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# How do you compute an indifference point?

The net economic impact provides an assessment which is valid under very specify circumstances. Indeed, it depends on the accuracy of forecasts and estimates used to compute it. If any of the underlying assumptions is not met, the conclusion it supports may be compromised. Since neither forecasts nor estimates are perfectly reliable, it is important to ask whether the conclusion is robust to slight variations of the underlying estimates. This is the idea behind both the indifference point and sensitivity analyses.

The indifference point is the value of an estimate (volume, price, unit variable cost or fixed costs) for which the net economic impact is null and therefore the decision maker is indifferent between the two alternatives, keeping the other estimates constant.

The basic idea of the indifference point is to ask for which volume, price, units variable costs, or fixed costs one decision alternative or course of action is strictly equivalent from an economic perspective to the other. This is called the indifference point because for this set of values the manager is indifferent between either course of action because they yield equivalent costs and benefits.

You already have seen a special case of indifference point: the break-even point. The volume at break-even is the volume at which the decision maker is indifferent between starting the activity and doing nothing, since profit is null. It is a special case in the sense that it considers all the costs and revenues as relevant, i.e. avoidable.

Solution.

Switching to virgin mojitos becomes advantageous with a minimum increase in volume of 167 units, so a new volume of 1,667:

\begin{aligned} 0 = & + \Delta Q \times (7-2.5) \\ & + (1,500 + \Delta Q) \times (6-7) \\ & - (1,500 + \Delta Q) \times (1.8-2.5) \\ & - 250 \\ \leftrightarrow \\ 0 = & 4.2 \times \Delta Q - 700 \\ \leftrightarrow \\ \Delta Q = & 166.66667 \end{aligned}

Switching to virgin mojitos is advantageous with a maximum decrease in price of 1.08 euros, so a new price of 5.92:

\begin{aligned} 0 = & + 200 \times (7-2.5) \\ & + 1,700 \times \Delta P \\ & - 1,700 \times (1.8-2.5) \\ & - 250 \\ \leftrightarrow \\ 0 = & + 1,700 \times \Delta P + 1,840 \\ \leftrightarrow \\ \Delta P = & -1.0823 \end{aligned}

Switching to virgin mojitos is advantageous with a minimum decrease in unit variable cost of 0.62 euros, so a new unit variable cost of 1.88:

\begin{aligned} 0 = & + 200 \times (7-2.5) \\ & + 1,700 \times (6-7) \\ & - 1,700 \times \Delta V_c \\ & - 250 \\ \leftrightarrow \\ 0 = & - 1,700 \times \Delta V_c - 1,050 \\ \leftrightarrow \\ \Delta V_c = & -0.61765 \end{aligned}

Finally, an increase in 250+140 = 390 of fixed costs is enough to make both options equivalent from en economic perspective. If the percentage change necessary to go from the scenario to the indifference point, we can see that these percentages are small except for the fixed costs. This suggests that the conclusion might not be very robust, since small changes are enough to make the decision maker indifferent:

Estimate Scenario Indifference point Difference
Volume 1,700.00 1,667.00 -1.94%
Price 6.00 5.92 -1.33%
Unit variable cost 1.80 1.88 4.44%
Fixed costs 250.00 390.00 56.00%

Computing indifference points is a form of sensitivity analysis because it helps the decision maker determine over what range of an estimate the decision is unchanged. If the initial set of assumptions is very far from the indifference points, the conclusion is robust to large changes in the estimates. If on the contrary the estimates are very close to the indifference points, a modest variation is enough to reverse the conclusion which is therefore highly risky. And here again you can see the parallel between indifference point and break-even point: operating leverage, therefore risk, is also maximal at break-even.

Note that which magnitude of the distance between the estimate and the indifference point makes the conclusion robust depends on the quality of the cost system. A crude costing system is likely to result in unreliable estimates, the true value of which may be sometimes far from what the cost system reports. Being far from the indifference point then gives a misleading impression of safety. On the contrary, if the cost system is very accurate, the estimate can be very close to the indifference point and the conclusion still robust.

