Differential Equations
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Research Brief March 2017 Publication #2017-16
Research Brief March 2017 Publication #2017-16 Flourishing From the Start: What Is It and How Can It Be Measured? Kristin Anderson Moore, PhD, Child Trends Christina D. Bethell, PhD, The Child and Adolescent Health Measurement Introduction Initiative, Johns Hopkins Bloomberg School of Every parent wants their child to flourish, and every community wants its Public Health children to thrive. It is not sufficient for children to avoid negative outcomes. Rather, from their earliest years, we should foster positive outcomes for David Murphey, PhD, children. Substantial evidence indicates that early investments to foster positive child development can reap large and lasting gains.1 But in order to Child Trends implement and sustain policies and programs that help children flourish, we need to accurately define, measure, and then monitor, “flourishing.”a Miranda Carver Martin, BA, Child Trends By comparing the available child development research literature with the data currently being collected by health researchers and other practitioners, Martha Beltz, BA, we have identified important gaps in our definition of flourishing.2 In formerly of Child Trends particular, the field lacks a set of brief, robust, and culturally sensitive measures of “thriving” constructs critical for young children.3 This is also true for measures of the promotive and protective factors that contribute to thriving. Even when measures do exist, there are serious concerns regarding their validity and utility. We instead recommend these high-priority measures of flourishing -
The Origin of the Peculiarities of the Vietnamese Alphabet André-Georges Haudricourt
The origin of the peculiarities of the Vietnamese alphabet André-Georges Haudricourt To cite this version: André-Georges Haudricourt. The origin of the peculiarities of the Vietnamese alphabet. Mon-Khmer Studies, 2010, 39, pp.89-104. halshs-00918824v2 HAL Id: halshs-00918824 https://halshs.archives-ouvertes.fr/halshs-00918824v2 Submitted on 17 Dec 2013 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Published in Mon-Khmer Studies 39. 89–104 (2010). The origin of the peculiarities of the Vietnamese alphabet by André-Georges Haudricourt Translated by Alexis Michaud, LACITO-CNRS, France Originally published as: L’origine des particularités de l’alphabet vietnamien, Dân Việt Nam 3:61-68, 1949. Translator’s foreword André-Georges Haudricourt’s contribution to Southeast Asian studies is internationally acknowledged, witness the Haudricourt Festschrift (Suriya, Thomas and Suwilai 1985). However, many of Haudricourt’s works are not yet available to the English-reading public. A volume of the most important papers by André-Georges Haudricourt, translated by an international team of specialists, is currently in preparation. Its aim is to share with the English- speaking academic community Haudricourt’s seminal publications, many of which address issues in Southeast Asian languages, linguistics and social anthropology. -
Chapter 11. Three Dimensional Analytic Geometry and Vectors
Chapter 11. Three dimensional analytic geometry and vectors. Section 11.5 Quadric surfaces. Curves in R2 : x2 y2 ellipse + =1 a2 b2 x2 y2 hyperbola − =1 a2 b2 parabola y = ax2 or x = by2 A quadric surface is the graph of a second degree equation in three variables. The most general such equation is Ax2 + By2 + Cz2 + Dxy + Exz + F yz + Gx + Hy + Iz + J =0, where A, B, C, ..., J are constants. By translation and rotation the equation can be brought into one of two standard forms Ax2 + By2 + Cz2 + J =0 or Ax2 + By2 + Iz =0 In order to sketch the graph of a quadric surface, it is useful to determine the curves of intersection of the surface with planes parallel to the coordinate planes. These curves are called traces of the surface. Ellipsoids The quadric surface with equation x2 y2 z2 + + =1 a2 b2 c2 is called an ellipsoid because all of its traces are ellipses. 2 1 x y 3 2 1 z ±1 ±2 ±3 ±1 ±2 The six intercepts of the ellipsoid are (±a, 0, 0), (0, ±b, 0), and (0, 0, ±c) and the ellipsoid lies in the box |x| ≤ a, |y| ≤ b, |z| ≤ c Since the ellipsoid involves only even powers of x, y, and z, the ellipsoid is symmetric with respect to each coordinate plane. Example 1. Find the traces of the surface 4x2 +9y2 + 36z2 = 36 1 in the planes x = k, y = k, and z = k. Identify the surface and sketch it. Hyperboloids Hyperboloid of one sheet. The quadric surface with equations x2 y2 z2 1. -
Applications the Formula Y = Mx + B Sometimes Appears with Different
