Symmetry Numbers and Chemical Reaction Rates
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11 Practice Lesso N 4 R O U N D W H Ole Nu M Bers U N It 1
CC04MM RPPSTG TEXT.indb 11 © Practice and Problem Solving Curriculum Associates, LLC Copying isnotpermitted. Practice Lesson 4 Round Whole Numbers Whole 4Round Lesson Practice Lesson 4 Round Whole Numbers Name: Solve. M 3 Round each number. Prerequisite: Round Three-Digit Numbers a. 689 rounded to the nearest ten is 690 . Study the example showing how to round a b. 68 rounded to the nearest hundred is 100 . three-digit number. Then solve problems 1–6. c. 945 rounded to the nearest ten is 950 . Example d. 945 rounded to the nearest hundred is 900 . Round 154 to the nearest ten. M 4 Rachel earned $164 babysitting last month. She earned $95 this month. Rachel rounded each 150 151 152 153 154 155 156 157 158 159 160 amount to the nearest $10 to estimate how much 154 is between 150 and 160. It is closer to 150. she earned. What is each amount rounded to the 154 rounded to the nearest ten is 150. nearest $10? Show your work. Round 154 to the nearest hundred. Student work will vary. Students might draw number lines, a hundreds chart, or explain in words. 100 110 120 130 140 150 160 170 180 190 200 Solution: ___________________________________$160 and $100 154 is between 100 and 200. It is closer to 200. C 5 Use the digits in the tiles to create a number that 154 rounded to the nearest hundred is 200. makes each statement true. Use each digit only once. B 1 Round 236 to the nearest ten. 1 2 3 4 5 6 7 8 9 Which tens is 236 between? Possible answer shown. -
Molecular Symmetry
Molecular Symmetry Symmetry helps us understand molecular structure, some chemical properties, and characteristics of physical properties (spectroscopy) – used with group theory to predict vibrational spectra for the identification of molecular shape, and as a tool for understanding electronic structure and bonding. Symmetrical : implies the species possesses a number of indistinguishable configurations. 1 Group Theory : mathematical treatment of symmetry. symmetry operation – an operation performed on an object which leaves it in a configuration that is indistinguishable from, and superimposable on, the original configuration. symmetry elements – the points, lines, or planes to which a symmetry operation is carried out. Element Operation Symbol Identity Identity E Symmetry plane Reflection in the plane σ Inversion center Inversion of a point x,y,z to -x,-y,-z i Proper axis Rotation by (360/n)° Cn 1. Rotation by (360/n)° Improper axis S 2. Reflection in plane perpendicular to rotation axis n Proper axes of rotation (C n) Rotation with respect to a line (axis of rotation). •Cn is a rotation of (360/n)°. •C2 = 180° rotation, C 3 = 120° rotation, C 4 = 90° rotation, C 5 = 72° rotation, C 6 = 60° rotation… •Each rotation brings you to an indistinguishable state from the original. However, rotation by 90° about the same axis does not give back the identical molecule. XeF 4 is square planar. Therefore H 2O does NOT possess It has four different C 2 axes. a C 4 symmetry axis. A C 4 axis out of the page is called the principle axis because it has the largest n . By convention, the principle axis is in the z-direction 2 3 Reflection through a planes of symmetry (mirror plane) If reflection of all parts of a molecule through a plane produced an indistinguishable configuration, the symmetry element is called a mirror plane or plane of symmetry . -
Girls' Elite 2 0 2 0 - 2 1 S E a S O N by the Numbers