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# zbMATH — the first resource for mathematics

The existence of large solutions of non-variational type singular quasilinear elliptic system on $${{\text{R}}^N}$$. (Chinese. English summary) Zbl 1413.35219
Summary: This paper considers a class of non-variational type singular quasilinear elliptic system: ${\text{div}}\left ( {{{\left| x \right|}^{ - ap}}{{\left| {\nabla u} \right|}^{p - 2}}\nabla u} \right) = f\left ( x \right){u^\alpha}{v^\gamma},\;{\text{div}}\left ( {{{\left| x \right|}^{-bq}}{{\left| {\nabla v} \right|}^{q-2}}\nabla v} \right) = g\left ( x \right){u^\delta}{v^\beta}, x \in {{\text{R}}^N},$ with $$u\left ( x \right)$$, $$v\left ( x \right) > 0$$, and $$u\left ( x \right)$$, $$v\left ( x \right) \to + \infty$$ as $$\left| x \right| \to + \infty$$, where $$0 \leq \alpha < p - 1$$, $$0 \leq \beta < q - 1$$, $$\gamma, \delta > 0$$, $$0 \leq a < \left ( {N - p} \right)/p$$, $$0 \leq b < \left ( {N - q} \right)/q$$, and $$\sigma = \left ( {p - 1 - \alpha} \right)\left ( {q - 1 - \beta} \right) - \gamma \delta < 0$$. Through constructing the upper and lower solution method, it is proved that, under appropriate conditions, there is at least one set of large solutions to this equation system.
##### MSC:
 35J62 Quasilinear elliptic equations 35J75 Singular elliptic equations
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# Mathematical keyboard for pc

