities for math symbols , as well as LaTeX commands. LaTeX forum ⇒ Math & Science ⇒ Mathematical Expectation symbol Information and discussion about LaTeX's math and science related features (e. 09 (2002-03-22) 5 3. Solid Geometry. In our project, we have this module meant strictly for our custom API endpoints for our mobile applications to use. Inserting Images; Tables; Positioning Images and Tables; Lists of Tables and Figures; Drawing Diagrams Directly in LaTeX; TikZ package References and Citations. The package cmbright. All common mathematical symbols are implemented, and you can find a listing on the LaTeX cheat sheet. Also, the letters are not in italics by default. what is the symbol of permutation, how to write permutation on latex, latex combination pe, latex typeset perm, latex command for permutation symbol, combination notation latex, Symbol in of permutations and combinations, how to write conbination and parmutTion symbol in latex, permutation latex, How to write permutation in latex, permutation. latex dot product symbol; If this is your first visit, be sure to check out the FAQ by clicking the link above. Put a label inside it using \label{foo} and then use \ref{foo} to typeset the equation number. But \mathcal only seems to have upper case letters. LaTeX Command Symbols _{exp} To get an expression exp to appear as a subscript. Math Symbols used as Relation Symbols. If you've ever tried to create web pages that contain mathematical notation for expressions and equations, you've learned just how inconvenient HTML (HyperText Markup Language) is for such tasks. ~\cite{latex}. There are countless packages, all for different purposes in my tutorials I will explain some of the most useful. In conjunction with the previous tutorial on math, by the end of the session, you will be in pretty good shape to write almost anything that your work will require. Spacing in Math Mode. List of Greek Letters and Math Symbols - ShareLaTeX, Online LaTeX Editor - Free download as PDF File (. Click HERE for a reference document outlining symbols available in the amssymb package. You have to be clever if you want to use LaTeX in your Prezi talk. For example, the following example illustrates that \sum is one of these elite symbols whereas \Sigma is not. Spacing in math mode; Integrals, sums and limits; Display style in math mode; List of Greek letters and math symbols; Mathematical fonts Figures and tables. Accessibility is a must for any quality solution. The full text of this document is also posted on our class Blackboard page, under. Under Pictures & Tables, click Symbol. Word has a new math ribbon with an explicit LaTeX option as shown in the article Linear format equations using UnicodeMath and LaTeX in Word. ;; Copyright (c) 1999, 2000, 2001 ;; John Palmieri ;; Author: John Palmieri ;; Maintainer: John.$\boldsymbol{=}$The equals sign "=" has a standard meaning in math: "x = y" means x and y are two different names for the same mathematical object. If you want the same body in all the letters, you may want to consider putting the entire body in a new command like \newcommand {\BODY}{actual body} and then using \BODY in all the letters. In general, if you're used to Latex, then you can simply enter Latex codes such as \rightarrow in math mode, and LyX will display most of the symbols correctly (you may have to press the SPACE key or move the cursor before LyX displays the symbol). com offers free software downloads for Windows, Mac, iOS and Android computers and mobile devices. No installation, real-time collaboration, version control, hundreds of LaTeX templates, and more. Mathematical Symbols. Note that math mode ignores whitespace, in fact, this whole code could have been put on one line and still would have compiled correctly. Because you type the mathematics directly, it is quick and easy to include a lot of mathematics in your text. Text Math Macro Category Requirements Comments 000A5 ¥ U \yen mathord amsfonts YEN SIGN 000AE ® r \circledR mathord amsfonts REGISTERED SIGN 000F0 ð g \eth mathalpha amssymb arevmath eth 00302 x̂ (bx) \hat mathaccent # \widehat (amssymb), circumﬂex accent. Or, using Tools > Catalog, you can define symbols that use a specific font, so you still have all of Math's text categories available. ? If this question is repeated, I am sorry I just searched and couldn't find an answer. If you want to use them in text just put the arrow command between two$ like this example: $\uparrow$ now you got an up arrow in text. mathalpha cursive small l. Letters are printed in italics, with more space left in-between, spaces are ignored. tex and cutting the pictures out of the resulting preview. I want to thank all the developer for providing such flexible tool. Formal letters, Cover letters, Newsletters 17 Topics 41 Posts. Special Symbols in LaTeX. Fill in The Unit Circle Positive: Negative: Positive: Negative: Positive: Negative: ( Positive: Negative: EmbeddedMath. Letters are printed in italics, with more space left in-between, spaces are ignored. They include the latex degree symbol, does-not-equal sign, greater-than-or-equal-to, less-than-or-equal-to signs, omega symbol, approximately symbol, etc. Learn about the people and activities that make UC Berkeley one of the best places in the world for advanced research, graduate and undergraduate study in mathematics. Only symbols of type \mathalpha will be affected by math alphabet commands: within the argument of a math alphabet command they will produce the character in slot of that math alphabet's font. Mathematical genealogy and list of Ph. Page breaks in math environments []. , together with an easy way to refer to these numbers. Depending on your preferred input format, you can create equations in Word in either one of UnicodeMath or LaTeX formats by selecting the format from the Equations tab. \infty \Rightarrow \surd \bigotimes ∞⇒ √N 4. Sigma notation provides a way to compactly and precisely express any sum, that is, a sequence of things that are all to be added together. for {Windows, Mac OS X, Linux}. Word has a new math ribbon with an explicit LaTeX option as shown in the article Linear format equations using UnicodeMath and LaTeX in Word. No installation, real-time collaboration, version control, hundreds of LaTeX templates, and more. I have looked thru several documents re math in Latex, and have not found one which collects the common math symbols in one place. The Comprehensive LATEX Symbol List Scott Pakin ∗ 22 September 2005 Abstract This document lists 3300 symbols and the corresponding LATEX commands that produce them. As mention above, a plain text editor (Notepad) will not be able to show you symbols and mathematical formulas, etc. MATHCOUNTS Trainer LaTeX TeXeR MIT PRIMES My daughter was already very good at math before she took Prealgebra through AoPS. List of all mathematical symbols and signs - meaning and examples. For example, Edmodo will show the formula shown in the left column below if you send a note with the text shown in the right column. txt) or read online for free. This video explains how to add latex formatted text and math symbols in a scilab plot. Refer to the external references at the end of this article for more information. Math I: Super/Subscripts and Common Commands Introduction This tutorial will show you how to do some basic typesetting of math symbols, equations and matrices. LaTeX Mathematics Symbols. Including math equations, symbols, and more in your Top Hat questions and discussions is possible using the Inline Symbol Selector or LaTex, a popular markup language. I hope someone can help me :) I use GnuPlot to. A list of accent marks that are available in math-mode in LaTeX. In my presentation below, all squares and the main formula are products of LaTeX, the rest is Prezi. In certain cases it may be desirable to include "normal text" within an equation. Spacing in math mode; Integrals, sums and limits; Display style in math mode; List of Greek letters and math symbols; Mathematical fonts Figures and tables. I have looked thru several documents re math in Latex, and have not found one which collects the common math symbols in one place. 1These symbols are also available in math mode through the use of the mathcomppackage. Greek Letter 2. Type the name of the symbol you're looking for in the text box below to search all of the commands listed on this website. […] gaudetteje Says: February 5, 2014 at 9:37 am | Reply. We will use \LaTeX, which is based on \TeX\ and has many higher-level commands (macros) for formatting, making tables, etc. In reading about this issue, I came across a nice Blog post [A Math Prezi]. , braces { }. In my presentation below, all squares and the main formula are products of LaTeX, the rest is Prezi. 