Balanced Binary Trees

Size: px
Start display at page:

Download "Balanced Binary Trees"

Transcription

1 Balanced Binary Trees 1 Binary searc trees provide O(log N) searc times provided tat te nodes are distributed in a reasonably balanced manner. Unfortunately, tat is not always te case and performing a sequence of deletions and insertions can often exacerbate te problem. Wen a BST becomes badly unbalanced, te searc beavior can degenerate to tat of a sorted linked list, O(N). Tere are a number of strategies for dealing wit tis problem; most involve adding some sort of restructuring to te insert/delete algoritms. Tat can be effective only if te restructuring reduces te average dept of a node from te root of te BST, and if te cost of te restructuring is, on average, O(log N). We will examine one suc restructuring algoritm

2 2 AVL tree*: a binary searc tree in wic te eigts of te left and rigt subtrees of te root differ by at most 1, and in wic te left and rigt subtrees are temselves AVL trees. Eac AVL tree node as an associated balance factor indicating te relative eigts of its subtrees (left-iger, equal, rigt-iger). Normally, tis adds one data element to eac tree node and an enumerated type is used. How effective is tis? Te eigt of an AVL tree wit N nodes never exceeds 1.44 log N and is typically muc closer to log N. *G. M. Adelson-Velskii and E. M. Landis, 192.

3 Examples Tis is an AVL tree... Notation: - means te subtrees of te node are te same eigt means tat te rigt subtree of te node is iger (by one) tan te left subtree (rigt-iger) / means tat te left subtree of te node is iger (by one) tan te rigt subtree (left-iger) / 3...and tis is not. / /

4 Unbalance from Insertion 4 Consider inserting te value 4 into te AVL tree: Te result would be unbalanced at te node containing 2: Te unbalance is repaired by applying one of two types of rotation to te unbalanced subtree

5 Rebalancing via Subtree Restructuring Te subtree rooted at 2 is rigt-iger We restructure te subtree, resulting in a balanced subtree: Te transformation is relatively simple, requiring only a few operations, and results in a subtree tat as equal balance. 8

6 AVL Insertion Case: rigt-iger Tere are two unbalance cases to consider, eac defined by te state of te subtree tat just received a new node. For simplicity, assume for now tat te insertion was to te rigt subtree (of te subtree). Let be te root of te newly unbalanced subtree, and suppose tat its rigt subtree is now rigt-iger: rigt In tis case, te subtree rooted at rigt was previously equally balanced (wy?) and te subtree rooted at was previously rigtiger (wy?). T 1 Te eigt labels follow from tose observations. T 2 +1 T 3 Balance can be restored by rotating te values so tat rigt becomes te subtree root node and becomes te left cild.

7 AVL Left Rotation Te manipulation just described is known as a left rotation and te result is: rigt rigt T 1 T 2 +1 T 3 Overall eigt of eac subtree is now te same. T 1 T 2 T 3 Tat covers te case were te rigt subtree as become rigt-iger te case were te left subtree as become left-iger is analogous and solved by a rigt rotation.

8 Unbalance from Insertion 8 Consider inserting te value 1 into tis AVL tree: Te result would be unbalanced at te node containing 2: Te unbalance is repaired by applying one of two types of rotation to te unbalanced subtree

9 Rebalancing via Subtree Restructuring 9 0 Te subtree rooted at 2 is left-iger We restructure te subtree, resulting in a balanced subtree: 0 20 Te transformation is again relatively simple, requiring only a few operations, and results in a subtree tat as equal balance

10 AVL Rigt Rotation Te previous manipulation is known as a rigt rotation and te result is: 10 // left left / +1 T 3 T 2 T 1 Overall eigt of eac subtree is now te same. T 3 T 2 T 1 Tat covers te case were te left subtree as become left-iger.

11 AVL Insertion Case: left-iger Now suppose tat te rigt subtree as become left-iger: 11 T 1 rigt-left? / rigt Te insertion occurred in te left subtree of te rigt subtree of. In tis case, te left subtree of te rigt subtree (rooted at rigt-left) may be eiter left-iger or rigt-iger, but not balanced (wy?). -1 T 2 or T 3 T 4 Surprisingly (peraps), tis case is more difficult. Te unbalance cannot be removed by performing a single left or rigt rotation.

12 AVL Double Rotation Applying a single rigt rotation to te subtree rooted at rigt produces 12 / rigt rigt-left rigt-left?? rigt -1 T 4 T 2 T 2 or T 3 T 3 T 4 a subtree rooted at rigt-left tat is now rigt-iger

13 AVL Double Rotation 13 Now, applying a single left rotation to te subtree rooted at produces rigt-left? Balance factors ere depend on original balance factor of rigt-left. rigt? rigt-left? rigt T 2 T 3 T 4 T 1 T 2 T 3 T 4 a balanced subtree. -1 or Te case were te left subtree of is rigt-iger is andled similarly (by a double rotation: left: rigt).

14 Unbalance from Deletion 14 Deleting a node from an AVL tree can also create an imbalance tat must be corrected. Te effects of deletion are potentially more complex tan tose of insertion. Te basic idea remains te same: delete te node, track canges in balance factors as te recursion backs out, and apply rotations as needed to restore AVL balance at eac node along te pat followed down during te deletion. However, rebalancing after a deletion may require applying single or double rotations at more tan one point along tat pat. As usual, tere are cases Here, we will make te following assumptions: - te lowest imbalance occurs at te node root (a subtree root) - te deletion occurred in te left subtree of root

15 AVL Deletion Case: rigt-iger 1 Suppose we ave te subtree on te left prior to deletion and tat on te rigt after deletion: rigt rigt rigt -1 Note: "rigt-iger" refers to te balance factor of te root of te rigt subtree (labeled rigt ere) Ten a single left rotation at will rebalance te subtree.