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Our unique speech MathTalk™ Works on both PC and Mac. You now have no excuse not to use the equation editor on a casual basis Free Advanced Kurdish Keyboard APPS Latest Download For PC Windows 7/8/10/XP Advanced Kurdish Keyboard Apps Latest Download For PC Windows Full Version. We all know that the keyboard is an input device that functions in accordance to the instructions of the user. To erase the last character - [Backspace] (arrow keys). Matrices in QuickMath can be as complicated as you like. You can help protect yourself from scammers by verifying that the contact is a Microsoft Agent or Microsoft Employee and that the phone number is an official Microsoft global customer service number. Scanning your homework (the easiest way!) Due to the difficulties of typing math, chemistry, & physics equations & symbols, I HIGHLY recommend that you scan homework problems from your book or homework sheet and email them as an attached file with The mathematical notepad comes in also with a piano. If you already know the TeX typesetting language, you can enter equations directly into MathType or Microsoft Word documents. 0 or 3. I have a Studio 17. Windows alt codes and keyboard symbols on Mac and Linux. Scientific Keyboard is an app for iPad aimed at the scientific and academic community to facilitate writing mathematical symbolism on your device How to Type Math Symbols. Formatting text in RTF fields . Complete table with all Alt codes and characters that they produce. Screenshot button. How do you make the computer keyboard type math powers like 5 to the second power but with the little number in the right corner??? If you're on a pc then you'll Each iteration of Windows comes with new keyboard shortcuts that make it faster to do pretty much anything on a PC. It has to be indistinguishable from actual USB keyboard. We’ve previously shown you how to add keyboard shortcuts to symbols in Word 2013 to make it easier to insert them into your documents. Tablet Keyboards, Keyboard Cases, Keyboard Folios | Logitech IE8/IE9/IE10 is no longer a supported browser. 8704. It's easy to use: Common symbols have keyboard shortcuts so that a veteran user need  Enter or edit scanned math problems using an intuitive math keyboard. It comprises circuits, switches, and processors that help in transferring keystroke messages to the computer. . It types out long phrases and mathematical expressions into various cells of the spreadsheet, and so on. Advance Kurdish Keyboard is the best and fastest malti-language Android keyboard for writing Kurdish-Farsi-Arabic-English with full Kurdish characters support on just one layout. Macintosh, Option+5, Hold the Option key and  Press/hold Alt key while typing the numbers on the keypad (with Num Lock on). The camera has a very powerful maths keyboard. This functionality is accessed by keyboard shortcuts and - on Mac - you have greater flexibility: Command + Shift + 3 - captures entire screen; Command + Shift + 4 - captures selected region. For example, you can create APL (programming language) keyboard layout, or for LaTeX/XeTeX, or simply as a system to type math symbols in plain text. For example, you can create  In mathematics, the operators provided on keyboard are quite clear for addition, subtraction and divide: + - / . It does seem that Word will render the symbol by "copy and paste". In Windows, the key combined with numeric codes can access characters that aren't readily available on a normal keyboard. Windows shorcuts. Usable in any application. ca. mathematical and scientific expressions, however, and many candidates will be better off using Microsoft Word with the Efofex Maths or Science Pack. Download Symbol Keyboard - 2000+ Signs and enjoy it on your iPhone, iPad, and iPod touch. The base of the keyboard is metal, and has a retro vibe. Other companies adjusted to IBM's dominance by building IBM clones, computers that were internally almost the same as the IBM PC, but that cost less. I worked on a math quiz in Math for set theory where questions are pulled into a text file within Flash. Basically, just an annoying little problem with this keyboard, for no apparent reason a few weeks ago, the keyboard decided to switch the " and @ buttons arround. Photomath for PC provides an easy way to provide solutions to your math equations. It was all about that to Know how to type and use Mathematical Equations and Formulas in Microsoft Word 2016, as you all know that nowadays if we want to share our scientific knowledge with others through the Internet or books we must to use Ms Word and through the Ms Word we need to Know how to Write Equations and Formulas. Find how to type sigma summary sign Σ directly from your keyboard. For example. It can also be used to insert symbols – simply click on a symbol to insert into documents or emails. Most any programming language can use addition, subtraction, multiplication, and division between Computer programming/Variables to put the results into new Variables. Math Keyboard is a free and awesome Tools app. Math for the physically challenged – without the need for a keyboard or mouse. 0 Write Edit Your Mathematical Symbols Easily. The calculator is designed for rapid use from the keyboard and to minimize screen use. Mathematical keys on numeric pad on Microsoft keyboard no longer working. Hold the Alt key. Windows character codes (Hold down the Alt key and type the specified number on the numeric keypad. free online English keyboard to engage with internet or touch-screen computers in your native language. A quick glance at the unicode provision for mathematical symbols (e. Bold CTRL-B Italic CTRL-I Underline CTRL-U Use our sample 'Alt Key Symbols for PC. This app adds mathematical and scientific keyboards to your typing. Although Keyboard shortcuts are not just for designers! Work more effectively by using them in Microsoft Office with this handy reference poster. Use your numeric keypad with your NUM LOCK on and you will be good to go! Symbol Description Shortcut ¶ paragraph sign ALT+0182 ± plus-or-minus sign ALT+ The best all-in-one PC for video editing. Typing Greek letters with Keyboard Shortcuts To insert Greek letter type Ctrl+G ( Command G on Mac OS ) and then type Latin letter mentioned in the table below. Scan. submitted 20 hours ago by 2n1c0l4s3. The key will also turn How do you make a half fraction (1/2) symbol on ur keyboard ? 9 following . 