4 Math-mode accent marks ^a a a a nhatfag ncheckfag nbrevefag nacutefag a ~a a ~a ngravefag ntildefag nbarfag nvecfag a_ a a 0 ndotfag nddotfag anspfnprimeg Greek Letters nalpha nbeta ngamma ndelta nepsilon" # nvarepsilon nzeta neta ntheta nvartheta niota nkappa nlambda nmu nnu ˘ ˇ \$ ˆ % nxi npi nvarpi nrho nvarrho ˙ & ˝ ˛ ˚. For the author byline, use the formatting and symbols included in the template. Download MathType for Windows now from Softonic: 100% safe and virus free. The notation was introduced by the German mathematician Gottfried Wilhelm Leibniz in 1675 in his private writings; it first appeared publicly in the article "De Geometria Recondita et analysi indivisibilium atque infinitorum" (On a hidden geometry and analysis of indivisibles and infinites), published in Acta Eruditorum in June 1686. Mathematical Symbols. Here is what your formula looks like with the Cambria font in MS Word: If you are considering a career as an academic, and you'll be publishing a lot of papers containing mathematics, then learning LaTeX is definitely worthwhile. Most math symbols are Latin or Greek letters, but occasionally you'll run into Russian or Hebrew letters. Math mode accents 12. When I asked my students for feedback on L a T e X the consensus was that it is pretty easy but they need a list of symbols. trigonometry symbols, find the equivalent of the expression tan tither /sec theta, what does the symbol of tither mean in mathematics, Cot square tither is equal, titer sysbol, symboy of titer, math titer. 07 (2000/07/19) 4 Note 1. This is a cheat sheet for writing mathematics with L a T e X. In order to access all the math functions and symbols we will introduce in the guide pages, you'll have to include a number of packages. In a math environment, LaTeX ignores the spaces you type and puts in the spacing that it thinks is best. Letters are. Use the templates to create educational math illustrations with the shapes of plane and solid geometric figures, trigonometrical functions and Greek letters. Also, let or be a positive function and or any function. We just made a new paragraph. Inserting Greek symbols, complicated technical. The value of a counter can be changed with a command of the type \setcounter{equation}{0}. \textbf|apply to these Greek letters as to usual text and the font is upright in an upright environment. Latex symbols in Math mode. One also needs to be able to change fonts. Note that math mode ignores whitespace, in fact, this whole code could have been put on one line and still would have compiled correctly. com and in the control panel set your grabs to be "private" instead of public. Text Math Macro Category Requirements Comments 000A5 ¥ U \yen mathord amsfonts YEN SIGN 000AE ® r \circledR mathord amsfonts REGISTERED SIGN 000F0 ð g \eth mathalpha amssymb arevmath eth 00302 x̂ (bx) \hat mathaccent # \widehat (amssymb), circumﬂex accent. Let be an integer variable which tends to infinity and let be a continuous variable tending to some limit. Jupyter notebook recognizes LaTeX code written in markdown cells and renders the symbols in the browser using the MathJax JavaScript library. The closest I can seem to get is by using \wedge, which isn't the same. It is also crowned to be one among the most useful LaTeX editor there is. Also, let or be a positive function and or any function. They also need to fully understand the equations and formula themselves. com and download a free version of math type. LaTeX is a powerful tool to typeset math. But \mathcal only seems to have upper case letters. An online LaTeX editor that's easy to use. A LaTeX letter class, oxmathletter. Cursive small letter in math mode Hi All, I want to add a cursive small letter "r" to my equations, like the kind you find in Griffiths' book on E&M when he is talking about separation vectors. Some of these symbols are guaranteed to be available in every LATEX2𝜀system; others require fonts and. For instance the obsolete eqnarray environment frequently appears in questions of new LaTeX users and many people including me usually answer: don’t use eqnarray and give advice how to use the align environment of amsmath instead. 9 List of Mathematical Symbols 45 3. pdf), Text File (. You can find them in Wikipedia's list of mathematical symbols. The more unusual symbols are not defined in base LATEX (NFSS) and require usepackage{amssymb}. Selected LaTeX Math Symbols Note: there is another version of this document featuring HTML entities for math symbols, as well as LaTeX commands. This list of mathematical symbols by subject shows a selection of the most common symbols that are used in modern mathematical notation within formulas, grouped by mathematical topic. The project has settled on using both HTML and Template:TeX because each has advantages in some situations. They let me in even though my undergrad GPA was abysmal (2. Different classes of mathematical symbols are characterized by different formatting (for example, variables are italicized, but operators are not) and different spacing. Most letters and symbols are simple in LaTeX, yet a few characters are reserved for LaTeX commands, i. The corresponding right delimiters are of course obtained by typing ), ] and \}. latex-workshop. LaTeX is a math markup language familiar to many in the science and math community, but unfortunately is not currently supported by screenreader technlogy. explains how symbols are spaced in math mode, presents a LATEX ASCII and Latin 1 tables, and provides some information about this document itself. \infty \Rightarrow \surd \bigotimes ∞⇒ √N 4. The usual font selection commands|e. tex file (the source) for copying. Math symbols and math fonts 3. Refer to the external references at the end of this article for more information. 18List of Mathematical Symbols 19Summary 20Notes 21Further reading 22External links Mathematics environments LaTeX needs to know beforehand that the subsequent text does indeed contain mathematical elements. In the Equation Editor Design ribbon, go to the Conversions group and click LaTeX. Log-like Symbols. To insert symbols, Click More > Insert tab. You should visit the following links: For vectors: An introduction to beautiful math on Quora For matrices: An introduction to beautiful math on Quora. The maths styles can be set explicitly. How to write two dot above a letter? Ask Question Asked 5 years, 8 months ago. In this regard, the package provides \bigpumpkin \greatpumpkin. Sometimes math uses a new font rather than a new alphabet, such as Fraktur. This package defines the following commands:. The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. Secondly, the words don't look quite right --- the letters are more spaced out than normal. The Wolfram Language by default interprets any sequence of letters or letter-like forms as the name of a symbol. The advantages of LaTeX include that it is public domain, platform and printer independent, allows mathematical symbols and equations to be entered much easier and quicker than word processors, and produces camera ready text. The mathematical community almost universally accepts a typesetting language called LaTeX. Typesetting mathematics is one of LaTeX's greatest strengths. LaTeX: stack three lines in math mode. sty does not provide bold maths, whereas with sfmath. LaTeX Mathematics Symbols. The four basic operations are denoted by the following symbols: “+” implies addition, “-“ implies subtraction, “x” implies multiplication, and “/” implies division. The Comprehensive LATEX Symbol List Scott Pakin 9 November 2009 Abstract This document lists 5913 symbols and the corresponding LATEX commands that produce them. http://quicklatex. I want to put a left arrow over letter in math mode. Search results for MATH font, free downloads of MATH fonts at Fonts101. This article shows several fonts for use in math mode. module file like so: my_project_mobile_api. Inserting Images; Tables; Positioning Images and Tables; Lists of Tables and Figures; Drawing Diagrams Directly in LaTeX; TikZ package References and Citations. Math Mode Accents. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. Bibliography management in. Si, au contraire, on souhaite que LaTeX puisse couper à un endroit on rajoutera un \linebreak (qui suggère un point de coupure mais ne le force pas obligatoirement). I hope someone can help me :) I use GnuPlot to. They also need to fully understand the equations and formula themselves. Just as with \pagebreak, \displaybreak can take an optional argument between 0 and 4 denoting the level of desirability of a page break. For this example, plot y = x 2 sin (x) and draw a vertical line at x = 2. It is also crowned to be one among the most useful LaTeX editor there is. Many classes of sets are denoted using doublestruck characters. MathJax basic tutorial and quick reference.