GIRLS' ELITE 2 0 2 0 - 2 1 S E A S O N BY THE NUMBERS COMPARING NORMAL SEASON TO 2020-21 NORMAL 2020-21 SEASON SEASON SEASON LENGTH SEASON LENGTH 6.5 Months; Dec - Jun 6.5 Months, Split Season The 2020-21 Season will be split into two segments running from mid-September through mid-February, taking a break for the IHSA season, and then returning May through mid- June. The season length is virtually the exact same amount of time as previous years. TRAINING PROGRAM TRAINING PROGRAM 25 Weeks; 157 Hours 25 Weeks; 156 Hours The training hours for the 2020-21 season are nearly exact to last season's plan. The training hours do not include 16 additional in-house scrimmage hours on the weekends Sep-Dec. Courtney DeBolt-Slinko returns as our Technical Director. 4 new courts this season. STRENGTH PROGRAM STRENGTH PROGRAM 3 Days/Week; 72 Hours 3 Days/Week; 76 Hours Similar to the Training Time, the 2020-21 schedule will actually allow for a 4 additional hours at Oak Strength in our Sparta Science Strength & Conditioning program. These hours are in addition to the volleyball-specific Training Time. Oak Strength is expanding by 8,800 sq. ft. RECRUITING SUPPORT RECRUITING SUPPORT Full Season Enhanced Full Season In response to the recruiting challenges created by the pandemic, we are ADDING livestreaming/recording of scrimmages and scheduled in-person visits from Lauren, Mikaela or Peter. This is in addition to our normal support services throughout the season. TOURNAMENT DATES TOURNAMENT DATES 24-28 Dates; 10-12 Events TBD Dates; TBD Events We are preparing for 15 Dates/6 Events Dec-Feb. -
Basic Combinatorics
Basic Combinatorics Carl G. Wagner Department of Mathematics The University of Tennessee Knoxville, TN 37996-1300 Contents List of Figures iv List of Tables v 1 The Fibonacci Numbers From a Combinatorial Perspective 1 1.1 A Simple Counting Problem . 1 1.2 A Closed Form Expression for f(n) . 2 1.3 The Method of Generating Functions . 3 1.4 Approximation of f(n) . 4 2 Functions, Sequences, Words, and Distributions 5 2.1 Multisets and sets . 5 2.2 Functions . 6 2.3 Sequences and words . 7 2.4 Distributions . 7 2.5 The cardinality of a set . 8 2.6 The addition and multiplication rules . 9 2.7 Useful counting strategies . 11 2.8 The pigeonhole principle . 13 2.9 Functions with empty domain and/or codomain . 14 3 Subsets with Prescribed Cardinality 17 3.1 The power set of a set . 17 3.2 Binomial coefficients . 17 4 Sequences of Two Sorts of Things with Prescribed Frequency 23 4.1 A special sequence counting problem . 23 4.2 The binomial theorem . 24 4.3 Counting lattice paths in the plane . 26 5 Sequences of Integers with Prescribed Sum 28 5.1 Urn problems with indistinguishable balls . 28 5.2 The family of all compositions of n . 30 5.3 Upper bounds on the terms of sequences with prescribed sum . 31 i CONTENTS 6 Sequences of k Sorts of Things with Prescribed Frequency 33 6.1 Trinomial Coefficients . 33 6.2 The trinomial theorem . 35 6.3 Multinomial coefficients and the multinomial theorem . 37 7 Combinatorics and Probability 39 7.1 The Multinomial Distribution . -
The Wavelet Tutorial Second Edition Part I by Robi Polikar
THE WAVELET TUTORIAL SECOND EDITION PART I BY ROBI POLIKAR FUNDAMENTAL CONCEPTS & AN OVERVIEW OF THE WAVELET THEORY Welcome to this introductory tutorial on wavelet transforms. The wavelet transform is a relatively new concept (about 10 years old), but yet there are quite a few articles and books written on them. However, most of these books and articles are written by math people, for the other math people; still most of the math people don't know what the other math people are 1 talking about (a math professor of mine made this confession). In other words, majority of the literature available on wavelet transforms are of little help, if any, to those who are new to this subject (this is my personal opinion). When I first started working on wavelet transforms I have struggled for many hours and days to figure out what was going on in this mysterious world of wavelet transforms, due to the lack of introductory level text(s) in this subject. Therefore, I have decided to write this tutorial for the ones who are new to the topic. I consider myself quite new to the subject too, and I have to confess that I have not figured out all the theoretical details yet. However, as far as the engineering applications are concerned, I think all the theoretical details are not necessarily necessary (!). In this tutorial I will try to give basic principles underlying the wavelet theory. The proofs of the theorems and related equations will not be given in this tutorial due to the simple assumption that the intended readers of this tutorial do not need them at this time. -