PRIMARY CONTENT MODULE Algebra I -Linear Equations & Inequalities T-71 Applications The formula y = mx + b sometimes appears with different symbols. For example, instead of x, we could use the letter C. Instead of y, we could use the letter F. Then the equation becomes F = mC + b. All temperature scales are related by linear equations. For example, the temperature in degrees Fahrenheit is a linear function of degrees Celsius. © 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATION PRIMARY CONTENT MODULE Algebra I -Linear Equations & Inequalities T-72 Basic Temperature Facts Water freezes at: 0°C, 32°F Water Boils at: 100°C, 212°F F • (100, 212) • (0, 32) C Can you solve for m and b in F = mC + b? © 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATION PRIMARY CONTENT MODULE Algebra I -Linear Equations & Inequalities T-73 To find the equation relating Fahrenheit to Celsius we need m and b F – F m = 2 1 C2 – C1 212 – 32 m = 100 – 0 180 9 m = = 100 5 9 Therefore F = C + b 5 To find b, substitute the coordinates of either point. 9 32 = (0) + b 5 Therefore b = 32 Therefore the equation is 9 F = C + 32 5 Can you solve for C in terms of F? © 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATION PRIMARY CONTENT MODULE Algebra I -Linear Equations & Inequalities T-74 Celsius in terms of Fahrenheit 9 F = C + 32 5 5 5 9 F = æ C +32ö 9 9è 5 ø 5 5 F = C + (32) 9 9 5 5 F – (32) = C 9 9 5 5 C = F – (32) 9 9 5 C = (F – 32) 9 Example: How many degrees Celsius is77°F? 5 C = (77 – 32) 9 5 C = (45) 9 C = 25° So 72°F = 25°C © 1999, CISC: Curriculum and Instruction Steering Committee The WINNING EQUATION PRIMARY CONTENT MODULE Algebra I -Linear Equations & Inequalities T-75 Standard 8 Algebra I, Grade 8 Standards Students understand the concept of parallel and perpendicular lines and how their slopes are related. -
Form Y-203-I, If You Had More Than One Job, Or If You Had a Job for Only Part of the Year
Department of Taxation and Finance Yonkers Nonresident Earnings Tax Return Y-203 For the full year January 1, 2020, through December 31, 2020, or fiscal year beginning and ending Name as shown on Form IT-201 or IT-203 Social Security number A Were you a Yonkers resident for any part of the taxable year? (mark an X in the appropriate box) Yes No (see instructions) (See the instructions for Form IT-201 or IT-203 for the definition of a resident.) If Yes: 1. Give period of Yonkers residence. From (mmddyyyy) to (mmddyyyy) 2. Are you reporting Yonkers resident income tax surcharge on your New York State return? ..................................................................................... Yes No (submit explanation) 3. You must complete and submit Form IT-360.1 (see instructions). B Did you or your spouse maintain an apartment or other living quarters in Yonkers during any part of the year?...................................................................................... Yes No If Yes, give address below and enter the number of days spent in Yonkers during 2020: days Address: C Are you reporting income from self-employment (on line 2 below)?......... Yes No If Yes, complete the following: Business name Business address Employer identification number Principal business activity Form of business: Sole proprietorship Partnership Other (explain) Calculation of nonresident earnings tax 1 Gross wages and other employee compensation (see instructions; if claiming an allocation, include amount from line 22) ............................................... 1 .00 2 Net earnings from self-employment (see instructions; if claiming an allocation, include amount from line 32; if a loss, write loss on line 2) ............................................................................................... 2 .00 3 Add lines 1 and 2 (if line 2 is a loss, enter amount from line 1) ........................................................... -
A Quick Algebra Review
A Quick Algebra Review 1. Simplifying Expressions 2. Solving Equations 3. Problem Solving 4. Inequalities 5. Absolute Values 6. Linear Equations 7. Systems of Equations 8. Laws of Exponents 9. Quadratics 10. Rationals 11. Radicals Simplifying Expressions An expression is a mathematical “phrase.” Expressions contain numbers and variables, but not an equal sign. An equation has an “equal” sign. For example: Expression: Equation: 5 + 3 5 + 3 = 8 x + 3 x + 3 = 8 (x + 4)(x – 2) (x + 4)(x – 2) = 10 x² + 5x + 6 x² + 5x + 6 = 0 x – 8 x – 8 > 3 When we simplify an expression, we work until there are as few terms as possible. This process makes the expression easier to use, (that’s why it’s called “simplify”). The first thing we want to do when simplifying an expression is to combine like terms. For example: There are many terms to look at! Let’s start with x². There Simplify: are no other terms with x² in them, so we move on. 10x x² + 10x – 6 – 5x + 4 and 5x are like terms, so we add their coefficients = x² + 5x – 6 + 4 together. 10 + (-5) = 5, so we write 5x. -6 and 4 are also = x² + 5x – 2 like terms, so we can combine them to get -2. Isn’t the simplified expression much nicer? Now you try: x² + 5x + 3x² + x³ - 5 + 3 [You should get x³ + 4x² + 5x – 2] Order of Operations PEMDAS – Please Excuse My Dear Aunt Sally, remember that from Algebra class? It tells the order in which we can complete operations when solving an equation. -
