Construction Actuarial Model for Aggregate Loss. under Exponentiated Inverted Weibull. Distribution

Size: px
Start display at page:

Download "Construction Actuarial Model for Aggregate Loss. under Exponentiated Inverted Weibull. Distribution"

Transcription

1 Applied Matheatical Sciences, Vol. 8, 4, no. 6, HIKARI td, Constuction Actuaial Model fo Aggegate oss unde Eponentiated Inveted Weibull Distibution Osaa Hanafy Mahoud Depatent of Matheatics, Statistics and Insuance Sadat Acadey fo Manageent Sciences, Egypt Copyight 4 Osaa Hanafy Mahoud. This is an open access aticle distibuted unde the Ceative Coons Attibution icense, which peits unesticted use, distibution, and epoduction in any ediu, povided the oiginal wok is popely cited. Abstact The poble of planning einsuance policies in popety and causality insuance copanies and how to estiate the loss eseve play an ipotant ole fo the esults of the insuance copany. Also, they have past o pesent data fo nube of clais and its aounts which want to use in pediction futue clai fequency and clai seveity. Many statistical distibution ae fitting to find an appopiate distibution to epesent ou data. In this pape, we intoduce a statistical distibution known as Eponentiated Inveted Weibull (EIW distibution to epesent the clai aount and its chaacteistics fo applying it in actuaial studies. Second, we test the tail weight of the distibution and aiu likelihood estiation fo its paaetes. we pesent ou aggegate loss odel unde collective isk theoy when the clai fequency distibution is Poisson o egative Binoial distibution. Also, we pesent how to calculate the einsuance pue peiu in case of stop loss einsuance. Finally, The siulation nueical eaple is given to epesent ou esults. Keywods: Eponentiated Inveted Weibull Distibution, Tail Weight of Distibution, Maiu ikelihood Estiation, Aggegate oss Model

2 886 Osaa Hanafy Mahoud. Intoduction Insuance copanies need to investigate clais epeience and apply atheatical techniques fo any puposes such as ateaking, eseving, einsuance aangeents and solvency. Many papes have been pesented to aggegate losses as: Heckan and Meyes (983 discussed aggegate loss distibutions fo the pespective of collective isk theoy fo seveity and count distibutions. They include eaples fo calculating the pue peiu fo a policy with an aggegate liit, calculating the pue peiu of an aggegate stop-loss policy fo goup life insuance; and calculating the insuance chage fo a ulti-line etospective ating plan, including a line which is itself subject to an aggegate liit. Vente (983, Distibution functions ae intoduced based on powe tansfoations of beta and gaa distibutions, and popeties of these distibutions ae discussed. The gaa, beta, F, Paeto, Bu, Weibull and loglogistic distibutions ae special cases. The tansfoed gaa is used to odel aggegate distibutions by atching oents. The tansfoed beta is used to account fo paaete uncetainty in this odel. Robetson (99, Povided an application of the fast Fouie tansfo to the coputation of aggegate loss distibutions fo abitay fequency and seveity distibutions. Papush el al (, addessed the question what type of oal, ognoal and Gaa distibutions is the ost appopiate to use to appoiate aggegate loss distibution. Vila et al. (8, descibed a nonpaaetic appoach to ake infeence fo aggegate loss odels in the insuance faewok by assuing that an insuance copany povides a histoical saple of clais given by clai occuence ties and clai sizes. Botoluzzo et al. (9, aied estiating clai size in the auto insuance by using zeo adjusted Invese Gaussian distibution. Shevchenko ( eviewed nueical algoiths that can be successfully used to calculate the aggegate loss distibutions. In paticula Monte Calo, Panje ecusion and Fouie tansfoation ethods ae pesented and copaed. Also, seveal closed-fo appoiations based on oent atching and asyptotic esult fo heavy-tailed distibutions ae eviewed. One of the ost significant goals of any insuance isk activity is to achieve a satisfactoy odel fo the pobability distibution of the total clai aount. In this pape, we intoduce a statistical distibution known as Eponentiated Inveted Weibull (EIW distibution to epesent the clai aount and its chaacteistics fo applying it in actuaial studies. This pape is oganized as follows: Section we pesentsthe Model clai seveity unde Eponentiated Inveted Weibull Distibution and test the tail weight

3 Constuction actuaial odel fo aggegate loss 887 of a distibution. In Section 3 we discuss the poble of estiating the paaetes of distibution by using aiu likelihood ethod. Section 4 we pesent ou aggegate loss odel unde collective isk theoy when the clai fequency distibution is Poisson o egative Binoial distibution. Section 5, how to calculate the einsuance pue peiu in case of stop loss einsuance. Finally, The siulation nueical eaple is given to epesent ou esults.. The Model unde Eponentiated Inveted Weibull Distibution Recently any studies in pobability distibutions and its applications pesented the Eponentiated Inveted Weibull distibution as: Flaih et al (, Consideed the standad eponentiated inveted weibull distibution (EIW that genealizes the standad inveted weibull distibution (IW, the new distibution has two shape paaetes. The oents, edian, suvival function, hazad function, aiu likelihood estiatos, least-squaes estiatos, fishe infoation ati and asyptotic confidence intevals have been discussed. A eal data set is analyzed and it is obseved that the (EIW distibution can povide a bette fitting than (IW distibution. Aljouhaah Aljuaid, (3, pesented Bayes and classical estiatos have been obtained fo two paaetes eponentiated inveted Weibull distibution when saple is available fo coplete and type II censoing schee. Hassan (3, dealt with the optial designing of failue step- stess patially acceleated life tests with two stess levels unde type-i censoing. The lifetie of the test ites is assued to follow eponentiated inveted Weibull distibution. Hassan et al. (4, pesented estiation of population paaetes fo the eponentiated inveted Weibull distibution based on gouped data with equi and unequi-spaced gouping. Seveal altenative estiation schees, such as, the ethod of aiu likelihood, least squaes, iniu chi-squae, and odified iniu chi-squae ae consideed. If ou clais aount of insuance potfolio,, 3,, follow the n Eponentiated Inveted Weibull (EIW distibution with paaetes and in the following fo fo the pobability density function (pdf: f ( ( e (,, ( Theefoe, its cuulative pobability function (cpf can be witten in the fo: F( ( e,, ( The (ight- tail of a distibution is the potion of the distibution coesponding to