text:
# Assembling a digital voltage display

J

#### JoeSpareBedroom

Jan 1, 1970
0
I need to assemble a digital voltage display for, of all things, a bass
guitar which uses two 9v batteries to supply power for tone control
circuitry. I need some tips. The problem to be solved is this: Unscrewing
the battery hatch in the instrument is no big deal, but checking the
batteries involves flexing the wires, and this has caused failures twice in
the past. So, I'm thinking of mounting something like this on the surface of
the instrument:

http://tinyurl.com/2yt6mx

I'd actually need a display which also showed a decimal point and tenths of
volts, but the example should be enough to illustrate the basic idea here.
In addition to the display, I'll probablly want to mount a button or switch
to disconnect the batteries from the circuitry, and enable the display just
long enough to check voltage. I need to measure as low as about 6.5 volts,
at which point the circuitry ceases to operate, and any lower voltage is
irrelevant.

So:

1) If components like the LED display could operate without a few other
parts involved, that would be too easy, right? If someone can recommend a
decent book which might contain info on what I'd need to add, in order to
make this work, that would be great. (I'm old - I know how to operate a
library card).

2) I haven't checked all 28 billion google results yet, but if anyone can
suggest a better source than Radio Shack for LED displays, that would be
great.

Of course, I could just mount a banana plug jack on the face of the
instrument, and plug in a voltmeter when necessary, but that's one more
contraption I don't have room for on top of the amp during performances.

T

#### Tim

Jan 1, 1970
0
I need to assemble a digital voltage display for, of all things, a bass
guitar which uses two 9v batteries to supply power for tone control
circuitry. I need some tips. The problem to be solved is this: Unscrewing
the battery hatch in the instrument is no big deal, but checking the
batteries involves flexing the wires, and this has caused failures twice in
the past. So, I'm thinking of mounting something like this on the surface of
the instrument:

http://tinyurl.com/2yt6mx

I'd actually need a display which also showed a decimal point and tenths of
volts, but the example should be enough to illustrate the basic idea here.
In addition to the display, I'll probablly want to mount a button or switch
to disconnect the batteries from the circuitry, and enable the display just
long enough to check voltage. I need to measure as low as about 6.5 volts,
at which point the circuitry ceases to operate, and any lower voltage is
irrelevant.

So:

1) If components like the LED display could operate without a few other
parts involved, that would be too easy, right? If someone can recommend a
decent book which might contain info on what I'd need to add, in order to
make this work, that would be great. (I'm old - I know how to operate a
library card).

2) I haven't checked all 28 billion google results yet, but if anyone can
suggest a better source than Radio Shack for LED displays, that would be
great.

Of course, I could just mount a banana plug jack on the face of the
instrument, and plug in a voltmeter when necessary, but that's one more
contraption I don't have room for on top of the amp during performances.
Any device you put on to monitor your batteries is going cause more
drain. Instead of LED type, you might want to consider LCD, or perhaps a
low battery warning with no display, something that beeps when you need
to replace the cells.

My 2 cents worth anyways... (and that's CDN cents too...)

- Tim -

J

#### JoeSpareBedroom

Jan 1, 1970
0
Tim said:
Any device you put on to monitor your batteries is going cause more
drain. Instead of LED type, you might want to consider LCD, or perhaps a
low battery warning with no display, something that beeps when you need
to replace the cells.

My 2 cents worth anyways... (and that's CDN cents too...)

- Tim -

LCD would be fine. A bit less visible, but not a big problem. As far as the
beep idea, it would never be heard during a performance.

T

#### Tim

Jan 1, 1970
0
LCD would be fine. A bit less visible, but not a big problem. As far as the
beep idea, it would never be heard during a performance.
Well my idea of a low battery warning, would be at the point where you
would have less than a few hours left on cells, not when you had a few
minutes, so if you had a beep before the set, you changed batteries. A
beep after or during the set would not be a concern, as you would have
enough power to finish the set.

- Tim -

E

#### ehsjr

Jan 1, 1970
0
JoeSpareBedroom said:
Of course, I could just mount a banana plug jack on the face of the
instrument, and plug in a voltmeter when necessary, but that's one more
contraption I don't have room for on top of the amp during performances.

That's your best option. Get some Velcro with
adhesive backing, and hang the voltmeter on the
side of the amp.You can get a dirt cheap voltmeter
on sale from Harbor Freight that will be fine for
this function. It's on sale now for $4.99 - in the past it has gone for as low as$2.99. ITEM 90899-2VGA
http://www.harborfreight.com/

Ed

A

#### [email protected]

Jan 1, 1970
0
Why so complicated? Why not a good old d'Arsonval movement? Drains
microamps.

J

#### JoeSpareBedroom

Jan 1, 1970
0
Why so complicated? Why not a good old d'Arsonval movement? Drains
microamps.

Needle type meter? I wondered about that, but I also wonder about
durability. The bass doesn't get banged around much, but still....

And on the other hand, I've met old Simpson meters that never seem to die.

G

#### Gary Tait

Jan 1, 1970
0
LCD would be fine. A bit less visible, but not a big problem. As far
as the beep idea, it would never be heard during a performance.