16 AVL Deletion Case: equal-eigt Suppose te rigt subtree root as balance factor equal-eigt: 1 rigt Again, a single left rotation at root will rebalance te subtree. / rigt Te difference is te resulting balance factor at te old subtree root node,, wic depends upon te original balance factor of te node rigt.

17 AVL Deletion Case: left-iger If te rigt subtree root was left-iger, we ave te following situation: 1 1 rigt-left? or -2? / rigt 4-1 Deleting a node from te left subtree of now will cause to become double rigt iger. As you sould expect, te resulting imbalance can be cured by first applying a rigt rotation at te node rigt, and ten applying a left rotation at te node. However, we must be careful because te balance factors will depend upon te original balance factor at te node labeled rigt-left

18 AVL Deletion Case: left-iger, left-iger If te rigt-left subtree root was also left-iger, we obtain: 18 rigt-left / rigt rigt 1 rigt-left /

19 AVL Deletion Case: left-iger, rigt-iger If te rigt-left subtree root was rigt-iger, we obtain: 19 rigt-left / rigt / rigt 1 rigt-left And, finally, if te rigt-left subtree root was equal-eigt, we'd obtain a tree were all tree of te labeled nodes ave equal-eigt.

20 AVL Deletion Cases: Summary 20 We ave considered a number of distinct deletion cases, assuming tat te deletion occurred in te left subtree of te imbalanced node. Tere are an equal number of entirely similar, symmetric cases for te assumption te deletion was in te rigt subtree of te imbalanced node. Drawing diagrams elps Tis discussion also as some logical implications for ow insertion is andled in an AVL tree. Te determination of te balance factors in te tree, following te rotations, involves similar logic in bot cases.

Red Green Black Trees: Extension to Red Black Trees

Red Green Black Trees: Extension to Red Black Trees Red Green Black Trees: Extension to Red Black Trees Seyfeddine Zouana*, Djamel Eddine Zegour Laboratoire de la Communication dans les Systèmes Informatiques, Ecole nationale Supérieure d'informatique,

More information

16.1 Volume of Prisms and Cylinders

16.1 Volume of Prisms and Cylinders Name Class Date 16.1 Volume of Prisms and Cylinders Essential Question: How do te formulas for te volume of a prism and cylinder relate to area formulas tat you already know? Explore G.11.D Apply te formulas

More information

234 The National Strategies Secondary Mathematics exemplification: Y7

234 The National Strategies Secondary Mathematics exemplification: Y7 234 Te National Strategies Secondary Matematics exemplification: Y7 Pupils sould learn to: Deduce and use formulae to calculate lengts, perimeters, areas and volumes in 2-D and 3-D sapes As outcomes, Year

More information

Physics Engineering PC 1431 Experiment P2 Heat Engine. Section B: Brief Theory (condensed from Serway & Jewett)

Physics Engineering PC 1431 Experiment P2 Heat Engine. Section B: Brief Theory (condensed from Serway & Jewett) Pysics Engineering PC 1431 Experiment P2 Heat Engine Section A: Introduction Te invention of steam engine played a very significant role in te Industrial Revolution from te late 1700s to early 1800s. Te

More information

Math Practice Use a Formula

Math Practice Use a Formula 9.4 Volumes of Prisms How can you find te volume of a prism? ACTIVITY: Pearls in a Treasure Cest Work wit a partner. A treasure cest is filled wit valuable pearls. Eac pearl is about centimeter in diameter

More information

Applications. 38 Looking for Pythagoras. Find the missing length(s).

Applications. 38 Looking for Pythagoras. Find the missing length(s). Applications. A rigt triangle as legs of lengt inces and inces. a. Find te area of a square drawn on te ypotenuse of te triangle. b. Wat is te lengt of te ypotenuse?. Use te Pytagorean Teorem to find te

More information

To find the volume of a pyramid and of a cone

To find the volume of a pyramid and of a cone - Volumes of Pyramids and Cones Common Core State Standards G-GMD.A. Use volume formulas for... pyramids, cones... to solve problems. G-MG.A. Use geometric sapes, teir measures, and teir properties to

More information

Overall stability of multi-span portal sheds at right-angles to the portal spans

Overall stability of multi-span portal sheds at right-angles to the portal spans Overall stability of multi-span portal seds at rigt-angles to te portal spans SCI s Senior Manager for Standards, Carles M King, explains te approac for design of long-span portal seds. 1. Introduction

More information

Optimization Model of Oil-Volume Marking with Tilted Oil Tank

Optimization Model of Oil-Volume Marking with Tilted Oil Tank Open Journal of Optimization 1 1 - ttp://.doi.org/1.36/ojop.1.1 Publised Online December 1 (ttp://www.scirp.org/journal/ojop) Optimization Model of Oil-olume Marking wit Tilted Oil Tank Wei Xie 1 Xiaojing

More information

Goal: Measure the pump curve(s)

Goal: Measure the pump curve(s) Pump Performance Tes;ng Goal: Measure te pump curve(s) Head versus flow rate: Efficiency versus flow rate: Maximum ead at = 0 Maximum flow rate at = 0 η η = 0 wen = 0 and = 0 Maximum efficiency Pump tes;ng

More information

Math GPS. 2. Art projects include structures made with straws this week.