Numb3rs Episode Guide Episodes 001–118
Numb3rs Episode Guide Episodes 001–118 Last episode aired Friday March 12, 2010 www.cbs.com c c 2010 www.tv.com c 2010 www.cbs.com c 2010 www.redhawke.org c 2010 vitemo.com The summaries and recaps of all the Numb3rs episodes were downloaded from http://www.tv.com and http://www. cbs.com and http://www.redhawke.org and http://vitemo.com and processed through a perl program to transform them in a LATEX file, for pretty printing. So, do not blame me for errors in the text ^¨ This booklet was LATEXed on June 28, 2017 by footstep11 with create_eps_guide v0.59 Contents Season 1 1 1 Pilot ...............................................3 2 Uncertainty Principle . .5 3 Vector ..............................................7 4 Structural Corruption . .9 5 Prime Suspect . 11 6 Sabotage . 13 7 Counterfeit Reality . 15 8 Identity Crisis . 17 9 Sniper Zero . 19 10 Dirty Bomb . 21 11 Sacrifice . 23 12 Noisy Edge . 25 13 Man Hunt . 27 Season 2 29 1 Judgment Call . 31 2 Bettor or Worse . 33 3 Obsession . 37 4 Calculated Risk . 39 5 Assassin . 41 6 Soft Target . 43 7 Convergence . 45 8 In Plain Sight . 47 9 Toxin............................................... 49 10 Bones of Contention . 51 11 Scorched . 53 12 TheOG ............................................. 55 13 Double Down . 57 14 Harvest . 59 15 The Running Man . 61 16 Protest . 63 17 Mind Games . 65 18 All’s Fair . 67 19 Dark Matter . 69 20 Guns and Roses . 71 21 Rampage . 73 22 Backscatter . 75 23 Undercurrents . 77 24 Hot Shot . 81 Numb3rs Episode Guide Season 3 83 1 Spree ............................................. -
Probabilities of Outcomes and Events
Probabilities of outcomes and events Outcomes and events Probabilities are functions of events, where events can arise from one or more outcomes of an experiment or observation. To use an example from DNA sequences, if we pick a random location of DNA, the possible outcomes to observe are the letters A, C, G, T. The set of all possible outcomes is S = fA, C, G, Tg. The set of all possible outcomes is also called the sample space. Events of interest might be E1 = an A is observed, or E2 = a purine is observed. We can think of an event as a subset of the set of all possible outcomes. For example, E2 can also be described as fA; Gg. A more traditional example to use is with dice. For one roll of a die, the possible outcomes are S = f1; 2; 3; 4; 5; 6g. Events can be any subset of these. For example, the following are events for this sample space: • E1 = a 1 is rolled • E2 = a 2 is rolled • Ei = an i is rolled, where i is a particular value in f1,2,3,4,5,6g • E = an even number is rolled = f2; 4; 6g • D = an odd number is rolled = f1; 3; 5g • F = a prime number is rolled = f2; 3; 5g • G = f1; 5g where event G is the event that either a 1 or a 5 is rolled. Often events have natural descriptions, like \an odd number is rolled", but events can also be arbitrary subsets like G. Sample spaces and events can also involve more complicated descriptions. -
Combinatorics of K-Shapes and Genocchi Numbers
FPSAC 2011, Reykjavík, Iceland DMTCS proc. AO, 2011, 493–504 Combinatorics of k-shapes and Genocchi numbers Florent Hivert†and Olivier Mallet‡ LITIS, Université de Rouen, Saint-Étienne-du-Rouvray, France Abstract. In this paper we present a work in progress on a conjectural new combinatorial model for the Genocchi numbers. This new model called irreducible k-shapes has a strong algebraic background in the theory of symmetric functions and leads to seemingly new features on the theory of Genocchi numbers. In particular, the natural q-analogue coming from the degree of symmetric functions seems to be unknown so far. Résumé. Dans cet article, nous présentons un travail en cours sur un nouveau modèle combinatoire conjectural pour les nombres de Genocchi. Ce nouveau modèle est celui des k-formes irréductibles, qui repose sur de solides bases algébriques en lien avec la théorie des fonctions symétriques et qui conduit à des aspects apparemment nouveaux de la théorie des nombres de Genocchi. En particulier, le q-analogue naturel venant du degré des fonctions symétriques semble inconnu jusqu’ici. Keywords: partitions, cores, symmetric functions Contents 1 Introduction 494 2 Background 495 2.1 Genocchinumbers ................................. ......495 2.2 Integerpartitionsandskewpartitions. ................495 2.3 k-cores and k-shapes ......................................496 3 Irreducible k-shapes 497 3.1 Additionofrectangles. ..........497 3.2 Maintheorem..................................... 