If you want a small battery level meter, a simple bar meter will do (button
activated) , or even a simple comparater lighting a "battery good" LED, or
a "battery low" LED

You could esaily attach a coaxial jack on each device you wish to test, and
use an external tester that would be no bigger than a 9V battery.

L

#### Lostgallifreyan

Jan 1, 1970
0
or even a simple comparater lighting a "battery good" LED, or
a "battery low" LED

I was thinking this too. Never came up with the goods though so I let it
go... I was thinking of MOSFETS. There might be a way to keep one turned
off when the gate voltage is high enough, so that the total current draw is
in the nanoamp range, but the LED begins to glow more as voltage falls.
Obviously the limited remaining charge will be used even more rapidly, but
usefully, and no significant drain would begin till there was a need to
indicate. I'd hoped to work out something with one FET, an LED, and no more
than two resistors, but it eluded me. Maybe it can't be done that simply,
but it seems like the way to go, to get as close to that as possible.

R

#### rpbc

Jan 1, 1970
0
by "JoeSpareBedroom" <[email protected][EMAIL PROTECTED] > May 5, 2007 at 03:16
PM

<[email protected][EMAIL PROTECTED]
wrote in message
Why so complicated? Why not a good old d'Arsonval movement? Drains
microamps.

Needle type meter? I wondered about that, but I also wonder about
durability. The bass doesn't get banged around much, but still....

And on the other hand, I've met old Simpson meters that never seem to
die.

rpbc: Why not build a regulated 9 volt supply and feed it from the power
supply of the bass amp... or just buy a little wall type transformer of
the right voltage wired to the bass amp power switch, and add filter and
regulation to that? Then you won't have to worry about the battery.

J

#### JoeSpareBedroom

Jan 1, 1970
0
rpbc said:
by "JoeSpareBedroom" <[email protected][EMAIL PROTECTED] > May 5, 2007 at
03:16
PM

<[email protected][EMAIL PROTECTED]
wrote in message
Why so complicated? Why not a good old d'Arsonval movement? Drains
microamps.

Needle type meter? I wondered about that, but I also wonder about
durability. The bass doesn't get banged around much, but still....

And on the other hand, I've met old Simpson meters that never seem to
die.

rpbc: Why not build a regulated 9 volt supply and feed it from the power
supply of the bass amp... or just buy a little wall type transformer of
the right voltage wired to the bass amp power switch, and add filter and
regulation to that? Then you won't have to worry about the battery.

Because I play 99% of the time with a Sennheiser wireless setup. I move
around too much to have wires underfoot.

R

#### rpbc

Jan 1, 1970
0
by "JoeSpareBedroom" <[email protected][EMAIL PROTECTED] > May 12, 2007 at
09:36 PM

"rpbc" <[email protected][EMAIL PROTECTED]
.com> wrote in message
by "JoeSpareBedroom" <[email protected][EMAIL PROTECTED] PROTECTED] > May 5, 2007 at
03:16
PM

<[email protected][EMAIL PROTECTED] PROTECTED]
wrote in message
Why so complicated? Why not a good old d'Arsonval movement? Drains
microamps.

Needle type meter? I wondered about that, but I also wonder about
durability. The bass doesn't get banged around much, but still....

And on the other hand, I've met old Simpson meters that never seem to
die.

rpbc: Why not build a regulated 9 volt supply and feed it from the power
supply of the bass amp... or just buy a little wall type transformer of
the right voltage wired to the bass amp power switch, and add filter and
regulation to that? Then you won't have to worry about the battery.

Because I play 99% of the time with a Sennheiser wireless setup. I move
around too much to have wires underfoot.

rpbc: Oh, I see. Think I only got half the picture. Could you install a
little female jack on the compartment wired to the battery and have a male
plug on the leads of a voltmeter so you can just plug in an measure? You
could measure with the unit on so the reading will be under load.

J

#### JoeSpareBedroom

Jan 1, 1970
0
rpbc said:
by "JoeSpareBedroom" <[email protected][EMAIL PROTECTED] > May 12, 2007 at
09:36 PM

"rpbc" <[email protected][EMAIL PROTECTED]
.com> wrote in message
by "JoeSpareBedroom" <[email protected][EMAIL PROTECTED] PROTECTED] > May 5, 2007 at
03:16
PM

<[email protected][EMAIL PROTECTED] PROTECTED]
wrote in message
Why so complicated? Why not a good old d'Arsonval movement? Drains
microamps.

Needle type meter? I wondered about that, but I also wonder about
durability. The bass doesn't get banged around much, but still....

And on the other hand, I've met old Simpson meters that never seem to
die.

rpbc: Why not build a regulated 9 volt supply and feed it from the power
supply of the bass amp... or just buy a little wall type transformer of
the right voltage wired to the bass amp power switch, and add filter and
regulation to that? Then you won't have to worry about the battery.

Because I play 99% of the time with a Sennheiser wireless setup. I move
around too much to have wires underfoot.

rpbc: Oh, I see. Think I only got half the picture. Could you install a
little female jack on the compartment wired to the battery and have a male
plug on the leads of a voltmeter so you can just plug in an measure? You
could measure with the unit on so the reading will be under load.

That's the solution I'm leaning toward right now. The compartment is
precisely big enough for the two 9v batteries. I'm taking the bass to a
luthier later this week to discuss the safest direction in which to rout out
enough space for a banana jack, without threatening the integrity of the
wooden body.

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## Numerical methods for mean field games - Lecture 2: Monotone finite difference schemes Achdou, Yves | CIRM H

Post-edited

Recently, an important research activity on mean field games (MFGs for short) has been initiated by the pioneering works of Lasry and Lions: it aims at studying the asymptotic behavior of stochastic differential games (Nash equilibria) as the number $n$ of agents tends to infinity. The field is now rapidly growing in several directions, including stochastic optimal control, analysis of PDEs, calculus of variations, numerical analysis and computing, and the potential applications to economics and social sciences are numerous.
In the limit when $n \to +\infty$, a given agent feels the presence of the others through the statistical distribution of the states. Assuming that the perturbations of a single agent's strategy does not influence the statistical states distribution, the latter acts as a parameter in the control problem to be solved by each agent. When the dynamics of the agents are independent stochastic processes, MFGs naturally lead to a coupled system of two partial differential equations (PDEs for short), a forward Fokker-Planck equation and a backward Hamilton-Jacobi-Bellman equation.
The latter system of PDEs has closed form solutions in very few cases only. Therefore, numerical simulation are crucial in order to address applications. The present mini-course will be devoted to numerical methods that can be used to approximate the systems of PDEs.
The numerical schemes that will be presented rely basically on monotone approximations of the Hamiltonian and on a suitable weak formulation of the Fokker-Planck equation.
These schemes have several important features:

- The discrete problem has the same structure as the continous one, so existence, energy estimates, and possibly uniqueness can be obtained with the same kind of arguments

- Monotonicity guarantees the stability of the scheme: it is robust in the deterministic limit

- convergence to classical or weak solutions can be proved

Finally, there are particular cases named variational MFGS in which the system of PDEs can be seen as the optimality conditions of some optimal control problem driven by a PDE. In such cases, augmented Lagrangian methods can be used for solving the discrete nonlinear system. The mini-course will be orgamized as follows

1. Introduction to the system of PDEs and its interpretation. Uniqueness of classical solutions.

2. Monotone finite difference schemes

3. Examples of applications

4. Variational MFG and related algorithms for solving the discrete system of nonlinear equations
Recently, an important research activity on mean field games (MFGs for short) has been initiated by the pioneering works of Lasry and Lions: it aims at studying the asymptotic behavior of stochastic differential games (Nash equilibria) as the number $n$ of agents tends to infinity. The field is now rapidly growing in several directions, including stochastic optimal control, analysis of PDEs, calculus of variations, numerical analysis and ...

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## Geometry of jets and fields.Selected papers based on the presentations at the workshop. In honour of Professor Janusz GrabowskiBedlewo # May 10-16, 2015 Grabowska, Katarzyna ; Jozwikowski, Michal ; de Lucas, Javier ; Rotkiewicz, Mikolaj | Polish Academy Of Science Institute 2016

Congrès

- 311 p.
ISBN 978-83-86806-34-8

Banach center publications , 0110

Localisation : Salle des périodiques 1er étage

équation de Hamilton-Poincaré # équation de Hamilton-Jacobi # mécanique géométrique # dynamique hamiltonienne # algèbre de Lie # fonction de Wigner # théorème de Malus-Dupin # mécanique de Tulczyjew # théorème de Noether

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## Numerical methods for mean field games - Lecture 1: Introduction to the system of PDEs and its interpretation. Uniqueness of classical solutions Achdou, Yves | CIRM H

Multi angle

Recently, an important research activity on mean field games (MFGs for short) has been initiated by the pioneering works of Lasry and Lions: it aims at studying the asymptotic behavior of stochastic differential games (Nash equilibria) as the number $n$ of agents tends to infinity. The field is now rapidly growing in several directions, including stochastic optimal control, analysis of PDEs, calculus of variations, numerical analysis and computing, and the potential applications to economics and social sciences are numerous.
In the limit when $n \to +\infty$, a given agent feels the presence of the others through the statistical distribution of the states. Assuming that the perturbations of a single agent's strategy does not influence the statistical states distribution, the latter acts as a parameter in the control problem to be solved by each agent. When the dynamics of the agents are independent stochastic processes, MFGs naturally lead to a coupled system of two partial differential equations (PDEs for short), a forward Fokker-Planck equation and a backward Hamilton-Jacobi-Bellman equation.
The latter system of PDEs has closed form solutions in very few cases only. Therefore, numerical simulation are crucial in order to address applications. The present mini-course will be devoted to numerical methods that can be used to approximate the systems of PDEs.
The numerical schemes that will be presented rely basically on monotone approximations of the Hamiltonian and on a suitable weak formulation of the Fokker-Planck equation.
These schemes have several important features:

- The discrete problem has the same structure as the continous one, so existence, energy estimates, and possibly uniqueness can be obtained with the same kind of arguments

- Monotonicity guarantees the stability of the scheme: it is robust in the deterministic limit

- convergence to classical or weak solutions can be proved

Finally, there are particular cases named variational MFGS in which the system of PDEs can be seen as the optimality conditions of some optimal control problem driven by a PDE. In such cases, augmented Lagrangian methods can be used for solving the discrete nonlinear system. The mini-course will be orgamized as follows

1. Introduction to the system of PDEs and its interpretation. Uniqueness of classical solutions.

2. Monotone finite difference schemes

3. Examples of applications

4. Variational MFG and related algorithms for solving the discrete system of nonlinear equations
Recently, an important research activity on mean field games (MFGs for short) has been initiated by the pioneering works of Lasry and Lions: it aims at studying the asymptotic behavior of stochastic differential games (Nash equilibria) as the number $n$ of agents tends to infinity. The field is now rapidly growing in several directions, including stochastic optimal control, analysis of PDEs, calculus of variations, numerical analysis and ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Numerical methods for mean field games - Lecture 3: Variational MFG and related algorithms for solving the discrete system of nonlinear equations Achdou, Yves | CIRM H

Multi angle

Recently, an important research activity on mean field games (MFGs for short) has been initiated by the pioneering works of Lasry and Lions: it aims at studying the asymptotic behavior of stochastic differential games (Nash equilibria) as the number $n$ of agents tends to infinity. The field is now rapidly growing in several directions, including stochastic optimal control, analysis of PDEs, calculus of variations, numerical analysis and computing, and the potential applications to economics and social sciences are numerous.
In the limit when $n \to +\infty$, a given agent feels the presence of the others through the statistical distribution of the states. Assuming that the perturbations of a single agent's strategy does not influence the statistical states distribution, the latter acts as a parameter in the control problem to be solved by each agent. When the dynamics of the agents are independent stochastic processes, MFGs naturally lead to a coupled system of two partial differential equations (PDEs for short), a forward Fokker-Planck equation and a backward Hamilton-Jacobi-Bellman equation.
The latter system of PDEs has closed form solutions in very few cases only. Therefore, numerical simulation are crucial in order to address applications. The present mini-course will be devoted to numerical methods that can be used to approximate the systems of PDEs.
The numerical schemes that will be presented rely basically on monotone approximations of the Hamiltonian and on a suitable weak formulation of the Fokker-Planck equation.
These schemes have several important features:

- The discrete problem has the same structure as the continous one, so existence, energy estimates, and possibly uniqueness can be obtained with the same kind of arguments

- Monotonicity guarantees the stability of the scheme: it is robust in the deterministic limit

- convergence to classical or weak solutions can be proved

Finally, there are particular cases named variational MFGS in which the system of PDEs can be seen as the optimality conditions of some optimal control problem driven by a PDE. In such cases, augmented Lagrangian methods can be used for solving the discrete nonlinear system. The mini-course will be orgamized as follows

1. Introduction to the system of PDEs and its interpretation. Uniqueness of classical solutions.

2. Monotone finite difference schemes

3. Examples of applications

4. Variational MFG and related algorithms for solving the discrete system of nonlinear equations
Recently, an important research activity on mean field games (MFGs for short) has been initiated by the pioneering works of Lasry and Lions: it aims at studying the asymptotic behavior of stochastic differential games (Nash equilibria) as the number $n$ of agents tends to infinity. The field is now rapidly growing in several directions, including stochastic optimal control, analysis of PDEs, calculus of variations, numerical analysis and ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Homogenizations for Hamilton-Jacobi PDEs and Hamiltonian ODEs Rezakhanlou, Fraydoun | CIRM H

Multi angle

Traditionally homogenization asks whether average behavior can be discerned from Hamilton-Jacobi equations that are subject to high-frequency fluctuations in spatial variables. A similar question can be asked for the associated Hamiltonian ODEs. When the Hamiltonian function is convex in momentum variable, these two questions turn out to be equivalent. This equivalence breaks down for general Hamiltonian functions. In this talk I will give a dynamical system formulation for homogenization and address some result concerning weak and strong homogenization phenomena. Traditionally homogenization asks whether average behavior can be discerned from Hamilton-Jacobi equations that are subject to high-frequency fluctuations in spatial variables. A similar question can be asked for the associated Hamiltonian ODEs. When the Hamiltonian function is convex in momentum variable, these two questions turn out to be equivalent. This equivalence breaks down for general Hamiltonian functions. In this talk I ...