Math GPS. 2. Art projects include structures made with straws this week. Number of Plants Mat GPS. List te measurements in order from greatest to least., inces,5 feet mile 75 yards Greatest. Art projects include structures made wit straws tis week. Number of Projects, p Total

More information

Revision Topic 12: Area and Volume Area of simple shapes

Revision Topic 12: Area and Volume Area of simple shapes Revision Topic : Area and Volume Area of simple sapes You need to learn ALL of te following area formulae: Rectangle Triangle W L b Area = lengt widt Area = base eigt = ½ b Parallelogram Trapezium a b

More information

青藜苑教育 Example : Find te area of te following trapezium. 7cm 4.5cm cm To find te area, you add te parallel sides 7

青藜苑教育 Example : Find te area of te following trapezium. 7cm 4.5cm cm To find te area, you add te parallel sides 7 青藜苑教育 www.tetopedu.com 00-6895997 3095457 Area of simple sapes Revision Topic : Area and Volume You need to learn ALL of te following area formulae: Rectangle Triangle W L Area = lengt widt Area = b base

More information

Numerical Simulation of Stresses in Thin-rimmed Spur Gears with Keyway B. Brůžek, E. Leidich

Numerical Simulation of Stresses in Thin-rimmed Spur Gears with Keyway B. Brůžek, E. Leidich Numerical Simulation of Stresses in Tin-rimmed Spur Gears wit Keyway B. Brůžek, E. Leidic Tis paper contains an investigation of te key on a stress distribution in a tin-rimmed spur gear. A stress analysis

More information

ANALYSIS OF WORK ROLL THERMAL BEHAVIOR FOR 1450MM HOT STRIP MILL WITH GENETIC ALGORITHM

ANALYSIS OF WORK ROLL THERMAL BEHAVIOR FOR 1450MM HOT STRIP MILL WITH GENETIC ALGORITHM Journal of Teoretical and Applied Information Tecnology 3 t September 2. Vol. 43 No.2 5-2 JATIT & LLS. All rigts reserved. ANALYSIS OF WORK ROLL THERMAL BEHAVIOR FOR 45MM HOT STRIP MILL WITH GENETIC ALGORITHM

More information

Calculation of Theoretical Torque and Displacement in an Internal Gear Pump

Calculation of Theoretical Torque and Displacement in an Internal Gear Pump TECHNICAL REPORT Calculation of Teoretical Torque and Displacement in an Internal Gear Pump Y. INAGUMA Tis paper describes numerical determination of teoretical torque (ideal torque) and teoretical stroke

More information

Fixation effects: do they exist in design problem solving?

Fixation effects: do they exist in design problem solving? Environment and Planning B: Planning and Design, 1993, volume 20, pages 333-345 Fixation effects: do tey exist in design problem solving? A T Purcell, P Williams, J S Gero, B Colbron Department of Arcitectural

More information

Volumes of Pyramids. Essential Question How can you find the volume of a pyramid?

Volumes of Pyramids. Essential Question How can you find the volume of a pyramid? 11.6 Volumes of Pyramids Essential Question How can you find te volume of a pyramid? Finding te Volume of a Pyramid Work wit a partner. Te pyramid and te prism ave te same eigt and te same square base.

More information

Applying Trigonometric Functions. ENTERTAINMENT The circus has arrived and the roustabouts must put

Applying Trigonometric Functions. ENTERTAINMENT The circus has arrived and the roustabouts must put 5-4 OJETIVE Use trigonometry to find te measures of te sides of rigt triangles. pplying Trigonometric Functions ENTERTINMENT Te circus as arrived and te roustabouts must put up te main tent in a field

More information

2 2D 2F. 1pc for each 20 m of wire. h (min. 45) h (min. 45) 3AC. see details J, E

2 2D 2F. 1pc for each 20 m of wire. h (min. 45) h (min. 45) 3AC. see details J, E TEXTILE AIR DIFFUSERS - - INSTRUCTIONS AIR FOR MOUNTING 1 1D 1F see details A, B, C 2 2D 2F see details A, B, C (min. 32) min. every 0 mm 1pc for eac 20 m of wire min. every 0 mm 1pc for eac 20 m of wire

More information

Point Pollution Sources Dimensioning

Point Pollution Sources Dimensioning Point Pollution Sources Diensioning Georgeta CUCULEANU 1 ABSTRACT In tis paper a etod for deterining te ain pysical caracteristics of te point pollution sources is presented. It can be used to find te

More information

Prediction of steel plate deformation due to triangle heating using the inherent strain method

Prediction of steel plate deformation due to triangle heating using the inherent strain method J Mar Sci Tecnol (005) 10:11 16 DOI 10.1007/s00773-005-00-5 Prediction of steel plate deformation due to triangle eating using te inerent strain metod Cang Doo Jang 1, Tae Hoon Kim, Dae Eun Ko 3, Tomas

More information

Analysing the energy consumption of air handling units by Hungarian and international methods

Analysing the energy consumption of air handling units by Hungarian and international methods Analysing te energy consumption of air andling units by Hungarian and international metods László Kajtár 1, Miklós Kassai 2,* 1,2 Budapest University of Tecnology and Economics (BUTE), Budapest, Hungary

More information

20.1 Heights and distances

20.1 Heights and distances 20 Heigts an istances INTROUTION In tis capter, we will learn te practical use of trigonometry in our ay-to-ay life. We will see ow trigonometry is use for fining te eigts an istances of various objects,

More information

Ground Improvement Using Preloading with Prefabricated Vertical Drains

Ground Improvement Using Preloading with Prefabricated Vertical Drains DISCUSSION of: Ground Improvement Using Preloading wit Prefabricated Vertical Drains Full Reference: Dar, A.S., Siddique, A., Ameen, S.F., (211). Ground Improvement using Pre-loading wit Prefabricated

More information

1/1 FULL SIZE 3/4 QUARTER SIZE 1/2 HALF SIZE EXTRA LARGE SIZE EXTRA LONG SIZE

1/1 FULL SIZE 3/4 QUARTER SIZE 1/2 HALF SIZE EXTRA LARGE SIZE EXTRA LONG SIZE STERILE CONTAINER SYSTEMS BIO-BARRIER 1/1 FULL SIZE 3/4 QUARTER SIZE 1/2 HALF SIZE EXTRA LARGE SIZE EXTRA LONG SIZE Aygün Bio-Barrier model sterilization container systems are designed wit mecanical valves