4 888 Osaa Hanafy Mahoud lage values of the ando vaiable. A distibution is said to be a heavy-tailed distibution if it significantly puts oe pobability on lage values of the ando vaiable. We also say that the distibution has a lage tail weight. In contast, a distibution that puts less and less pobability fo lage values of the ando vaiable is said to be light-tailed distibution. To test the tail weight of a distibution, we can use the Eistence of Moents ethod as follows: A distibution f ( is said to be light-tailed if E ( fo all and the distibution f ( is said to be heavy-tailed if eithe does not eist fo all o the oents eist only up to a cetain value of a positive intege, Finan (4. The th oents of the eponentiated inveted weibull distibution is given as follows: ( ( e d,, This can be witten as: (,, (3 Poof: The pdf of the EIW distibution is: f ( ( e (,, The th oents function can be witten in the fo: f ( d ( e ( d By taking tansfoation H We can wite the th oents function as: ( H H H H e By siplification of the above equation,we can get H e H dh dh This integal known as gaa function, theefoe the th oents function is:

5 Constuction actuaial odel fo aggegate loss 889 Fo the above equation, we can find to obtain the th oent ust the value of geate than to be eist. Since the oents ae not finite fo all positive ; the eponentiated inveted weibull distibution is heavy-tailed. Fo the above equation, we can find the ean and the vaiance of EIW distibution as follows: By putting = (4 (,, And the second oent by putting = in the fo: (,, (5 Thus the vaiance is: V( ( ( ( 3. Maiu ikelihood Estiation (ME fo paaetes Suppose that we have postulated a pobability odel, such as the Eponented Inveted Weibull distibution, to descibe a given loss aount distibution. The net step in ou pocedue should be to estiate values fo the paaetes of the odel. We use the aiu likelihood ethod (ME fo estiating the unknown paaetes and of Eponented Inveted Weibull distibution, as follows:- (, f ( i i Then the likelihood function is as follows, (, i ( e ( e ( i ( i i ( ( i i by taking the natual logaith fo the likelihood function, we get (6

6 89 Osaa Hanafy Mahoud i i ( ln i i ln (, ln ln (7 So, we need to estiate the two paaetes and. The fist deivatives fo the natual logaith of the likelihood function with espect to and, ae given by ln (, i (8 i ln (, ( i ln i ln (9 i i The aiu likelihood estiatos of and could be obtained by equating the equations (8 and (9 by zeo, and solving the siultaneously using an iteative technique. We obtain the appoiate vaiance covaiance ati by eplacing epected values by thei aiu likelihood estiatos and inveting the Fishe infoation ati, defined by: ln I ln ln ln Whee, the second deivatives of the natual logaith of likelihood function defined in equation (6 ae given as follows: i ln (, ( ln (, ( i ln i ( ln (, i i ( i (ln i The ME ˆ and ˆ have an asyptotic vaiance covaiance ati obtained by inveting the Fishe infoation ati. 4. Aggegate loss odel unde collective Risk Theoy Suppose that potfolio has clais in the past peiod of tie in ou epeience and each unit has i is the clai size which is independent identical distibuted (

7 Constuction actuaial odel fo aggegate loss 89 eponented inveted Weibull with paaetes and its p.d.f in the equation ( and cuulative pobability function in the equation (. Then the aggegate losses is S whee the su of clai aounts as: S 3 Suppose also that the individual loss aounts i ae independent on the annual loss fequency. Then it follows that: The pobability density function (pdf of aggegate losses is k * k f ( S p( k f ( s (3 s * Whee f k ( s is called the k th fold convolution of 3 the k th fold convolutions ae often eteely difficult to copute in pactice and theefoe one encountes difficulties dealing with the pobability distibution of S: An altenative appoach is to use vaious appoiation techniques. We conside a technique known as the Panje ecusive foula. The ean and vaiance of aggegate loss distibution can get as: s V ( s V ( V ( (4 The picing poble usually educes to finding oent of S. A coon picing foula is pice s k v( s Whee the pice is the epected payout plus a isk loading which k ties the vaiance of the payout fo soe k. The epected payout E (s is also known as the pue peiu and it can be shown to be E (. Estiation the Mean and the Vaiance of Aggegate losses Distibution: We will conside Poisson and egative Binoial distibutions fo the fequency distibution of losses as follows: I. Poisson Distibution Suppose that the annual fequency of losses fo a potfolio follows a Poisson distibution with paaete. In this case the ean of the loss distibution is:

8 89 Osaa Hanafy Mahoud E ( s ( (5 V ( s ( (6 II. egative Binoial Distibution Suppose that the annual fequency of losses fo a potfolio follows a egative Binoial distibution with paaetes and p. In this case the ean of the loss distibution is: p E ( s ( (7 p p p V ( s ( ( p (8 p 5. Stop oss Reinsuance Gauge and Hosking (8 and Finan (4 pesented the stop loss einsuance as: When a deductible D is applied to the aggegate loss S ove a definite peiod, then the insuance payent will be, S D S D MaS D, S S^ D S D, S D the einsue will pay the insue an aount equal to S D. The insue's etained loss is thus S^ D. The ain poble is how to calculate the einsuance pue peiu?. the einsuance pue peiu is payent as the stop-loss e insuance. Its epected cost is called the net stop-loss peiu and can be coputed as: E S D F ( d d f ( d (9 6. ueical Results D S S D In this section, we will pesent a nueical investigation of the aiu likelihood estiation fo the paaetes of and. We need to estiate the two paaetes and by using the aiu likelihood ethod. So, we will need to solve the thee non-linea equations of