2 for Android (math-keyboard. Click to copy — press down alt for multiple Clear As HTML. In typography, these straight double quotation marks are often referred to as dumb quotes when used as quotation marks. The World's Weirdest Keyboards Keyboards without keys, a vertical keyboard with mirrors on the side so you can see your fingers, and keyboards on which you type on the back: Get ready for some For that part of my work, I have an on screen keyboard that automates literally hundreds of tasks. This is similar, though not perhaps as severe, to the problem of trying to write in Japanese using either kanji or kana on a keyboard. On a standard keyboard, the " symbol (Shift+') is most often called a quotation mark. Using OneNote, you can insert fractions, exponentials, logarithms, and other mathematical structures in your notes. is short for personal computer or IBM PC. If you are looking for alt key shortcuts in image format, click the below links to get download the shortcuts images. The format is to hold the first two keys down simultaneously, release, then type the vowel you wish to be accented. To use free online calculator you can use both ordinary numeric buttons at the top of a keyboard and numeric buttons on the right of a keyboard. Mathematics Keyboard v. keyboard, follow the instructions for Activating Keyboard Locales to activate and switch Microsoft keyboards. Welcome to Useful Shortcuts, THE Alt Code resource!. They assume familiarity with the basics of PowerPoint. The pi symbol (π) is a mathematical sign which is also used in Greek letters. apk). Keyboard Layout based on UK with special characters that are Greek letters; Commonly used mathematical symbols; Symbols . How can I achieve this? A solution that works with any of Ubuntu Linux 14 and above, OS X 10. Press Shift or Ctrl + Alt for additional English letters that are not visible on the keyboard. On Windows, you have to install international support to get the left-to-right order correct. You can use your computer keyboard or mouse to type English letters with this online keyboard. There are several ways to display a pi symbol using HTML and unicode. Word will automatically convert the hyphen to an en-dash like –this, but you will have to The Invention of the PC . It worked in implementation of Word (Office 10), and rendered as Cambria Math (font), with size $13$, which can be scaled to a different font size. 0, this will allow you to type complexe fomulas. D). Math can be a daunting task when you don't have the right support. So we created a Companion keyboard cheat sheet you can use as a quick reference guide. It is a simple and easy to navigate program which is based on C#. MathJax is a full fledged open source JavaScript display engine for mathematics and works in all browsers. Windows 10 tip: Access symbols, emojis, and other special characters. the keyboard shortcut is: b. List of infinity symbols where used in math, physics and more. Numbers you can type on your keyboard's Num Pad to get special symbols. The forearms should be approximately parallel to the floor when keying. 4 Symbols not on the keyboard . Symbol Many of these seem to automatically use the Cambria math font. Infinity Symbol on Mac. While this is a serious limitation, multi-level formulas are not always needed and even when they are needed, proper math symbols still look better than improvised ASCII approximations. Mathematical Equation Symbols ∩ ∩ 239 Mathematical Equation Symbols ≡ ≡ 240 Mathematical Equation Symbols ± ± 241 Mathematical Equation Symbols ≥ ≥ 242 Mathematical Equation Symbols ≤ ≤ 243 Mathematical Equation Symbols ⌠ ⌠ 244 Mathematical Equation Symbols ⌡ ⌡ 245 Mathematical Equation Symbols ÷ ÷ 246 Mathematical Visit Logitech for keyboards and keyboard cases for your iPad or Android tablet. A good keyboard that comes close is the "Space Cadet" keyboard that was popular at MIT a long time ago; it was used on Lisp machines running MIT's "Incompatible Timesharing System", an early mainframe OS. Get this platform-independent Java program and use it in your Windows or Linux or Mac This online mathematical keyboard is limited to what can be achieved with Unicode characters. Almost all computer systems today use the ASCII code to represent characters and texts. Wolfram Science. 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The Mathematica Trajectory It's Come a Long Way in Three Decades. In today's technology-driven world, everyone is aware about computing, and how to use a PC. As a result, the small, relatively inexpensive “microcomputer”–soon known as A Few Tips on How to Use PowerPoint for Mathematical Presentations What These Are About These tips may help you produce math-heavy PowerPoint presentations more efficiently, and get them to look better. Technology-enabling science of the computational universe. To enter [ + ] - key [ + ] at the top or [ + ] key on the numeric keypad on Télécharger Mathematical keyboard B This is a soft keyboard that is convenient for writing math problems, expressions, etc. Pi Symbol. Advanced Kurdish Keyboard Apps Full Version Download for PC. If you are working on a Unix workstation (like those in the Chemical Engineering Department’s Cody Lab), you will need to open a terminal and then type mathematica on the command line. 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Greek Alphabet Symbols & Characters: mathematical uses The Greek alphabet is widely used in mathematical and scientific equations with letters like psi, rho, eta, mu, omega and many more being widely used. → Read More: Typing Math on the Computer To type the square root symbol on a PC, hold the Alt key. Name Unicode Glyph Unicode Name Description Aliases; alefsym: 02135: ALEF SYMBOL : Alpha: 00391: GREEK CAPITAL LETTER ALPHA : alpha: 003B1: GREEK SMALL LETTER ALPHA P. Doing Math on a Computer. You can either use the tilde (the single wiggly line, probably close to the "ESC" key on your keyboard) or a regular "equals" sign followed by the notation "(approx)", indicating that the answer is an approximate value. MathType is the editor of mathematical formulas rich, compatible with most of the Office applications, makes it easy to create the characters, mathematical formulas in any text editor, such as MS Office, OpenOffice, Gmail, TeX, LaTeX, MathML, etc . 4. Hold down the Alt key. Find a Small World Toys Math Keyboard, Multiplication at Staples. Clicking this link will start the installer to download Greek Keyboard free for Windows. 1 you can enter unicode characters with the following directions. The following keys do not work on the numeric pad: / * + -. Once you bring up the calculator function, there is often a circle or square to give you the operations which you perform using the Menu button on the phone. Macintosh Accent Codes Accented Vowels. How to Type Symbols Using the ALT Key. Plus it can be easily customized with color schemes and calculator skins. In 2016, SwiftKey was acquired by Microsoft for an impressive amount IBM includes support for this code page in the hardware of its model 5150, known as "IBM-PC", considered the first personal computer. Type and handwrite mathematical notation with MathType. I am a hard core Mac user and this keyboard works flawless with Mac! These software are nothing but numpad emulator software for your Windows PC. Download Advanced Kurdish Keyboard Apps Latest Version for PC,Laptop,Windows. If you are an average computer user, you might find it difficult on how to type division or divided by symbol (÷). Quick typing of mathematical and other symbols Word 2016 2013 2010 2007 2003 Mathematical and other texts require a large number of special symbols that are not present on the keyboard. Ctrl + Alt + M on Windows & Linux. Type the specific numeric combination The Keyboard Layout Project is an attempt to design a fully optimized keyboard layout, with no restrictions. , here) shows that there are too many of them to fit on a standard keyboard with 100-odd keys, even with modifiers. Keyboard temperaments are designed such that the notes all have a primary name or function at which they sound best, while they can also function to some extent as the enharmonically named note a PC away in either direction. mathematical keyboard for pc