More information

4.2 Using Similar Shapes

4.2 Using Similar Shapes LESSON 4.2 Using Similar Sapes Proportionalit 7.5. Generalize te critical attributes of similarit, including ratios witin and between similar sapes. ESSENTIL QUESTION How can ou use similar sapes to find

More information

1/1 FULL SIZE 3/4 QUARTER SIZE 1/2 HALF SIZE EXTRA LARGE SIZE EXTRA LONG SIZE

1/1 FULL SIZE 3/4 QUARTER SIZE 1/2 HALF SIZE EXTRA LARGE SIZE EXTRA LONG SIZE BIO-BARRIER 1/1 FULL SIZE 3/4 QUARTER SIZE 1/2 HALF SIZE EXTRA LARGE SIZE EXTRA LONG SIZE Aygün Bio-Barrier model sterilization container systems are designed wit mecanical valves bot in bottom and lid

More information

Essential Question How can you find the surface area and the volume of a cone? 3 in. π

Essential Question How can you find the surface area and the volume of a cone? 3 in. π 11.7 Suface Aeas and Volumes of Cones Essential Question How can you find te suface aea and te volume of a cone? Finding te Suface Aea of a Cone Wok wit a patne. Constuct a cicle wit a adius of 3 inces.

More information

OD DVOSTRUKO ZASTAKLJENOG PROZORA DO DVOSTRUKE FASADE INDIKATORI PRENOSA TOPLOTE STACIONARNOG STANJA

OD DVOSTRUKO ZASTAKLJENOG PROZORA DO DVOSTRUKE FASADE INDIKATORI PRENOSA TOPLOTE STACIONARNOG STANJA OD DVOSTRUKO ZASTAKLJENOG PROZORA DO DVOSTRUKE FASADE INDIKATORI PRENOSA TOPLOTE STACIONARNOG STANJA FROM DOUBLE-GLAZED WINDOW TO DOUBLE-SKIN FACADE STEADY STATE HEAT TRANSFER INDICATORS Gabriel NĂSTASE

More information

Calculation Methodology of Translucent Construction Elements in Buildings and Other Structures

Calculation Methodology of Translucent Construction Elements in Buildings and Other Structures MATEC Web of Conferences 96, 005 (08) ttps://doi.org/0.05/matecconf/0896005 XXVII R-S-P Seminar 08, Teoretical Foundation of Civil Engineering Calculation Metodology of Translucent Construction Elements

More information

THE REDESIGNED CANADIAN MONTHLY WHOLESALE AND RETAIL TRADE SURVEY: A POSTMORTEM OF THE IMPLEMENTATION

THE REDESIGNED CANADIAN MONTHLY WHOLESALE AND RETAIL TRADE SURVEY: A POSTMORTEM OF THE IMPLEMENTATION ASA Section on Survey Researc Metods THE REDESIGNED CANADIAN MONTHLY WHOLESALE AND RETAIL TRADE SURVEY: A POSTMORTEM OF THE IMPLEMENTATION Julie Trépanier, Statistics Canada Julie Trépanier, Business Survey

More information

Reflections on the drinking bowl 'Balance'

Reflections on the drinking bowl 'Balance' Supplement to Fun wit oueold object and centre of ma, originally publied in te German journal Pyik in unerer Zeit, 9-96 eflection on te drinking bowl Balance I te bowl made of maive tainle teel? No: ma

More information

Bribery and Favoritism by Auctioneers in Sealed-Bid Auctions

Bribery and Favoritism by Auctioneers in Sealed-Bid Auctions Bribery an Favoritism by Auctioneers in Seale-Bi Auctions Roberto Burguet an Martin K. Perry Abstract We consier a moel of bribery in an asymmetric procurement auction. In return for a bribe from te isonest

More information

Geometry Supplement for Math 60 Perimeter, Area, and Volume

Geometry Supplement for Math 60 Perimeter, Area, and Volume Geomety Suppement fo Mat 60 Peimete, Aea, and Voume Geomety comes fom te Geek wods geo meaning eat and meton meaning measue. Today we wi ean about ow to measue cetain featues of two- and tee-dimensiona

More information

Influence of the mass flow ratio water-air on the volumetric mass transfer coefficient in a cooling tower

Influence of the mass flow ratio water-air on the volumetric mass transfer coefficient in a cooling tower International Journal of CemTec Researc CODEN (UA): IJCRGG, IN: 974-49, IN(Online):455-9555 Vol.11 No.1, pp 167-173, 18 Influence of te mass flow ratio water-air on te volumetric mass transfer coefficient

More information

Description of Danish Practices in Retail Trade Statistics.

Description of Danish Practices in Retail Trade Statistics. Description of Danis Practices in Retail Trade Statistics. 1. Statistical units and reporting units Units and population Te enterprises in te Retail Trade Index are all legal units. In te Central Business

More information

5.10. Area and Perimeter INSERT

5.10. Area and Perimeter INSERT 5.10 Aea and Peimete INSERT A Peimete We egin tis section y eviewing te definition of a polygon, and te definition of peimete. Definition A polygon is a closed geometic figue, wit at least tee sides, in

More information

Annex 16. Methodological Tool. Tool to determine project emissions from flaring gases containing methane

Annex 16. Methodological Tool. Tool to determine project emissions from flaring gases containing methane CDM Met Panel Twenty-fourt meeting Page 1 Metodological Tool Tool to determine project emissions from flaring es containing metane I. DEFINITIONS, SCOPE, APPLICABILITY AND PARAMETERS Definitions For te

More information

p x The revenue function is 5. What is the maximum vertical distance between the line

p x The revenue function is 5. What is the maximum vertical distance between the line SETION 4.7 OTIMIZTION ROLEMS 331 and Ris called te revenue function. Te derivative R of te revenue function is called te marginal revenue function and is te rate of cange of revenue wit respect to te numer

More information

Installation the DELTABEAM Frame

Installation the DELTABEAM Frame Tese installation instructions are intended to be used togeter wit te project s erection metod statement were te instructions may be complemented. If tere are differences between te erection metod statement

More information

We Protect Your Yarn Like No One Else

We Protect Your Yarn Like No One Else FOR FURTHER INFORMATION VISIT WWW.SPINCAN.NET We Protect Your Yarn Like No One Else SPINCAN MANUFACTURING COMPANY REGD OFFICE Sakespeare Sarani, Century Towers, Room no. 501 Kolkata 700 017, India PHONE

More information

Ice Cream. Ice Cream. 1 of 9. Copyright 2007, Exemplars, Inc. All rights reserved.