9 Constuction actuaial odel fo aggegate loss 893 logaith likelihood function (8 and (9 siultaneously using ewton-raphson ethod.the iteative technique, can be applied as follows: A C whee and ln ln ln ln C Assuing initial values fo each of and, the ewton-raphson iteative pocedue is continued until eithe the nube of iteations will be ( o when X X+ < 5-5. In the following table, the estiates of unknown paaetes, the elative bias which is the absolute diffeence between the estiated paaete and its tue value divided by its tue value. - ˆ Bais Re ltive And the ean squae eo (MSE which is the ean squae of the diffeence between the estiated paaete ae pesented fo all the estiated paaetes consideing diffeent initial points of the paaetes. ˆ M SE whee is the nube of epeients cay out. A ln ln, ˆ ˆ, ˆ ˆ

10 894 Osaa Hanafy Mahoud Table ( Estiatos fo paaetes of EIW distibution, Relative Bias and MSE Paaetes Estiato Relative Bias MSE Table (, shows The Estiatos of the paaetes and of the odel, Relative Bias, and MSE. We can notice that the absolute value of the diffeence between the tue value of the paaete and its estiato is sall value conveges to zeo, so these estiatos ae said to be consistent estiatos. Estiate the ean and the vaiance of EIW distibution By substituting the estiated values of the paaetes ˆ and ˆ in equations (4 and (5, we can get the ean and the vaiance of EIW distibution as shown in Table (: Table ( The estiated ean and vaiance of EIW distibution ˆ ˆ E ( E ( V (

11 Constuction actuaial odel fo aggegate loss 895 Fo Table (, we can notice thee is diect elationship between the value of ˆ and the value of the ean and the vaiance of distibution. Also, thee is invese elationship between the value of ˆ and the value of the ean and the vaiance of distibution. Estiation the ean and the vaiance of Aggegate losses distibution: When the annual fequency of losses fo a potfolio follows a Poisson distibution with paaete 8 by substituting in equations (5 and (6, o the egative Binoial distibution with paaetes and p. 6 by substituting in equations (7 and (8 in table (3 as follows: Table (3 Estiation the ean and the vaiance of Aggegate losses distibution ˆ ˆ Poisson distibution egative Binoial distibution E (s V (s E (s V (s Concluding eaks: In this study, we addess the eponentaited inveted weubil distibution issue and its epiical application of aggegate losses. By testing the tail of the EIW distibution, we find it has heavy tail. The aiu likelihood ethod was applied fo estiating the paaetes of distibution. Unde collective isk odel, we estiate the ean and the vaiance of the aggegate losses distibution whee the fequency distibution fo clai counts is Poisson o egative Binoial. If we identify the aggegate losses distibution, we can depend on it to ateaking, aangeent fo stop of loss einsuance and estiate the needed loss eseve.

12 896 Osaa Hanafy Mahoud Refeences [] A. Aljuaid, Estiating the Paaetes of an Eponentiated Inveted Weibull Distibution unde Type-II Censoing, Applied Matheatical Sciences, 7 (3, 35, [] A. B. Botoluzzo, D. P. Clao, M. A. Caetano and R. Ates, Estiating Clai Size and Pobability in the Auto-insuance Industy: the Zeo adjusted Invese Gaussian (ZAIG Distibution, Inspe Woking Pape WPE: 75 (9. [3] M. B. Finan M. B., An Intoductoy Guide in the Constuction of Actuaial Models, Akansas Tech Univesity, 4. [4] A. Flaih, H. Elsalloukh, E. Mendi and M. Milanova. The Eponentiated Inveted Weibull Distibution, Applied Matheatics & Infoation Sciences, 6 (,, [5] M. Gauge and M. Hosking, Constuction of Actuaial Models, Bpp Pofessional Education, Inc, (8. [6] A. S. Hassan, On the Optial Design of Failue Step-Stess Patially Acceleated ife Tests fo Eponentiated Inveted Weibull with Censoing, Austalian Jounal of Basic and Applied Sciences, 7 (3,, [7] A. Hassan, A. Mawa,H. Zahe and E. Elshepiny, Copaison of Estiatos fo Eponentiated Inveted Weibull Distibution Based on Gouped Data, Int. Jounal of Engineeing Reseach and Applications, 4 (4, 4, [8] Heckan, Philip E. Meyes, Glenn G. (983, "The Calculation of Aggegate oss Distibutions fo Clai Seveity and Clai Count Distibutions", Poceedings of the Casualty Actuaial Society Casualty Actuaial Society - Alington, Viginia 983: XX - 6. [9] Papush D. E., Pateik, G. S. and Podgaits F., (, "Appoiations of the aggegate distibutions", CAS Fou, pp [] Robetson John, (99, "The Coputation of Aggegation loss distibutions", PCAS, pp [] Shevchenko P. V., (, "Calculation of aggegate loss distibutions", The Jounal of Opeational Risk 5 (, pp. 3-4.

13 Constuction actuaial odel fo aggegate loss 897 [] Vente G. (983, "Tansfoed Beta and Gaa distibutions and the aggegate losses" PCAS, XX, pp [3] Vila J., Cao R., Ausín M. C. and C. González-Fagueio C., (8, "onpaaetic analysis of aggegate loss odels", nd Intenational Wokshop on Coputational and Financial Econoetics (CFE'8, euchatel (Suiza, 9 a de junio de 8. Received: Octobe 7, 4; Published: ovebe 8, 4

Products of the Second Pillar Pension

Products of the Second Pillar Pension Óbuda Univesity e-bulletin Vol. 4, No. 1, 2014 Poducts of the Second Pilla Pension Jana Špiková Depatent of Quantitative Methods and Infoation Systes, Faculty of Econoics, Matej Bel Univesity Tajovského

More information

9.5 Amortization. Objectives

9.5 Amortization. Objectives 9.5 Aotization Objectives 1. Calculate the payent to pay off an aotized loan. 2. Constuct an aotization schedule. 3. Find the pesent value of an annuity. 4. Calculate the unpaid balance on a loan. Congatulations!

More information

Mechanics 1: Motion in a Central Force Field

Mechanics 1: Motion in a Central Force Field Mechanics : Motion in a Cental Foce Field We now stud the popeties of a paticle of (constant) ass oving in a paticula tpe of foce field, a cental foce field. Cental foces ae ve ipotant in phsics and engineeing.