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## Semi-Lagrangian approximation schemes for linear and Hamilton-Jacobi equations Falcone, Maurizio ; Ferretti, Roberto | Society For Industrial And Applied Mathematics 2014

Ouvrage

- xii; 319 p.
ISBN 978-1-611973-04-4

Localisation : Ouvrage RdC (FALC)

équation de Hamilton-Jacobi # théorie de l'approximation # convergence # approximation de premier ordre # approximation d'ordre supérieur # PDEs hyperboliques # viscosité # dynamique des fluides # contrôle optimal # traitement des images

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## Variational methods for the numerical solution of nonlinear elliptic problems Glowinski, Roland | Society For Industrial And Applied Mathematics 2015

Ouvrage

- xix; 462 p.
ISBN 978-1-611973-77-8

CBMS-NSF regional conference series in applied mathematics , 0086

Localisation : Collection 1er étage

analyse fonctionnelle non linéaire # fonction elliptique # fonction de Lagrange # équation iconale # méthode variationnelle # espace de Hilbert # méthode des moindres carrés # flot de Bingham # problème de valeurs propres non linéaires

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# If n and y are positive integers and 450y=n^3

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If n and y are positive integers and 450y=n^3 [#permalink]  11 Apr 2010, 22:56
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59% (02:09) correct 41% (01:39) wrong based on 507 sessions
If x and y are positive integers and 450y=x^3, which of the following must be an integer?

i) $$\frac{y}{{3*2^2*5}}$$
ii) $$\frac{y}{{3^2*2*5}}$$
iii) $$\frac{y}{{3*2*5^2}}$$

a. None
b. i only
c. ii only
d. iii only
e. i, ii and iii

[Reveal] Spoiler:
B
[Reveal] Spoiler: OA

Last edited by abhi758 on 11 Apr 2010, 23:58, edited 1 time in total.
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Re: Number Properties [#permalink]  12 Apr 2010, 04:54
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abhi758 wrote:
If x and y are positive integers and $$450y=x^3$$, which of the following must be an integer?

i) $$\frac{y}{{3*2^2*5}}$$
ii) $$\frac{y}{{3^2*2*5}}$$
iii) $$\frac{y}{{3*2*5^2}}$$

a. None
b. i only
c. ii only
d. iii only
e. i, ii and iii

[Reveal] Spoiler:
B

"Must be an integer" means for the lowest possible value of $$y$$.

$$450y=x^3$$ --> $$2*3^2*5^2*y=x^3$$. As $$x$$ and $$y$$ are integers, $$y$$ must complete the powers of 2, 3, and 5 to cubes (generally to the multiple of 3). Thus $$y_{min}=2^2*3*5$$, in this case $$2*3^2*5^2*y=(2*3*5)^3=x^3$$. Notice that for this value of $$y$$ only the first option is an integer: $$\frac{y}{{3*2^2*5}}=\frac{2^2*3*5}{{3*2^2*5}}=1$$.

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Re: Number Properties [#permalink]  13 Apr 2010, 01:58
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shrivastavarohit wrote:
Moderator,

Can you elaborate more on the solution, seems unfathomable for simple minds like mine .

How did we deduce that "Minimum value of Y"?

$$x$$ and $$y$$ are integers and $$450y=x^3$$ --> $$450y$$ equals to cube of an integer. $$450y=2*3^2*5^2*y=x^3$$. The smallest value of $$y$$ for which $$2*3^2*5^2*y$$ is a cube of an integer is when $$y=2^2*3*5$$. In this case $$450y=(2*3^2*5^2)*(2^2*3*5)=(2*3*5)^3$$. Of course $$y$$ can take another values as well, for example $$y=2^5*3^4*5^7$$ and in this case $$450y=(2*3^2*5^2)*(2^5*3^4*5^7)=(2^3*3^2*5^3)^3$$, but the smallest value of $$y$$ is when $$y=2^2*3*5$$.

You can check the similar problems at:
og-quantitative-91750.html#p704028
division-factor-88388.html#p666722
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Re: 450y=n^3, finding integer [#permalink]  19 Jun 2012, 21:45
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enigma123 wrote:
If n and y are positive integers and 450y = n^3, which of the following must be an integer?

1. $$\frac{Y}{3 * 2^2 * 5}$$

2. $$\frac{Y}{3^2 * 2 * 5}$$

3. $$\frac{Y}{3 * 2 * 5^2}$$

A) None

B) I only

C) II Only

D) III only

E) I, II and III onmly.

The critical point in this question is that n and y are integers.
Since n is an integer, n^3 must be the cube of an integer. So in n^3, all the prime factors of n must be cubed (or have higher powers which are multiples of 3)

Now consider 450y = n^3
450 is not a perfect cube. So whatever is missing in 450, must be provided by y to make a perfect cube.