Ice Cream. Ice Cream. 1 of 9. Copyright 2007, Exemplars, Inc. All rights reserved. Pat loves ice cream. He went to the store to buy an ice cream cone. They had strawberry, vanilla and chocolate ice cream. He could have a sugar cone or a plain cone. How many different ways could Pat have

More information

Russell James Department of Scientific and Industrial Research Taupo-ldairakei, New Zealand

Russell James Department of Scientific and Industrial Research Taupo-ldairakei, New Zealand MEASUREMENT OF STEAM-TJATER FLOWS FOR THE TOTAL FLOW TURBIlJE Russell James Department of Scientific and Industrial Researc Taupo-ldairakei, New Zealand Hot water geotermal fields discarge steam-water

More information

10 Fingers of Death: Algorithms for Combat Killing Roger Smith and Don Stoner Titan Corporation

10 Fingers of Death: Algorithms for Combat Killing Roger Smith and Don Stoner Titan Corporation 10 Fingers of Deat: Algoritms for Combat Killing Roger Smit and Don Stoner Titan Cororation Good sooting games need good killing algoritms. Tis gem rovides a series of combat algoritms tat can be used

More information

László Mester. The new physical-mechanical theory of granular materials

László Mester. The new physical-mechanical theory of granular materials László Mester Te new pysical-mecanical teory of granular materials 9 - - Contents Introduction 3 Granular material as a distinct state of matter 4 Pysical properties of te granular material in relation

More information

Using tree-grammars for training set expansion in page classification

Using tree-grammars for training set expansion in page classification Using tree-grammars for training set expansion in page classification Stefano Baldi Simone Marinai Gioanni Soda DSI - Uniersity of Florence - Italy Email: marinai@dsi.unifi.it Abstract In tis paper we

More information

MAMA SID'S PIZZA by Faith Goddard-Allen

MAMA SID'S PIZZA by Faith Goddard-Allen MAMA SID'S PIZZA by Faith Goddard-Allen The problem states: Every Friday night my friends and I go to Mama Sid's for dinner. If we want to order a different pizza every Friday for a whole year, how many

More information

International Plant Protection Convention Page 1 of 10

International Plant Protection Convention Page 1 of 10 International Plant Protection Convention Draft ISPM: Revision to Annex 1 and Annex 2 to ISPM 15 (Regulation of wood packaging material in international trade) 2006-010A&B [1]Draft revision of Annex 1

More information

10. Consider the following problem: A box with an open top is to. 11. A farmer wants to fence an area of 1.5 million square feet in a

10. Consider the following problem: A box with an open top is to. 11. A farmer wants to fence an area of 1.5 million square feet in a 8 HTER 4 LITIONS OF DIFFERENTITION 4.7 EXERISES 1. onsider te following prolem: Find two numers wose sum is and wose product is a maximum. (a) Make a tale of values, like te following one, so tat te sum

More information

CO-ROTATING FULLY INTERMESHING TWIN-SCREW COMPOUNDING: ADVANCEMENTS FOR IMPROVED PERFORMANCE AND PRODUCTIVITY

CO-ROTATING FULLY INTERMESHING TWIN-SCREW COMPOUNDING: ADVANCEMENTS FOR IMPROVED PERFORMANCE AND PRODUCTIVITY CO-ROTATING FULLY INTERMESHING TWIN-SCREW COMPOUNDING: ADVANCEMENTS FOR IMPROVED PERFORMANCE AND PRODUCTIVITY Paul G. Andersen, Coperion Corporation, Ramsey, NJ Frank Lecner, Coperion GmbH, Stuttgart,

More information

Background. Sample design

Background. Sample design Background Te National Statistics Centre (NSC) of te Lao Peoples Democratic Republic as conducted tree expenditure and consumption surveys in te last decade. Te first Lao Expenditure and Consumption Survey

More information

The household budget and expenditure data collection module (IOF 2014/2015) within a continuous multipurpose survey system (INCAF)

The household budget and expenditure data collection module (IOF 2014/2015) within a continuous multipurpose survey system (INCAF) MZ:2014:08 Te ouseold budget and expenditure data collection module (IOF 2014/2015) witin a continuous multipurpose survey system (INCAF) Report from a fift sort term mission to te National Statistical

More information

Study of Steam Export Transients in a Combined Cycle Power Plant

Study of Steam Export Transients in a Combined Cycle Power Plant Study of Steam Export Transients in a Combined Cycle ower lant Alfonso Junquera Delgado Departamento Mecánico, Empresarios Agrupados c\ Magallanes 3 Madrid 8003 ajd@empre.es Almudena Travesí de los Santos

More information

2. The differential pressure across control valves must not vary too much

2. The differential pressure across control valves must not vary too much 2. Te differential pressre across control valves mst not vary too mc Common roblems roblems, typical indicating tat condition nmber two is not met: - Continos oscillation of room temperatre. - Room temperatres

More information

Farm Structure Survey 2009/2010 Survey on agricultural production methods 2009/2010