Writing the Equation of a Line
Name______________________________ Writing the Equation of a Line When you find the equation of a line it will be because you are trying to draw scientific information from it. In math, you write equations like y = 5x + 2 This equation is useless to us. You will never graph y vs. x. You will be graphing actual data like velocity vs. time. Your equation should therefore be written as v = (5 m/s2) t + 2 m/s. See the difference? You need to use proper variables and units in order to compare it to theory or make actual conclusions about physical principles. The second equation tells me that when the data collection began (t = 0), the velocity of the object was 2 m/s. It also tells me that the velocity was changing at 5 m/s every second (m/s/s = m/s2). Let’s practice this a little, shall we? Force vs. mass F (N) y = 6.4x + 0.3 m (kg) You’ve just done a lab to see how much force was necessary to get a mass moving along a rough surface. Excel spat out the graph above. You labeled each axis with the variable and units (well done!). You titled the graph starting with the variable on the y-axis (nice job!). Now we turn to the equation. First we replace x and y with the variables we actually graphed: F = 6.4m + 0.3 Then we add units to our slope and intercept. The slope is found by dividing the rise by the run so the units will be the units from the y-axis divided by the units from the x-axis. -
Ffontiau Cymraeg
This publication is available in other languages and formats on request. Mae'r cyhoeddiad hwn ar gael mewn ieithoedd a fformatau eraill ar gais. [email protected] www.caerphilly.gov.uk/equalities How to type Accented Characters This guidance document has been produced to provide practical help when typing letters or circulars, or when designing posters or flyers so that getting accents on various letters when typing is made easier. The guide should be used alongside the Council’s Guidance on Equalities in Designing and Printing. Please note this is for PCs only and will not work on Macs. Firstly, on your keyboard make sure the Num Lock is switched on, or the codes shown in this document won’t work (this button is found above the numeric keypad on the right of your keyboard). By pressing the ALT key (to the left of the space bar), holding it down and then entering a certain sequence of numbers on the numeric keypad, it's very easy to get almost any accented character you want. For example, to get the letter “ô”, press and hold the ALT key, type in the code 0 2 4 4, then release the ALT key. The number sequences shown from page 3 onwards work in most fonts in order to get an accent over “a, e, i, o, u”, the vowels in the English alphabet. In other languages, for example in French, the letter "c" can be accented and in Spanish, "n" can be accented too. Many other languages have accents on consonants as well as vowels. -
The Geometry of the Phase Diffusion Equation
J. Nonlinear Sci. Vol. 10: pp. 223–274 (2000) DOI: 10.1007/s003329910010 © 2000 Springer-Verlag New York Inc. The Geometry of the Phase Diffusion Equation N. M. Ercolani,1 R. Indik,1 A. C. Newell,1,2 and T. Passot3 1 Department of Mathematics, University of Arizona, Tucson, AZ 85719, USA 2 Mathematical Institute, University of Warwick, Coventry CV4 7AL, UK 3 CNRS UMR 6529, Observatoire de la Cˆote d’Azur, 06304 Nice Cedex 4, France Received on October 30, 1998; final revision received July 6, 1999 Communicated by Robert Kohn E E Summary. The Cross-Newell phase diffusion equation, (|k|)2T =∇(B(|k|) kE), kE =∇2, and its regularization describes natural patterns and defects far from onset in large aspect ratio systems with rotational symmetry. In this paper we construct explicit solutions of the unregularized equation and suggest candidates for its weak solutions. We confirm these ideas by examining a fourth-order regularized equation in the limit of infinite aspect ratio. The stationary solutions of this equation include the minimizers of a free energy, and we show these minimizers are remarkably well-approximated by a second-order “self-dual” equation. Moreover, the self-dual solutions give upper bounds for the free energy which imply the existence of weak limits for the asymptotic minimizers. In certain cases, some recent results of Jin and Kohn [28] combined with these upper bounds enable us to demonstrate that the energy of the asymptotic minimizers converges to that of the self-dual solutions in a viscosity limit. 1. Introduction The mathematical models discussed in this paper are motivated by physical systems, far from equilibrium, which spontaneously form patterns. -