$$450 = 45*10 = 2 * 3^2 * 5^2$$

To make a perfect cube, we need at least two 2s, a 3 and a 5. These missing factors must be provided by y. Therefore, $$2^2*3*5$$ must be a factor of y.
This means $$y/2^2*3*5$$ must be an integer.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 21 Oct 2013 Posts: 194 Location: Germany GMAT 1: 660 Q45 V36 GPA: 3.51 Followers: 0 Kudos [?]: 22 [2] , given: 19 Re: If n and y are positive integers and 450y=n^3 [#permalink] 31 Oct 2013, 04:49 2 This post received KUDOS I finally get it. If you want the cuberoot of 450y to be an integer, you need the primefactors to be cubed. So the primefactors we have for 450 are 2, 3², 5². To be perfect cubes, we need to multiply by 2², 3, 5 which in this case equals y. so we get that (2*3²*5²) * (2²*3*5) = 2³*3³*5³. If we'd cuberoot x now, we'd get an integer. This leads to the conclusion that y / 2²*3*5 = 1 = integer. So answer B. I tried explaining in simpler words so I'd get it myself, I hope it helps the you other non-math-overbrains. Greets Manager Joined: 16 Apr 2010 Posts: 222 Followers: 3 Kudos [?]: 64 [1] , given: 12 Re: problem solving [#permalink] 27 Jun 2010, 05:37 1 This post received KUDOS I am not sure if I got the question right. The way I understand this Q isthat 450y = n*n*n and the question is whether the given options are integers. The answer of above Q is as follows: We know that: n = cubic root (450y) = cubic root (2X3X3X5X5) For n to be an integer, y should be factor of 2X2X3X5. So y=(2X2X3X5)k where k is any natural number. if k = 1, y=2X2X3X5 so the answer is b. I hope this explanation meets your satisfaction. Last edited by jakolik on 27 Jun 2010, 20:35, edited 1 time in total. Retired Moderator Joined: 02 Sep 2010 Posts: 805 Location: London Followers: 83 Kudos [?]: 602 [1] , given: 25 Re: Tough integer properties question! [#permalink] 11 Oct 2010, 23:14 1 This post received KUDOS atomjuggler wrote: Raising the white flag on this one. I really hope I'm not missing something obvious Source: GMATPrep Test #1 If n and y are positive integers and 450y=n^3, which of the following must be an integer? I. $$\frac{y}{3*2^2*5}$$ II. $$\frac{y}{3^2*2*5}$$ III. $$\frac{y}{3*2*5^2}$$ A. None B. I only C. II only D. III only E. I, II, and III $$450*y=n^3$$ Since 450y is a whole cube, in the prime factorization of 450y, all the exponents on the prime factors must be multiples of 3. $$450*y = y * 3^2 * 5^2 * 2$$ So y must have atleast $$3, 5, 2^2$$ as prime factors. y must be of the form form 3x5x4xA where A is also another perfect cube. By this logic the answer is (I) only or B, as in all cases y/(3x5x4) has to be an integer. (ii) or (iii) cannot be true if A=1 Answer is (b) _________________ Math Expert Joined: 02 Sep 2009 Posts: 28272 Followers: 4476 Kudos [?]: 45194 [1] , given: 6646 Re: If n and y are positive integers and 450y=n^3 [#permalink] 23 May 2014, 09:53 1 This post received KUDOS Expert's post 2 This post was BOOKMARKED Intern Joined: 29 Mar 2010 Posts: 43 Followers: 0 Kudos [?]: 10 [0], given: 1 Re: Number Properties [#permalink] 12 Apr 2010, 22:15 Moderator, Can you elaborate more on the solution, seems unfathomable for simple minds like mine . How did we deduce that "Minimum value of Y"? _________________ ------------------------------------------------------------------------- Ros. Nice Post + Some help + Lucid solution = Kudos The greatest pleasure in life is doing what people say you cannot do | Great minds discuss ideas, average minds discuss events, small minds discuss people. ------------------------------------------------------------------------- Intern Joined: 29 Mar 2010 Posts: 43 Followers: 0 Kudos [?]: 10 [0], given: 1 Re: Number Properties [#permalink] 13 Apr 2010, 02:28 Thanks for the quick response it makes more sense now I will check out the problems (similar) on the threads mentioned by you. Is this really a GMAT question from the calculation it looks solving this should take more than 2 mins. Posted from my mobile device _________________ ------------------------------------------------------------------------- Ros. Nice Post + Some help + Lucid solution = Kudos The greatest pleasure in life is doing what people say you cannot do | Great minds discuss ideas, average minds discuss events, small minds discuss people. ------------------------------------------------------------------------- Intern Joined: 29 Mar 2010 Posts: 43 Followers: 0 Kudos [?]: 10 [0], given: 1 Re: Number Properties [#permalink] 13 Apr 2010, 02:32 Oops !!! One more important thing why is plugging in values applicable to these kind of problems? It seemed pretty simple from the question to plug in 2 integer values in the final equation and check for the integer output btw which miserably failed on all three equations. Posted from my mobile device _________________ ------------------------------------------------------------------------- Ros. Nice Post + Some help + Lucid solution = Kudos The greatest pleasure in life is doing what people say you cannot do | Great minds discuss ideas, average minds discuss events, small minds discuss people. ------------------------------------------------------------------------- Senior Manager Joined: 16 Jul 2009 Posts: 262 Followers: 3 Kudos [?]: 107 [0], given: 3 Re: Number Properties [#permalink] 14 Apr 2010, 22:00 Thanks Bunnel! your first explanation makes it crystal clear.. Senior Manager Joined: 30 Aug 2009 Posts: 286 Location: India Concentration: General Management Followers: 3 Kudos [?]: 111 [0], given: 5 Re: Algebra [#permalink] 08 Jan 2012, 04:29 kotela wrote: Can anyone please help me in solving this problem....... lets find prime factors of 450 = 2* 3* 3* 5* 5 for 450* y to be equal to n^3 450y needs to have 2,3and 5 three times ( as n is an integer ) i.e. 450 y = (2* 3* 3* 5* 5) (2*2*3*5) * x = n^3 now y = (2*2*3*5) * x only option 1 will then give an integer GMAT Club Legend Joined: 09 Sep 2013 Posts: 5371 Followers: 310 Kudos [?]: 60 [0], given: 0 Re: If n and y are positive integers and 450y=n^3 [#permalink] 28 Oct 2013, 12:36 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Current Student Joined: 03 Aug 2012 Posts: 917 Concentration: General Management, General Management GMAT 1: 630 Q47 V29 GMAT 2: 680 Q50 V32 GPA: 3.7 WE: Information Technology (Investment Banking) Followers: 17 Kudos [?]: 349 [0], given: 322 Re: If n and y are positive integers and 450y=n^3 [#permalink] 19 Apr 2014, 21:11 Concept Tested: For a perfect square the powers should occur in pairs. For a perfect cube powers should occur in cubes. 450y = x^3 5^2 * 3^2 * 2 * y = x^3 For LHS to become a cube Y must be y= 5*3*2^2 Only (1) matches it. _________________ Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________ Manager Joined: 30 May 2013 Posts: 193 Location: India Concentration: Entrepreneurship, General Management GPA: 3.82 Followers: 0 Kudos [?]: 35 [0], given: 72 Re: If n and y are positive integers and 450y=n^3 [#permalink] 22 May 2014, 10:59 I could understand the options But tell y my alternate approach is wrong 450y = x^3 X and Y are integer 450 = 2*3^2*5^2 X=((2*3^2*5^2)y)/x^2 Note: as x is an integer if x = 2*3^2*5^2 X = y/ (2*3^2*5^2) And its option c). Please correct me. Thanks in advance. Intern Joined: 20 May 2014 Posts: 37 Location: India Schools: IIMC GMAT 1: 700 Q51 V32 Followers: 0 Kudos [?]: 24 [0], given: 16 Re: If n and y are positive integers and 450y=n^3 [#permalink] 22 May 2014, 12:11 Hi rrsnathan, Your approach is wrong because you are assuming 1 fixed value of $$x = 2*3^2*5^2$$ But question explicitly asks which option MUST be an integer always. In your assumption, Option C comes out to be an integer but that may not be true in other cases. So, Right method to solve it is: $$450y = x^3$$ $$(2*3^2*5^2) * y = x^3$$ For LHS to be a cube (As R.H.S is a cube), $$y = 2^2*3*5*k^3$$ (where k is a positive integer) Hence, Option (b) is always correct Rgds, Rajat _________________ If you liked the post, please press the'Kudos' button on the left Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5682 Location: Pune, India Followers: 1413 Kudos [?]: 7338 [0], given: 186 Re: If n and y are positive integers and 450y=n^3 [#permalink] 22 May 2014, 19:25 Expert's post rrsnathan wrote: I could understand the options But tell y my alternate approach is wrong 450y = x^3 X and Y are integer 450 = 2*3^2*5^2 X=((2*3^2*5^2)y)/x^2 Note: as x is an integer if x = 2*3^2*5^2 X = y/ (2*3^2*5^2) This is incorrect. Note that in the denominator, you have x^2, not x. You are assuming $$x = 2*3^2*5^2$$ and putting it as it is in the denominator. Also note that since you have the same x on the left hand side, if you put $$x = 2*3^2*5^2$$, you get $$2*3^2*5^2 = (2*3^2*5^2)*y/(2*3^2*5^2)^2$$ i.e. $$y = (2*3^2*5^2)^2$$ Basically, you have assumed a value of x and got a value of y. There is no reason for you to assume the value of x as $$2*3^2*5^2$$. The point here is that y must have some values such that when it multiplies 450, it gives a perfect cube. This is the method discussed above in my post. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: If n and y are positive integers and 450y=n^3   [#permalink] 22 May 2014, 19:25
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# Convert maidenhead grid square to lat/long in Excel?