More information

Software Engineering and Development

Software Engineering and Development I T H E A 67 Softwae Engineeing and Development SOFTWARE DEVELOPMENT PROCESS DYNAMICS MODELING AS STATE MACHINE Leonid Lyubchyk, Vasyl Soloshchuk Abstact: Softwae development pocess modeling is gaining

More information

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow

More information

An Introduction to Omega

An Introduction to Omega An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei isk-ewad chaacteistics? The Finance Development Cente 2002 1 Fom

More information

Portfolio Performance Attribution

Portfolio Performance Attribution Potfolio Pefoance Attibution Alia Biglova, Svetloa Rachev 2 Abstact In this pape, we povide futhe insight into the pefoance attibution by developent of statistical odels based on iniiing ETL pefoance isk

More information

Ilona V. Tregub, ScD., Professor

Ilona V. Tregub, ScD., Professor Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation

More information

ON THE (Q, R) POLICY IN PRODUCTION-INVENTORY SYSTEMS

ON THE (Q, R) POLICY IN PRODUCTION-INVENTORY SYSTEMS ON THE R POLICY IN PRODUCTION-INVENTORY SYSTEMS Saifallah Benjaafa and Joon-Seok Kim Depatment of Mechanical Engineeing Univesity of Minnesota Minneapolis MN 55455 Abstact We conside a poduction-inventoy

More information

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts

More information

Trading Volume and Serial Correlation in Stock Returns in Pakistan. Abstract

Trading Volume and Serial Correlation in Stock Returns in Pakistan. Abstract Tading Volume and Seial Coelation in Stock Retuns in Pakistan Khalid Mustafa Assistant Pofesso Depatment of Economics, Univesity of Kaachi e-mail: khalidku@yahoo.com and Mohammed Nishat Pofesso and Chaiman,

More information

A framework for the selection of enterprise resource planning (ERP) system based on fuzzy decision making methods

A framework for the selection of enterprise resource planning (ERP) system based on fuzzy decision making methods A famewok fo the selection of entepise esouce planning (ERP) system based on fuzzy decision making methods Omid Golshan Tafti M.s student in Industial Management, Univesity of Yazd Omidgolshan87@yahoo.com

More information

The transport performance evaluation system building of logistics enterprises

The transport performance evaluation system building of logistics enterprises Jounal of Industial Engineeing and Management JIEM, 213 6(4): 194-114 Online ISSN: 213-953 Pint ISSN: 213-8423 http://dx.doi.og/1.3926/jiem.784 The tanspot pefomance evaluation system building of logistics

More information

HEALTHCARE INTEGRATION BASED ON CLOUD COMPUTING

HEALTHCARE INTEGRATION BASED ON CLOUD COMPUTING U.P.B. Sci. Bull., Seies C, Vol. 77, Iss. 2, 2015 ISSN 2286-3540 HEALTHCARE INTEGRATION BASED ON CLOUD COMPUTING Roxana MARCU 1, Dan POPESCU 2, Iulian DANILĂ 3 A high numbe of infomation systems ae available

More information

The Role of Gravity in Orbital Motion

The Role of Gravity in Orbital Motion ! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State

More information

Chapter 3 Savings, Present Value and Ricardian Equivalence

Chapter 3 Savings, Present Value and Ricardian Equivalence Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,

More information

Electricity transmission network optimization model of supply and demand the case in Taiwan electricity transmission system

Electricity transmission network optimization model of supply and demand the case in Taiwan electricity transmission system Electicity tansmission netwok optimization model of supply and demand the case in Taiwan electicity tansmission system Miao-Sheng Chen a Chien-Liang Wang b,c, Sheng-Chuan Wang d,e a Taichung Banch Gaduate

More information

Who Files for Bankruptcy? State Laws and the Characteristics of Bankrupt Households

Who Files for Bankruptcy? State Laws and the Characteristics of Bankrupt Households Who iles fo Bankuptcy? State Laws and the Chaacteistics of Bankupt Households By MICHLL M. MILLR While pio papes have exained the ipact of state exeption and ganishent laws on the aveage household, this

More information

The Predictive Power of Dividend Yields for Stock Returns: Risk Pricing or Mispricing?

The Predictive Power of Dividend Yields for Stock Returns: Risk Pricing or Mispricing? The Pedictive Powe of Dividend Yields fo Stock Retuns: Risk Picing o Mispicing? Glenn Boyle Depatment of Economics and Finance Univesity of Cantebuy Yanhui Li Depatment of Economics and Finance Univesity

More information

Financial Planning and Risk-return profiles

Financial Planning and Risk-return profiles Financial Planning and Risk-etun pofiles Stefan Gaf, Alexande Kling und Jochen Russ Pepint Seies: 2010-16 Fakultät fü Mathematik und Witschaftswissenschaften UNIERSITÄT ULM Financial Planning and Risk-etun

More information

Infinite-dimensional Bäcklund transformations between isotropic and anisotropic plasma equilibria.

Infinite-dimensional Bäcklund transformations between isotropic and anisotropic plasma equilibria. Infinite-dimensional äcklund tansfomations between isotopic and anisotopic plasma equilibia. Infinite symmeties of anisotopic plasma equilibia. Alexei F. Cheviakov Queen s Univesity at Kingston, 00. Reseach

More information

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,

More information

Tracking/Fusion and Deghosting with Doppler Frequency from Two Passive Acoustic Sensors

Tracking/Fusion and Deghosting with Doppler Frequency from Two Passive Acoustic Sensors Tacking/Fusion and Deghosting with Dopple Fequency fom Two Passive Acoustic Sensos Rong Yang, Gee Wah Ng DSO National Laboatoies 2 Science Pak Dive Singapoe 11823 Emails: yong@dso.og.sg, ngeewah@dso.og.sg

More information

Exam #1 Review Answers

Exam #1 Review Answers xam #1 Review Answes 1. Given the following pobability distibution, calculate the expected etun, vaiance and standad deviation fo Secuity J. State Pob (R) 1 0.2 10% 2 0.6 15 3 0.2 20 xpected etun = 0.2*10%

More information

9.4 Annuities. Objectives. 1. Calculate the future value of an ordinary annuity. 2. Perform calculations regarding sinking funds.