Farm Structure Survey 2009/2010 Survey on agricultural production methods 2009/2010 Farm Structure Survey 2009/2010 Survey on agricultural production metods 2009/2010 National Metodological Report (NMR) According to Art. 12 of Regulation (EC) No 1166/2008 of te European Parliament and

More information

Study of microrelief influence on optical output coefficient of GaN-based LED

Study of microrelief influence on optical output coefficient of GaN-based LED Study of microrelief influence on optical output coefficient of GaN-based LED Danilina T.I., Cistoyedova I.A. and Popov A.A. Tomsk State University of Control Systems and Radioelectronics, Lenina prospect

More information

OXYGEN CONTENT OF COMMERCIAL FROZEN ORANGE

OXYGEN CONTENT OF COMMERCIAL FROZEN ORANGE HGGART: OXYGEN CONTENT OXYGEN CONTENT OF COMMERCIAL FROZEN ORANGE CONCENTRATE R. L. HGGART Florida Citrus Commission Lake Alfred Incorporation air into citrus products du ring processing exposes tem to

More information

HCR OF HEAT PUMP ROOM AIR CONDITIONER IN CHINA. Beijing , China

HCR OF HEAT PUMP ROOM AIR CONDITIONER IN CHINA. Beijing , China OF HEA PUMP ROOM AIR CONDIIONER IN CHINA Baolong Wang 1, Wenxing Si 1, uan Cen 1 1 Department of Building Sciencesingua University, Beijing 100084, Cina ABSRAC Definition of eating/cooling capacity ratio

More information

Questions. denotes answer available in Student Solutions Manual/Study Guide; O denotes objective question

Questions. denotes answer available in Student Solutions Manual/Study Guide; O denotes objective question Questions 407 Questions denotes answer available in Student Solutions Manual/Study Guide; O denotes objective question 1. O Figure Q14.1 sows aerial views from directly above two dams. Bot dams are equally

More information

Is urban food demand in the Philippines different from China?

Is urban food demand in the Philippines different from China? Singapore Management University Institutional Knowledge at Singapore Management University Researc Collection Scool Of Economics Scool of Economics 0-04 Is urban food demand in te Pilippines different

More information

Structures of Life. Investigation 1: Origin of Seeds. Big Question: 3 rd Science Notebook. Name:

Structures of Life. Investigation 1: Origin of Seeds. Big Question: 3 rd Science Notebook. Name: 3 rd Science Notebook Structures of Life Investigation 1: Origin of Seeds Name: Big Question: What are the properties of seeds and how does water affect them? 1 Alignment with New York State Science Standards

More information

Managing Measurement Uncertainty in Building Acoustics

Managing Measurement Uncertainty in Building Acoustics Buildings 2015, 5, 1389-1413; doi: 10.3390/buildings5041389 Article OPEN ACCESS buildings ISSN 2075-5309 www.mdpi.com/journal/buildings/ Managing Measurement Uncertainty in Building Acoustics Ciara Scrosati

More information

Variance Estimation of the Design Effect

Variance Estimation of the Design Effect JSM 013 - Survey Researc Metods Section Variance Estimation of te Design Effect Alberto Padilla Banco de México Abstract Sample size determination is a crucial part of te planning process of a survey and

More information

h h h h h h Corporate Retreats Conferences Training Events Reunions Social Gatherings Getaways

h h h h h h Corporate Retreats Conferences Training Events Reunions Social Gatherings Getaways events Te Inn at Oio Nortern University At Te Inn our friendly and elpful staff follows te igest standards of ospitality, striving to reac a single goal for delivering outstanding, igly personalized service

More information

Do Regional Trade Pacts Benefit the Poor?

Do Regional Trade Pacts Benefit the Poor? Public Disclosure Autorized Public Disclosure Autorized Public Disclosure Autorized Public Disclosure Autorized Do Regional Trade Pacts Benefit te Poor? An Illustration from te Dominican Republic-Central

More information

TEMPERATURE CONDITIONS AND TOLERANCE OF AVOCADO FRUIT TISSUE

TEMPERATURE CONDITIONS AND TOLERANCE OF AVOCADO FRUIT TISSUE California Avocado Society 1961 Yearbook 45: 87-92 TEMPERATURE CONDITIONS AND TOLERANCE OF AVOCADO FRUIT TISSUE C. A. Schroeder and Ernest Kay Professor of Botany. University of California, Los Angeles;

More information

Unit 2, Lesson 15: Part-Part-Whole Ratios

Unit 2, Lesson 15: Part-Part-Whole Ratios Unit 2, Lesson 15: Part-Part-Whole Ratios Let s look at situations where you can add the quantities in a ratio together. 15.1: True or False: Multiplying by a Unit Fraction True or false? 15.2: Cubes of

More information

EXTERNAL SHOCKS AND POVERTY: HOW RECESSION IN EUROPE, JAPAN, AND CHINA AFFECTS THE INDONESIAN POOR

EXTERNAL SHOCKS AND POVERTY: HOW RECESSION IN EUROPE, JAPAN, AND CHINA AFFECTS THE INDONESIAN POOR External Socks And Poverty: How Recession In Europe, Japan, and Cina Affects Te Indonesian Poor 207 EXTERNAL SHOCKS AND POVERTY: HOW RECESSION IN EUROPE, JAPAN, AND CHINA AFFECTS THE INDONESIAN POOR Arief

More information

Effect of Twisted-tape Inserts on Heat Transfer in a Tube

Effect of Twisted-tape Inserts on Heat Transfer in a Tube Effect of Twisted-tae Inserts on Heat Transfer in a Tube Watcarin Nootong, Smit Eiamsa-ard and Pongjet Promvonge, * Deartment of Mecanical Engineering, Faculty of Engineering, King Mongkut s Institute

More information

Investigation 1: Ratios and Proportions and Investigation 2: Comparing and Scaling Rates