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# Are the integer index finite depth irreducible subfactors Kac-coideal?

Is every integer index finite depth irreducible subfactors planar algebra, the intermediate of an irreducible finite index depth $2$ subfactors planar algebra?
In other words, of the following form (called Kac-coideal): $(R^{\mathbb{J}} \subset R^{\mathbb{I}})$ with $\mathbb{A}$ a finite dimensional Kac algebra and $\mathbb{I} \subset \mathbb{J} \subset \mathbb{A}$ left coideal subalgebras.

Remark: it seems relevant because without the integer index assumption, they are weak-Kac-coideal (see here prop. 9.1.1 p 37) : an irreducible depth $d$ finite index irreducible subfactor $(N \subset M)$ is an intermediate of the depth $2$ (non nec. irreducible) subfactor $(N \subset M_{d-2})$ which is (planar algebra) equivalent to $(R^{\mathbb{A}} \subset R)$, with $\mathbb{A}$ a finite dim. weak Kac algebra, so that $(N \subset M)$ is (planar algebra) equivalent to $(R^{\mathbb{A}} \subset R^{\mathbb{I}})$ with $\mathbb{I}$ a left coideal subalgebra of $\mathbb{A}$, thanks to the Galois correspondence.

Remark: without the "finite depth" assumption, it's false because you can take a $A_{\infty} * A_{\infty}$ subfactor planar algebra whose first component is non-integer index $\alpha > 4$ and the second $n/\alpha$ with an integer $n > 4 \alpha$, so that the whole subfactor is index $n$, but can't be Kac-coideal (because the indices of the intermediate subfactors of a Kac-coideal subfactor are integer). Moreover, I don't know whether or not every $A_n$ or $A_{\infty}$ subfactor planar algebra of integer index are Kac-coideal.


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MathSciNet bibliographic data MR1609654 (99i:65109) 65M60 Wei, Dongming; Lefton, Lew A priori $L\sp \rho$$L\sp \rho$ error estimates for Galerkin approximations to porous medium and fast diffusion equations. Math. Comp. 68 (1999), no. 227, 971–989. Article

For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.