9.4 Annuities. Objectives. 1. Calculate the future value of an ordinary annuity. 2. Perform calculations regarding sinking funds. 9.4 Annuities Objectives 1. Calculate the futue value of an odinay annuity. 2. Pefo calculations egading sinking funds. Soewhee ove the ainbow... skies ae blue,... and the deas that you dae to dea...eally

More information

INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS

INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS Vesion:.0 Date: June 0 Disclaime This document is solely intended as infomation fo cleaing membes and othes who ae inteested in

More information

Optimal Pricing Decision and Assessing Factors in. Closed-Loop Supply Chain

Optimal Pricing Decision and Assessing Factors in. Closed-Loop Supply Chain Applied Matheatical Sciences, Vol. 5, 2011, no. 80, 4015-4031 Optial Picing Decision and Assessing Factos in Closed-Loop Supply Chain Yang Tan Picing Science and Engineeing Depatent, FedEx Expess Wold

More information

Continuous Compounding and Annualization

Continuous Compounding and Annualization Continuous Compounding and Annualization Philip A. Viton Januay 11, 2006 Contents 1 Intoduction 1 2 Continuous Compounding 2 3 Pesent Value with Continuous Compounding 4 4 Annualization 5 5 A Special Poblem

More information

Who Files for Bankruptcy? State Laws and the Characteristics of Bankrupt Households

Who Files for Bankruptcy? State Laws and the Characteristics of Bankrupt Households Who iles fo Bankuptcy? State Laws and the Chaacteistics of Bankupt Households Michelle M. Mille ssistant Pofesso Rutges Business School epatent of inance and Econoics Washington Pak, Roo 54 Newak, New

More information

Questions for Review. By buying bonds This period you save s, next period you get s(1+r)

Questions for Review. By buying bonds This period you save s, next period you get s(1+r) MACROECONOMICS 2006 Week 5 Semina Questions Questions fo Review 1. How do consumes save in the two-peiod model? By buying bonds This peiod you save s, next peiod you get s() 2. What is the slope of a consume

More information

Port Efficiency in apec 1

Port Efficiency in apec 1 Pot Efficiency in apec 1 Zoe Infante 2 Aiel Gutiéez 3 Abstact The ain goal of this eseach is to identify and analyze factos that ay significantly affect the levels of pot efficiency in apec counties (paticulaly

More information

Concept and Experiences on using a Wiki-based System for Software-related Seminar Papers

Concept and Experiences on using a Wiki-based System for Software-related Seminar Papers Concept and Expeiences on using a Wiki-based System fo Softwae-elated Semina Papes Dominik Fanke and Stefan Kowalewski RWTH Aachen Univesity, 52074 Aachen, Gemany, {fanke, kowalewski}@embedded.wth-aachen.de,

More information

Life Insurance Purchasing to Reach a Bequest. Erhan Bayraktar Department of Mathematics, University of Michigan Ann Arbor, Michigan, USA, 48109

Life Insurance Purchasing to Reach a Bequest. Erhan Bayraktar Department of Mathematics, University of Michigan Ann Arbor, Michigan, USA, 48109 Life Insuance Puchasing to Reach a Bequest Ehan Bayakta Depatment of Mathematics, Univesity of Michigan Ann Abo, Michigan, USA, 48109 S. David Pomislow Depatment of Mathematics, Yok Univesity Toonto, Ontaio,

More information

STABILITY ANALYSIS IN MILLING BASED ON OPERATIONAL MODAL DATA 1. INTRODUCTION

STABILITY ANALYSIS IN MILLING BASED ON OPERATIONAL MODAL DATA 1. INTRODUCTION Jounal of Machine Engineeing, Vol. 11, No. 4, 211 Batosz POWALKA 1 Macin CHODZKO 1 Kzysztof JEMIELNIAK 2 milling, chatte, opeational modal analysis STABILITY ANALYSIS IN MILLING BASED ON OPERATIONAL MODAL

More information

Financing Terms in the EOQ Model

Financing Terms in the EOQ Model Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad

More information

arxiv:1110.2612v1 [q-fin.st] 12 Oct 2011

arxiv:1110.2612v1 [q-fin.st] 12 Oct 2011 Maket inefficiency identified by both single and multiple cuency tends T.Toká 1, and D. Hováth 1, 1 Sos Reseach a.s., Stojáenská 3, 040 01 Košice, Slovak Republic Abstact axiv:1110.2612v1 [q-fin.st] 12

More information

Research on Risk Assessment of the Transformer Based on Life Cycle Cost

Research on Risk Assessment of the Transformer Based on Life Cycle Cost ntenational Jounal of Smat Gid and lean Enegy eseach on isk Assessment of the Tansfome Based on Life ycle ost Hui Zhou a, Guowei Wu a, Weiwei Pan a, Yunhe Hou b, hong Wang b * a Zhejiang Electic Powe opoation,

More information

Chris J. Skinner The probability of identification: applying ideas from forensic statistics to disclosure risk assessment

Chris J. Skinner The probability of identification: applying ideas from forensic statistics to disclosure risk assessment Chis J. Skinne The pobability of identification: applying ideas fom foensic statistics to disclosue isk assessment Aticle (Accepted vesion) (Refeeed) Oiginal citation: Skinne, Chis J. (2007) The pobability

More information

SLOT EXCHANGE AND PURCHASE PLANNING OF SHORT SEA SERVICES FOR LINER CARRIERS

SLOT EXCHANGE AND PURCHASE PLANNING OF SHORT SEA SERVICES FOR LINER CARRIERS Jounal of Maine Science and Technology, Vol. 18, No. 5, pp. 709-718 (2010) 709 SLOT EXCHNGE ND PURCHSE PLNNING OF SHORT SE SERVICES FOR LINER CRRIERS Hua-n Lu*, Shu-Ling Chen**, and Pete Lai*** Key wods

More information

Introduction to Stock Valuation. Background

Introduction to Stock Valuation. Background Intoduction to Stock Valuation (Text efeence: Chapte 5 (Sections 5.4-5.9)) Topics backgound dividend discount models paamete estimation gowth oppotunities pice-eanings atios some final points AFM 271 -