I have a list of maidenhead grid squares in an Excel sheet that I want to convert to latitude and longitude. I want to keep it as simple as possible. Does anyone know of a formula to convert from maidenhead to lat/long?

• A web search makes it look as though your task is too complicated for a formula. A macro could probably be written to do it. – rclocher3 Apr 27 '16 at 16:40
• Possibly related answer here. You could take apart the Maidenhead string and add it up. – tomnexus Apr 28 '16 at 5:52

Assuming for the sake of precision that the particular point in the grid square that you want the exact latitude and longitude for is the midpoint of the 6-character subsquare, this can be done readily with Excel formulas.

If the 6-character grid square data is in cell A1, in a format similar to AA00aa (i.e. upper-case, then digits, then lower-case), the formula for the latitude (based directly on the Python code posted previously) is:

=(CODE(MID(A1,2,1))-65)*10 + VALUE(MID(A1,4,1)) + (CODE(MID(A1,6,1))-97)/24 + 1/48 - 90

and the formula for the longitude is

=(CODE(MID(A1,1,1))-65)*20 + VALUE(MID(A1,3,1))*2 + (CODE(MID(A1,5,1))-97)/12 + 1/24 - 180

If you want the latitude and longitude of the southwest corner of the subsquare, just leave out the + 1/48 and + 1/24 terms. Add error-checking, upper- and lower-case conversion, conversion of four-character squares to six-character by adding 'mm', and other embellishments as you see fit.

Function FromMaidenhead(m As String) As Variant Dim lat As Double, lon As Double

lat = (Asc(Mid(m, 2, 1)) - 65) * 10 + Val(Mid(m, 4, 1)) + (Asc(Mid(m, 6, 1)) - 97) / 24 + 1 / 48 - 90 lon = (Asc(Mid(m, 1, 1)) - 65) * 20 + Val(Mid(m, 3, 1)) * 2 + (Asc(Mid(m, 5, 1)) - 97) / 12 + 1 / 24 - 180

FromMaidenhead = Format(lat, "00.000000" & "° ") & Format(lon, "000.000000" & "° ")

End Function

• Hi Bert, welcome to StackExchange! Is this a VBA function? Could you please add a few lines describing how to get this into Excel and read the appropriate cells? Regardless, your logic is clear and this should be straightforward to port to a language a reader may be more familiar with. Thank you for posting this. – Chris K8NVH Nov 25 '18 at 17:12

This seems to be impossible doing with a Macro correctly.

Even when you take the link provided by @tomnexus in the comments and reverse the process, you will not get a precise location.

Reason is: a Maidenhead locator is a square, and therefore consists of my combinations of lon/lat. Therefore a Macro cannot result in a single lon-lat.

However, I am sure that you can come up with a script/macro with 4 results, which represent ranges:

lon = (lon_start) to (lon_end)

lat = (lat_start) to (lat_end)

Can you please clarify what you are looking for ?

[edit 04-May]

I am not an excel person, but I know a bit of Python 3.x, so here is a script which actually translates Maidenhead to a range of lon/lat... use at your discretion, no warrantees made

# -*- coding: utf-8 -*-

__MH__ = 'HK34wh'

def GetLon(ONE, THREE, FIVE):
StrStartLon = ''
StrEndLon = ''

Field = ((ord(ONE.lower()) - 97) * 20)
Square = int(THREE) * 2
SubSquareLow = (ord(FIVE.lower()) - 97) * (2/24)
SubSquareHigh = SubSquareLow + (2/24)

StrStartLon = str(Field + Square + SubSquareLow - 180 )
StrEndLon = str(Field + Square + SubSquareHigh - 180 )

return StrStartLon, StrEndLon

def GetLat(TWO, FOUR, SIX):
StrStartLat = ''
StrEndLat = ''

Field = ((ord(TWO.lower()) - 97) * 10)
Square = int(FOUR)
SubSquareLow = (ord(SIX.lower()) - 97) * (1/24)
SubSquareHigh = SubSquareLow + (1/24)

StrStartLat = str(Field + Square + SubSquareLow - 90)
StrEndLat = str(Field + Square + SubSquareHigh - 90)

return StrStartLat, StrEndLat

(strStartLon, strEndLon) = GetLon(ONE, THREE, FIVE)
(strStartLat, strEndLat) = GetLat(TWO, FOUR, SIX)

print ('Start Lon = ' + strStartLon)
print ('End   Lon = ' + strEndLon)
print ()
print ('Start Lat = ' + strStartLat)
print ('End   Lat = ' + strEndLat)

return strStartLon, strEndLon, strStartLat, strEndLat

#BEGIN
if __name__ == '__main__':
main ()
sys.exit ('end of script: '+ os.path.basename(__file__) + os.linesep + 'by: Edwin van Mierlo')
#END