Investigation 1: Ratios and Proportions and Investigation 2: Comparing and Scaling Rates Comparing and Scaling: Ratios, Rates, Percents & Proportions Name: Per: Investigation 1: Ratios and Proportions and Investigation 2: Comparing and Scaling Rates Standards: 7.RP.1: Compute unit rates associated

More information

Bribery and Favoritism by Auctioneers in Sealed-Bid Auctions

Bribery and Favoritism by Auctioneers in Sealed-Bid Auctions Bribery an Favoritism by Auctioneers in Seale-Bi Auctions Roberto Burguet Institute for Economic Analysis (CSIC) an CREA Campus UAB Bellaterra, Barcelona, Spain 08193 Martin K. Perry * Department of Economics

More information

Total surface area: the area of the lateral faces combined with the area of both bases

Total surface area: the area of the lateral faces combined with the area of both bases Capte 9: Measuement and te Metic System Section 9.: Volume and Suface Aea Total Suface Aea of a Cylinde and a Pism Lateal aea: te aea of te egions bounded by te lateal faces of a pism Total suface aea:

More information

Structural Changes in Household Income Inequality in Korea: A New Decomposition Including Labor Supply Changes * Chulhee Lee

Structural Changes in Household Income Inequality in Korea: A New Decomposition Including Labor Supply Changes * Chulhee Lee Structural Cange in Houeold Income Inequality in Korea: A New Decompoition Including Labor Supply Cange Culee Lee Scool of Economic Seoul National Univerity San 56-1, Sillim-dong, Kwanak-gu Seoul, Korea

More information

APPENDIX C2: Design of Canard Aircraft

APPENDIX C2: Design of Canard Aircraft APPENDIX 2: Design of anard Aircraft Tis appendix is a part of te book General Aviation Aircraft Design: Applied Metods and Procedures by norri Gudundsson, publised by Elsevier, Inc. Te book is available

More information

Gas Flow into Rotary Valve Intake and Exhaust Mechanism in Internal Combustion Engine

Gas Flow into Rotary Valve Intake and Exhaust Mechanism in Internal Combustion Engine World Academy of Science, Engineering and Tecnology Vol:7, No:4, 13 Gas Flow into Rotary Valve Intake and Exaust Mecanism in Internal Combustion Engine R. Usubamatov, Z. A. Rasid International Science

More information

The Violin Bow: Taper, Camber and Flexibility

The Violin Bow: Taper, Camber and Flexibility Te Violin Bow: Taper, Camber and lexibility Colin Goug Scool of Pysics and Astronomy, University of Birmingam, B13 9SN,UK a) (Dated: 11/22/1) An analytic, small-deflection, simplified model of te modern

More information

A FIRST ANALYSIS OF THE FLOOD EVENTS OF AUGUST 2002 IN LOWER AUSTRIA BY USING A HYDRODYNAMIC MODEL

A FIRST ANALYSIS OF THE FLOOD EVENTS OF AUGUST 2002 IN LOWER AUSTRIA BY USING A HYDRODYNAMIC MODEL A FIRS ANALYSIS OF HE FLOOD EVENS OF AGS 00 IN LOWER ASRIA BY SING A HYDRODYNAMIC MODEL MICHAEL RIHAR, PEER MILBRAD Institute of Hdraulics, Hdrolog and Water Resources Management Vienna niversit of ecnolog

More information

Feeling Hungry. How many cookies were on the plate before anyone started feeling hungry? Feeling Hungry. 1 of 10

Feeling Hungry. How many cookies were on the plate before anyone started feeling hungry? Feeling Hungry. 1 of 10 One afternoon Mr. and Mrs. Baxter and their 3 children were busy working outside in their garden. Mrs. Baxter was feeling hungry, so she went inside to the kitchen where there was a plate full of cookies.

More information

All-Day Menu. Served daily from 12 midday til 9pm. Please also see our blackboard for any last minute additions to our current Specials

All-Day Menu. Served daily from 12 midday til 9pm. Please also see our blackboard for any last minute additions to our current Specials ll-day Menu Served daily from 12 midday til 9pm Please also see our blacboard for any last minute additions to our current Specials Disclaimer: Daily Special items are produced in limited quantities made

More information

THE ANNALS OF "DUNAREA DE JOS" UNIVERSITY OF GALATI FASCICLE III, 2003 ISSN X ELECTROTECHNICS, ELECTRONICS, AUTOMATIC CONTROL, INFORMATICS

THE ANNALS OF DUNAREA DE JOS UNIVERSITY OF GALATI FASCICLE III, 2003 ISSN X ELECTROTECHNICS, ELECTRONICS, AUTOMATIC CONTROL, INFORMATICS FASCICLE III, 003 ISSN -454X ELECTROTECHNICS, ELECTRONICS, AUTOMATIC CONTROL, INFORMATICS A NEW METHOD OF GENE CODING FOR A GENETIC ALGORITHM DESIGNED FOR PARAMETRIC OPTIMIZATION Rau Belea * an Liviu Beliman

More information

Section 2.3 Fibonacci Numbers and the Golden Mean

Section 2.3 Fibonacci Numbers and the Golden Mean Section 2.3 Fibonacci Numbers and the Golden Mean Goals Study the Fibonacci Sequence Recursive sequences Fibonacci number occurrences in nature Geometric recursion The golden ratio 2.3 Initial Problem

More information

All-Day Menu. Served daily from 12 midday til 9pm. Please also see our blackboard for any last minute additions to our current Specials

All-Day Menu. Served daily from 12 midday til 9pm. Please also see our blackboard for any last minute additions to our current Specials ll-day Menu Served daily from 12 midday til 9pm Please also see our blacboard for any last minute additions to our current Specials Disclaimer: Daily Special items are produced in limited quantities made