More information

Semipartial (Part) and Partial Correlation

Semipartial (Part) and Partial Correlation Semipatial (Pat) and Patial Coelation his discussion boows heavily fom Applied Multiple egession/coelation Analysis fo the Behavioal Sciences, by Jacob and Paticia Cohen (975 edition; thee is also an updated

More information

Model-based clustering of longitudinal data. McNicholas, Paul D.; Murphy, Thomas Brendan. Canadian Journal of Statistics, 38 (1): 153-168

Model-based clustering of longitudinal data. McNicholas, Paul D.; Murphy, Thomas Brendan. Canadian Journal of Statistics, 38 (1): 153-168 Povided by the autho(s) and Univesity College Dublin Libay in accodance with publishe policies Please cite the published vesion when available Title Model-based clusteing of longitudinal data Autho(s)

More information

PORTFOLIO OPTIMIZATION WHEN ASSET RETURNS HAVE THE GAUSSIAN MIXTURE DISTRIBUTION

PORTFOLIO OPTIMIZATION WHEN ASSET RETURNS HAVE THE GAUSSIAN MIXTURE DISTRIBUTION PORTFOLIO OPTIMIZATION WHEN ASSET RETURNS HAVE THE GAUSSIAN MIXTURE DISTRIBUTION IAN BUCKLEY, GUSTAVO COMEZAÑA, BEN DJERROUD, AND LUIS SECO Abstact. Potfolios of assets whose etuns have the Gaussian mixtue

More information

est using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.

est using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years. 9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,

More information

Simple way of teaching transistor amplifiers

Simple way of teaching transistor amplifiers ession 793 iple way of teaching tansisto aplifies ogdan M. Wilaowski Uniesity of Wyoing bstact Fo sall signal analysis a siple change fo coonly used tanconductance g to tansesistance /g leads to a significant

More information

Newton s Law of Universal Gravitation and the Scale Principle

Newton s Law of Universal Gravitation and the Scale Principle Newton s Law of Univesal avitation and the ale iniple RODOLO A. RINO July 0 Eletonis Enginee Degee fo the National Univesity of Ma del lata - Agentina (odolfo_fino@yahoo.o.a) Ealie this yea I wote a pape

More information

Insurance Pricing under Ambiguity

Insurance Pricing under Ambiguity Insuance Picing unde Ambiguity Alois Pichle a,b, a Univesity of Vienna, Austia. Depatment of Statistics and Opeations Reseach b Actuay. Membe of the Austian Actuaial Association Abstact Stating fom the

More information

Risk Sensitive Portfolio Management With Cox-Ingersoll-Ross Interest Rates: the HJB Equation

Risk Sensitive Portfolio Management With Cox-Ingersoll-Ross Interest Rates: the HJB Equation Risk Sensitive Potfolio Management With Cox-Ingesoll-Ross Inteest Rates: the HJB Equation Tomasz R. Bielecki Depatment of Mathematics, The Notheasten Illinois Univesity 55 Noth St. Louis Avenue, Chicago,

More information

Power and Sample Size Calculations for the 2-Sample Z-Statistic

Power and Sample Size Calculations for the 2-Sample Z-Statistic Powe and Sample Size Calculations fo the -Sample Z-Statistic James H. Steige ovembe 4, 004 Topics fo this Module. Reviewing Results fo the -Sample Z (a) Powe and Sample Size in Tems of a oncentality Paamete.

More information

Review of Vectors. Appendix A A.1 DESCRIBING THE 3D WORLD: VECTORS. 3D Coordinates. Basic Properties of Vectors: Magnitude and Direction.

Review of Vectors. Appendix A A.1 DESCRIBING THE 3D WORLD: VECTORS. 3D Coordinates. Basic Properties of Vectors: Magnitude and Direction. Appendi A Review of Vectos This appendi is a summa of the mathematical aspects of vectos used in electicit and magnetism. Fo a moe detailed intoduction to vectos, see Chapte 1. A.1 DESCRIBING THE 3D WORLD:

More information

Comparing Availability of Various Rack Power Redundancy Configurations

Comparing Availability of Various Rack Power Redundancy Configurations Compaing Availability of Vaious Rack Powe Redundancy Configuations By Victo Avela White Pape #48 Executive Summay Tansfe switches and dual-path powe distibution to IT equipment ae used to enhance the availability

More information

Things to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request.

Things to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request. Retiement Benefit 1 Things to Remembe Complete all of the sections on the Retiement Benefit fom that apply to you equest. If this is an initial equest, and not a change in a cuent distibution, emembe to

More information

Channel selection in e-commerce age: A strategic analysis of co-op advertising models

Channel selection in e-commerce age: A strategic analysis of co-op advertising models Jounal of Industial Engineeing and Management JIEM, 013 6(1):89-103 Online ISSN: 013-0953 Pint ISSN: 013-843 http://dx.doi.og/10.396/jiem.664 Channel selection in e-commece age: A stategic analysis of

More information

Wasting the Percentage of On-hand Inventory in an Instantaneous Economic Order Quantity Model Due to Deterioration

Wasting the Percentage of On-hand Inventory in an Instantaneous Economic Order Quantity Model Due to Deterioration Jounal of mathematics and compute Science 7 (2013) 154-159 Wasting the Pecentage of On-hand Inventoy in an Instantaneous Economic Ode Quantity Model Due to Deteioation Aticle histoy: Received Mach 2013

More information

Loyalty Rewards and Gift Card Programs: Basic Actuarial Estimation Techniques

Loyalty Rewards and Gift Card Programs: Basic Actuarial Estimation Techniques Loyalty Rewads and Gift Cad Pogams: Basic Actuaial Estimation Techniques Tim A. Gault, ACAS, MAAA, Len Llaguno, FCAS, MAAA and Matin Ménad, FCAS, MAAA Abstact In this pape we establish an actuaial famewok

More information

9. Mathematics Practice Paper for Class XII (CBSE) Available Online Tutoring for students of classes 4 to 12 in Physics, Chemistry, Mathematics

9. Mathematics Practice Paper for Class XII (CBSE) Available Online Tutoring for students of classes 4 to 12 in Physics, Chemistry, Mathematics Available Online Tutoing fo students of classes 4 to 1 in Physics, 9. Mathematics Class 1 Pactice Pape 1 3 1. Wite the pincipal value of cos.. Wite the ange of the pincipal banch of sec 1 defined on the