500 4 Work in progress 502 4.1 Mainconjecture.................................. .......502 4.2 Algebraicperspectives . ..........502 5 Table 503 †[email protected] ‡[email protected] 1365–8050 c 2011 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France 494 Florent Hivert and Olivier Mallet 1 Introduction The goal of this paper is to present some purely combinatorial results on certain partitions; these results are strongly motivated by the theory of symmetric functions. -
302Goldenrodrev7.26 Script
Goldenrod REV: 7/26/06 Green REV: 7/26/06 Yellow REV: 7/24/06 Pink REV: 7/20/06 Blue REV: 7/18/06 “Two Daughters” #302/Ep.39 Written by Ken Sanzel Directed by Alex Zakrzewski SCOTT FREE in association with CBS PARAMOUNT NETWORK TELEVISION, a division of CBS Studios. Copyright 2006 CBS Paramount Network Television. All Rights Reserved. This script is the property of CBS Paramount Network Television and may not be copied or distributed without the express written permission of CBS Paramount Network Television. This copy of the script remains the property of CBS Paramount Network Television. It may not be sold or transferred and it must be returned to CBS Paramount Network Television promptly upon demand. THE WRITING CREDITS MAY OR MAY NOT BE FINAL AND SHOULD NOT BE USED FOR PUBLICITY OR ADVERTISING PURPOSES WITHOUT FIRST CHECKING WITH TELEVISION LEGAL DEPARTMENT. Goldenrod REV July 26th, 2006 #302/Ep.39 “Two Daughters” GOLDENROD Revisions 7/26/2006 SCRIPT REVISION HISTORY COLOR DATE PAGES WHITE 7/14/06 (1-60) BLUE Rev 7/18/06 (1,2,3, 7,8,12,13,27,28,30,32,33 36,39,42,42A,48,49,50,53 54,55,55A) Pink Rev 7/20/06 (15,16,41,42, 42A,43,49,52,56,56A) Yellow Rev 7/24/06 (1,15,17,17A,22,24,25, 26,27,34,34A,36,44,49,52 52A,53,55,55A,57,58) Green Rev 7/26/06 (2,5,8,10,15,19,21,22, 23,24,27,28,29,31,32,32A 33,34,34A,36,38,42,42a, 44,45,49,51,54,55) Goldenrod Rev 7/26/06 (5,6,31) #302/Ep.39 “Two Daughters” GOLDENROD Revisions 7/26/2006 SET LIST INTERIORS EXTERIOR FBI PROCESSING AREA STREET BULLPEN WAR ROOM TWILIGHT MOTEL* INTERVIEW ROOM MOTEL ROOM INTERROGATION ROOM OBSERVATION ROOM DAVID & COLBY’S CAR HALLWAY TECH ROOM DON’S CAR COFFEE ROOM FBI BRIDGE MOTEL ROOM BATHROOM SUBURBAN HOUSE HOUSE CRYSTAL’S CAR GARAGE ROADBLOCK DAVID & COLBY’S CAR CALSCI CAMPUS DON’S CAR ABANDONED HOUSE HOSPITAL ROOM CORRIDOR LOBBY EPPES HOUSE LIVING ROOM CHARLIE’S OFFICE ADAM BENTON’S HOME OFFICE CRYSTAL’S CAR "TWO DAUGHTERS" TEASER BLACK BOX OPENING: 15.. -
Naso – Bamidbar/Numbers 4:21-7:89
Naso – Bamidbar/Numbers 4:21-7:89 The Text – Key verses in this parasha 6:1-3 The Lord spoke to Moses, saying: Speak to the Israelites and say to them: If anyone, man or woman, explicitly utters a nazirite’s vow, to set himself apart for the Lord, he shall abstain from wine and any other intoxicant; he shall not drink vinegar of wine or of any other intoxicant, neither shall he drink anything in which grapes have been steeped, nor eat grapes fresh or dried. 6:13-15 This is the ritual for the nazirite: On the day that his term as nazirite is completed, he shall be brought to the entrance of the Tent of Meeting. As his offering to the Lord he shall present: one male lamb in its first year, without blemish, for a burnt offering; one ewe lamb in its first year, without blemish, for a sin offering; one ram without blemish for an offering of well- being; a basket of unleavened cakes of choice flour with oil mixed in, and unleavened wafers spread with oil; and the proper meal offerings and libations. 6:20 The priest shall elevate them as an elevation offering before the Lord; and this shall be a sacred donation for the priest, in addition to the breast of the elevation offering and the thigh of gift offering. After that the nazirite may drink wine. The Context – The verses in plain English In Naso, God lays out for Moses the rules to be followed by Nazirites, people who, in devotion to God, abstain from drinking wine, let their hair grow long and avoid all contact with dead bodies. -