More information

MasterTop BC 309. A two component, clear, non-solvented (total solid), epoxy binder

MasterTop BC 309. A two component, clear, non-solvented (total solid), epoxy binder PRODUCT DESCRIPTION is a non-solvente, low viscous, clear an flui two-component epoxy resin. FIELDS OF APPLICATION is formulate to be use inoors for applications in inustrial an ecorative areas. MasterTop

More information

An application of cumulative prospect theory to travel time variability

An application of cumulative prospect theory to travel time variability Katrine Hjorth (DTU) Stefan Flügel, Farideh Ramjerdi (TØI) An application of cumulative prospect theory to travel time variability Sixth workshop on discrete choice models at EPFL August 19-21, 2010 Page

More information

Every second of your day is

Every second of your day is WEDDINGS THE START of YOUR DAY Every second of your day is precious from te moment you arrive to your final farewells. So it goes witout saying tat te setting you coose must be perfect. In te eart of te

More information

Prepare and serve wines. unit 614

Prepare and serve wines. unit 614 unit 614 Prepare and serve wines There s a lot more to serving wine than simply taking the cork out of the bottle and filling up the glass. This unit will help guide you through what you need to know and

More information

Characteristics and dead-time of GM-tube

Characteristics and dead-time of GM-tube Caracteristics ad dead-time of GM-tube GM-tubes are te most popular gas ioizatio detectors for te measuremet of - ad -radiatio. Gas ioizatio detectors ave tree types: ioizatio cambers, proportioal couters

More information

Lesson 41: Designing a very wide-angle lens

Lesson 41: Designing a very wide-angle lens Lesson 41: Designing a very wide-angle lens We are often asked about designing a wide-angle lens with DSEARCH. If you enter a wide-angle object specification in the SYSTEM section of the DSEARCH file,

More information

UNIT TITLE: PROVIDE GUERIDON SERVICE NOMINAL HOURS: 25

UNIT TITLE: PROVIDE GUERIDON SERVICE NOMINAL HOURS: 25 UNIT TITLE: PROVIDE GUERIDON SERVICE NOMINAL HOURS: 25 UNIT NUMBER: D1.HBS.CL5.11 UNIT DESCRIPTOR: This unit deals with skills and knowledge required to promote, prepare for and provide gueridon service

More information

Pevzner P., Tesler G. PNAS 2003;100: Copyright 2003, The National Academy of Sciences

Pevzner P., Tesler G. PNAS 2003;100: Copyright 2003, The National Academy of Sciences Two different most parsimonious scenarios that transform the order of the 11 synteny blocks on the mouse X chromosome into the order on the human X chromosome Pevzner P., Tesler G. PNAS 2003;100:7672-7677

More information

Chapter 1: The Ricardo Model

Chapter 1: The Ricardo Model Chapter 1: The Ricardo Model The main question of the Ricardo model is why should countries trade? There are some countries that are better in producing a lot of goods compared to other countries. Imagine

More information

Rail Haverhill Viability Study

Rail Haverhill Viability Study Rail Haverhill Viability Study The Greater Cambridge City Deal commissioned and recently published a Cambridge to Haverhill Corridor viability report. http://www4.cambridgeshire.gov.uk/citydeal/info/2/transport/1/transport_consultations/8

More information

Gail E. Potter, Timo Smieszek, and Kerstin Sailer. April 24, 2015

Gail E. Potter, Timo Smieszek, and Kerstin Sailer. April 24, 2015 Supplementary Material to Modelling workplace contact networks: the effects of organizational structure, architecture, and reporting errors on epidemic predictions, published in Network Science Gail E.

More information

CARCINOMA OF THE ESOPHAGUS*

CARCINOMA OF THE ESOPHAGUS* Reprint from Nortwest Medicine, Seattle, Vol. XXVIII, No. I, Page 25, January, 1929 CARCINOMA OF THE ESOPHAGUS* J. EARL ELSE, M.D. PORTLAND, ORE. Clinical Professor and Cairman, Department of General Surgery,

More information

FABRICATION AND TESTING OF A HIGH-TEMPERATURE PRINTED CIRCUIT HEAT EXCHANGER

FABRICATION AND TESTING OF A HIGH-TEMPERATURE PRINTED CIRCUIT HEAT EXCHANGER FABRICATION AND TESTING OF A HIGH-TEMPERATURE PRINTED CIRCUIT HEAT EXCHANGER Mingui Cen, Xiaodong Sun *, Ricard N. Cristensen Te Oio State University 201 W 19 t Ave, Columbus, OH 43210 cen.3370@osu.edu,

More information

Subject to sale, withdrawal or error. Published on 09/19/16

Subject to sale, withdrawal or error. Published on 09/19/16 SHOE BAR RANCH ECTOR COUNTY, TEXAS 25,572.35 Acres, More or Less We are proud to ave obtained an exclusive listing on one of te best Permian Basin rances to be offered for sale in sometime, te Soe Bar

More information

Sources and Propagation of International Cycles: Common. Shocks or Transmission? Universitat Pompeu Fabra. This revision: November, 1996.

Sources and Propagation of International Cycles: Common. Shocks or Transmission? Universitat Pompeu Fabra. This revision: November, 1996. Sources and Propagation of International Cycles: Common Socks or Transmission? Fabio Canova Universitat Pompeu Fabra; Universita' di Modena; and CEPR 3 Jane Marrinan Universitat Pompeu Fabra Tis revision:

More information

Conjoint Analysis: A Study of Canned Coffee in Taiwan

Conjoint Analysis: A Study of Canned Coffee in Taiwan 238 ICSNS International ournal of Computer Science and Network Security, VOL.8 No.8, August 2008 Conoint Analysis: A Study of Canned Coffee in aiwan Meng-Long Si 1, Cen-Yin Liu 2, Biing-Wen Huang 3, Souua

More information