More information

Multiband Microstrip Patch Antenna for Microwave Applications

Multiband Microstrip Patch Antenna for Microwave Applications IOSR Jounal of Electonics and Communication Engineeing (IOSR-JECE) ISSN: 2278-2834, ISBN: 2278-8735. Volume 3, Issue 5 (Sep. - Oct. 2012), PP 43-48 Multiband Micostip Patch Antenna fo Micowave Applications

More information

Cloud Service Reliability: Modeling and Analysis

Cloud Service Reliability: Modeling and Analysis Cloud Sevice eliability: Modeling and Analysis Yuan-Shun Dai * a c, Bo Yang b, Jack Dongaa a, Gewei Zhang c a Innovative Computing Laboatoy, Depatment of Electical Engineeing & Compute Science, Univesity

More information

Hadoop Performance Modeling for Job Estimation and Resource Provisioning

Hadoop Performance Modeling for Job Estimation and Resource Provisioning his aticle has been accepted fo publication in a futue issue of this jounal, but has not been fully edited. Content ay change pio to final publication. Citation infoation: DOI 0.09/PDS.05.40555, IEEE ansactions

More information

The LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero.

The LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero. Poject Decision Metics: Levelized Cost of Enegy (LCOE) Let s etun to ou wind powe and natual gas powe plant example fom ealie in this lesson. Suppose that both powe plants wee selling electicity into the

More information

Valuation of Floating Rate Bonds 1

Valuation of Floating Rate Bonds 1 Valuation of Floating Rate onds 1 Joge uz Lopez us 316: Deivative Secuities his note explains how to value plain vanilla floating ate bonds. he pupose of this note is to link the concepts that you leaned

More information

Cubic Spline Interpolation by Solving a Recurrence Equation Instead of a Tridiagonal Matrix

Cubic Spline Interpolation by Solving a Recurrence Equation Instead of a Tridiagonal Matrix Matematical Metods in Science and Engineeing Cubic Spline Intepolation by Solving a Recuence Equation Instead of a Tidiagonal Matix Pete Z Revesz Depatment of Compute Science and Engineeing Univesity of

More information

Comparing Availability of Various Rack Power Redundancy Configurations

Comparing Availability of Various Rack Power Redundancy Configurations Compaing Availability of Vaious Rack Powe Redundancy Configuations White Pape 48 Revision by Victo Avela > Executive summay Tansfe switches and dual-path powe distibution to IT equipment ae used to enhance

More information

Data Center Demand Response: Avoiding the Coincident Peak via Workload Shifting and Local Generation

Data Center Demand Response: Avoiding the Coincident Peak via Workload Shifting and Local Generation (213) 1 28 Data Cente Demand Response: Avoiding the Coincident Peak via Wokload Shifting and Local Geneation Zhenhua Liu 1, Adam Wieman 1, Yuan Chen 2, Benjamin Razon 1, Niangjun Chen 1 1 Califonia Institute

More information

9:6.4 Sample Questions/Requests for Managing Underwriter Candidates

9:6.4 Sample Questions/Requests for Managing Underwriter Candidates 9:6.4 INITIAL PUBLIC OFFERINGS 9:6.4 Sample Questions/Requests fo Managing Undewite Candidates Recent IPO Expeience Please povide a list of all completed o withdawn IPOs in which you fim has paticipated

More information

Strategic Asset Allocation and the Role of Alternative Investments

Strategic Asset Allocation and the Role of Alternative Investments Stategic Asset Allocation and the Role of Altenative Investments DOUGLAS CUMMING *, LARS HELGE HAß, DENIS SCHWEIZER Abstact We intoduce a famewok fo stategic asset allocation with altenative investments.

More information

MATHEMATICAL SIMULATION OF MASS SPECTRUM

MATHEMATICAL SIMULATION OF MASS SPECTRUM MATHEMATICA SIMUATION OF MASS SPECTUM.Beánek, J.Knížek, Z. Pulpán 3, M. Hubálek 4, V. Novák Univesity of South Bohemia, Ceske Budejovice, Chales Univesity, Hadec Kalove, 3 Univesity of Hadec Kalove, Hadec

More information

867 Product Transfer and Resale Report

867 Product Transfer and Resale Report 867 Poduct Tansfe and Resale Repot Functional Goup ID=PT Intoduction: This X12 Tansaction Set contains the fomat and establishes the data contents of the Poduct Tansfe and Resale Repot Tansaction Set (867)

More information

875 Grocery Products Purchase Order

875 Grocery Products Purchase Order 875 Gocey Poducts Puchase Ode Functional Goup ID=OG Intoduction: This X12 Tansaction Set contains the fomat establishes the data contents of the Gocey Poducts Puchase Ode Tansaction Set (875) fo use within

More information

Complex Envelope Vectorization for the solution of mid-high frequency acoustic problems. A. Sestieri

Complex Envelope Vectorization for the solution of mid-high frequency acoustic problems. A. Sestieri Complex Envelope Vectoization fo the solution of mid-high fequency acoustic poblems A. Sestiei Depatment of Mechanical and Aeospace Engineeing Univesity of Rome la Sapienza Pesentation layout - Low fequency

More information

Period #11 Notes: MECHANICS OF PORTLAND CEMENT CONCRETE (11.1)

Period #11 Notes: MECHANICS OF PORTLAND CEMENT CONCRETE (11.1) Peiod #11 Notes: MCHANICS OF PORTAND CMNT CONCRT A. Bie Oveview Potland ceent concete is a coposite ateial consisting o aggegate paticles and the hydated ceent paste atix that binds the togethe. The ass

More information

An Epidemic Model of Mobile Phone Virus

An Epidemic Model of Mobile Phone Virus An Epidemic Model of Mobile Phone Vius Hui Zheng, Dong Li, Zhuo Gao 3 Netwok Reseach Cente, Tsinghua Univesity, P. R. China zh@tsinghua.edu.cn School of Compute Science and Technology, Huazhong Univesity