Combinatorics and Counting Per Alexandersson 2 P
Combinatorics and counting Per Alexandersson 2 p. alexandersson Introduction Here is a collection of counting problems. Questions and suggestions Version: 15th February 2021,22:26 are welcome at [email protected]. Exclusive vs. independent choice. Recall that we add the counts for exclusive situations, and multiply the counts for independent situations. For example, the possible outcomes of a dice throw are exclusive: (Sides of a dice) = (Even sides) + (Odd sides) The different outcomes of selecting a playing card in a deck of cards can be seen as a combination of independent choices: (Different cards) = (Choice of color) · (Choice of value). Labeled vs. unlabeled sets is a common cause for confusion. Consider the following two problems: • Count the number of ways to choose 2 people among 4 people. • Count the number of ways to partition 4 people into sets of size 2. In the first example, it is understood that the set of chosen people is a special set | it is the chosen set. We choose two people, and the other two are not chosen. In the second example, there is no difference between the two couples. The answer to the first question is therefore 4 , counting the chosen subsets: {12, 13, 14, 23, 24, 34}. 2 The answer to the second question is 1 4 , counting the partitions: {12|34, 13|24, 14|23}. 2! 2 That is, the issue is that there is no way to distinguish the two sets in the partition. However, now consider the following two problems: • Count the number of ways to choose 2 people among 5 people. -
Democracy for All? V-Dem Annual Democracy Report 2018
INSTITUTE VARIETIES OF DEMOCRACY Democracy for All? V-DEM ANNUAL DEMOCRACY REPORT 2018 Table of Contents V-DEM ANNUAL REPOrt 2018 INTRODUCTION EXECUTivE SUMMARY V-DEM IN A NUTSHELL A WORD FROM THE V-DEM IN NUMBERS, TEAM COLLABORATIONS, METHODOLOGY, AND HisTORICAL V-DEM 05 06 08 SECTION 1 STATE OF THE WORLD 2017 – LiBERAL AND ELECTORAL DEMOCRACY 16 SECTION 2 INCLUsiON is AN ILLUsiON 34 SECTION 2.1 SECTION 2.2 SECTION 2.3 WOMEN’S INCLUsiON INCLUsiON OF SOCiaL POLITICAL EXCLUsiON AND ACCEss TO POWER GROUPS BasED ON SOCIO- ECONOMIC INEQUALITY 38 44 52 V-DEM UsERS V-DEM PUBLICATIONS REFERENCES PRACTITIONERS, ACadEMIC JOURNAL ACadEMICS, STUDENTS, ARTICLES FROM THE AND MUSEUMS V-DEM TEAM 58 60 69 APPENdiX COUNTRY SCORES FOR 2017 71 V-Dem is a unique approach to measuring democracy – historical, multidimensional, nuanced, and disaggregated – employing state- of-the-art methodology. Varieties of Democracy (V-Dem) produces the largest V-Dem measures hundreds of different attributes global dataset on democracy with some 19 million of democracy. V-Dem enables new ways to study data for 201 countries from 1789 to 2017. Involving the nature, causes, and consequences of democracy over 3,000 scholars and other country experts, embracing its multiple meanings. V-Dem is or has been funded by (not in order of magnitude): Development Agency, NORAD/the Norwegian Research Coun- Riksbankens Jubileumsfond, Knut & Alice Wallenberg Foundation, cil, International IDEA, Fundação Francisco Manuel dos Santos, Marianne & Marcus Wallenberg Foundation, the Swedish Research Aarhus University, the Quality of Government Institute and the Council, the Mo Ibrahim Foundation, the European Research University of Notre Dame, with co-funding from the Vice Chancel- Council, the Danish Research Council, the European Union/the lor, the Dean of the Social Sciences, and the Department of Politi- European Commission, the Ministry of Foreign Affairs-Sweden, the cal Science at University of Gothenburg.