Numerical Algebraic Geometry and Algebraic Kinematics
Numerical Algebraic Geometry and Algebraic Kinematics Charles W. Wampler∗ Andrew J. Sommese† January 14, 2011 Abstract In this article, the basic constructs of algebraic kinematics (links, joints, and mechanism spaces) are introduced. This provides a common schema for many kinds of problems that are of interest in kinematic studies. Once the problems are cast in this algebraic framework, they can be attacked by tools from algebraic geometry. In particular, we review the techniques of numerical algebraic geometry, which are primarily based on homotopy methods. We include a review of the main developments of recent years and outline some of the frontiers where further research is occurring. While numerical algebraic geometry applies broadly to any system of polynomial equations, algebraic kinematics provides a body of interesting examples for testing algorithms and for inspiring new avenues of work. Contents 1 Introduction 4 2 Notation 5 I Fundamentals of Algebraic Kinematics 6 3 Some Motivating Examples 6 3.1 Serial-LinkRobots ............................... ..... 6 3.1.1 Planar3Rrobot ................................. 6 3.1.2 Spatial6Rrobot ................................ 11 3.2 Four-BarLinkages ................................ 13 3.3 PlatformRobots .................................. 18 ∗General Motors Research and Development, Mail Code 480-106-359, 30500 Mound Road, Warren, MI 48090- 9055, U.S.A. Email: [email protected] URL: www.nd.edu/˜cwample1. This material is based upon work supported by the National Science Foundation under Grant DMS-0712910 and by General Motors Research and Development. †Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556-4618, U.S.A. Email: [email protected] URL: www.nd.edu/˜sommese. This material is based upon work supported by the National Science Foundation under Grant DMS-0712910 and the Duncan Chair of the University of Notre Dame. -
Bessel's Differential Equation Mathematical Physics
R. I. Badran Bessel's Differential Equation Mathematical Physics Bessel's Differential Equation: 2 Recalling the DE y n y 0 which has a sinusoidal solution (i.e. sin nx and cos nx) and knowing that these solutions can be treated as power series, we can find a solution to the Bessel's DE which is written as: 2 2 2 x y xy (x p )y 0 . The solution is represented by a series. This series very much look like a damped sine or cosine. It is called a Bessel function. To solve the Bessel' DE, we apply the Frobenius method by mn assuming a series solution of the form y an x . n0 Substitute this solution into the DE equation and after some mathematical steps you may find that the indicial equation is 2 2 m p 0 where m= p. Also you may get a1=0 and hence all odd a's are zero as well. The recursion relation can be found as a a n n2 (n m 2)2 p 2 with (n=0, 1, 2, 3, ……etc.). Case (1): m= p (seeking the first solution of Bessel DE) We get the solution 2 4 p x x y a x 1 2(2p 2) 2 4(2p 2)(2p 4) This can be rewritten as: x p2n J (x) y a (1)n p 2n n0 2 n!( p n)! 1 Put a 2 p p! The Bessel function has the factorial form x p2n J (x) (1)n p 2n p , n0 n!( p n)!2 R. -
Calculus Terminology
AP Calculus BC Calculus Terminology Absolute Convergence Asymptote Continued Sum Absolute Maximum Average Rate of Change Continuous Function Absolute Minimum Average Value of a Function Continuously Differentiable Function Absolutely Convergent Axis of Rotation Converge Acceleration Boundary Value Problem Converge Absolutely Alternating Series Bounded Function Converge Conditionally Alternating Series Remainder Bounded Sequence Convergence Tests Alternating Series Test Bounds of Integration Convergent Sequence Analytic Methods Calculus Convergent Series Annulus Cartesian Form Critical Number Antiderivative of a Function Cavalieri’s Principle Critical Point Approximation by Differentials Center of Mass Formula Critical Value Arc Length of a Curve Centroid Curly d Area below a Curve Chain Rule Curve Area between Curves Comparison Test Curve Sketching Area of an Ellipse Concave Cusp Area of a Parabolic Segment Concave Down Cylindrical Shell Method Area under a Curve Concave Up Decreasing Function Area Using Parametric Equations Conditional Convergence Definite Integral Area Using Polar Coordinates Constant Term Definite Integral Rules Degenerate Divergent Series Function Operations Del Operator e Fundamental Theorem of Calculus Deleted Neighborhood Ellipsoid GLB Derivative End Behavior Global Maximum Derivative of a Power Series Essential Discontinuity Global Minimum Derivative Rules Explicit Differentiation Golden Spiral Difference Quotient Explicit Function Graphic Methods Differentiable Exponential Decay Greatest Lower Bound Differential