More information

Monte Carlo Simulation-Based Supply Chain Disruption Management for Wargames

Monte Carlo Simulation-Based Supply Chain Disruption Management for Wargames CREATE Reseach Achive Non-published Reseach Repots 21 Monte Calo Simulation-Based Supply Chain Disuption Management fo Wagames Jun Zhuang Univesity of Buffalo, The State Univesity of New Yok, jzhuang@buffalo.edu

More information

Firstmark Credit Union Commercial Loan Department

Firstmark Credit Union Commercial Loan Department Fistmak Cedit Union Commecial Loan Depatment Thank you fo consideing Fistmak Cedit Union as a tusted souce to meet the needs of you business. Fistmak Cedit Union offes a wide aay of business loans and

More information

Performance Analysis of an Inverse Notch Filter and Its Application to F 0 Estimation

Performance Analysis of an Inverse Notch Filter and Its Application to F 0 Estimation Cicuits and Systems, 013, 4, 117-1 http://dx.doi.og/10.436/cs.013.41017 Published Online Januay 013 (http://www.scip.og/jounal/cs) Pefomance Analysis of an Invese Notch Filte and Its Application to F 0

More information

The Capital Asset Pricing Model. Chapter 9

The Capital Asset Pricing Model. Chapter 9 The Capital Asset Picing odel Chapte 9 Capital Asset Picing odel CAP centepiece of moden finance gives the elationship that should be obseved between isk and etun of an asset it allows fo the evaluation

More information

Physics 235 Chapter 5. Chapter 5 Gravitation

Physics 235 Chapter 5. Chapter 5 Gravitation Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus

More information

PAN STABILITY TESTING OF DC CIRCUITS USING VARIATIONAL METHODS XVIII - SPETO - 1995. pod patronatem. Summary

PAN STABILITY TESTING OF DC CIRCUITS USING VARIATIONAL METHODS XVIII - SPETO - 1995. pod patronatem. Summary PCE SEMINIUM Z PODSTW ELEKTOTECHNIKI I TEOII OBWODÓW 8 - TH SEMIN ON FUNDMENTLS OF ELECTOTECHNICS ND CICUIT THEOY ZDENĚK BIOLEK SPŠE OŽNO P.., CZECH EPUBLIC DLIBO BIOLEK MILITY CDEMY, BNO, CZECH EPUBLIC

More information

Strength Analysis and Optimization Design about the key parts of the Robot

Strength Analysis and Optimization Design about the key parts of the Robot Intenational Jounal of Reseach in Engineeing and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Pint): 2320-9356 www.ijes.og Volume 3 Issue 3 ǁ Mach 2015 ǁ PP.25-29 Stength Analysis and Optimization Design

More information

Millennium Theory of Inertia and Gravity. Copyright 2004 Joseph A. Rybczyk

Millennium Theory of Inertia and Gravity. Copyright 2004 Joseph A. Rybczyk Millenniu Theoy of Inetia and Gavity Copyight 004 Joseph A. Rybczyk Abstact Investigative analysis of Keple s laws of planetay otion lead to the evelation that Newton s laws of echanics ae incoplete and

More information

I- LACUNARY GENERALIZED DIFFERENCE CONVERGENT SEQUENCES IN n-normed SPACES

I- LACUNARY GENERALIZED DIFFERENCE CONVERGENT SEQUENCES IN n-normed SPACES Jounal of Mathematical Analysis ISSN: 17-341, URL: http://www.iliias.com Volume Issue 1(011), Pages 18-4. I- LACUNARY GENERALIZED DIFFERENCE CONVERGENT SEQUENCES IN n-normed SPACES NURTEN FISTIKÇI, MEHMET

More information

A Hybrid DCT-SVD Video Compression Technique (HDCTSVD)

A Hybrid DCT-SVD Video Compression Technique (HDCTSVD) A Hybid - Video Compession echnique (H) ong, Lin; Rao, K.R. Abstact A new hybid - (H) video compession technique is poposed in this pape. Discete cosine tansfom () is widely used in video coding due to

More information

Define What Type of Trader Are you?

Define What Type of Trader Are you? Define What Type of Tade Ae you? Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 1 Disclaime and Risk Wanings Tading any financial maket involves isk. The content of this

More information

MULTIPLE SOLUTIONS OF THE PRESCRIBED MEAN CURVATURE EQUATION

MULTIPLE SOLUTIONS OF THE PRESCRIBED MEAN CURVATURE EQUATION MULTIPLE SOLUTIONS OF THE PRESCRIBED MEAN CURVATURE EQUATION K.C. CHANG AND TAN ZHANG In memoy of Pofesso S.S. Chen Abstact. We combine heat flow method with Mose theoy, supe- and subsolution method with

More information

Database Management Systems

Database Management Systems Contents Database Management Systems (COP 5725) D. Makus Schneide Depatment of Compute & Infomation Science & Engineeing (CISE) Database Systems Reseach & Development Cente Couse Syllabus 1 Sping 2012

More information

Approximation Algorithms for Data Management in Networks

Approximation Algorithms for Data Management in Networks Appoximation Algoithms fo Data Management in Netwoks Chistof Kick Heinz Nixdof Institute and Depatment of Mathematics & Compute Science adebon Univesity Gemany kueke@upb.de Haald Räcke Heinz Nixdof Institute

More information

Liquidity and Insurance for the Unemployed*

Liquidity and Insurance for the Unemployed* Fedeal Reseve Bank of Minneapolis Reseach Depatment Staff Repot 366 Decembe 2005 Liquidity and Insuance fo the Unemployed* Robet Shime Univesity of Chicago and National Bueau of Economic Reseach Iván Wening

More information

There is considerable variation in health care utilization and spending. Geographic Variation in Health Care: The Role of Private Markets

There is considerable variation in health care utilization and spending. Geographic Variation in Health Care: The Role of Private Markets TOMAS J. PHILIPSON Univesity of Chicago SETH A. SEABUY AND Copoation LEE M. LOCKWOOD Univesity of Chicago DANA P. GOLDMAN Univesity of Southen Califonia DAIUS N. LAKDAWALLA Univesity of Southen Califonia

More information

Modal Characteristics study of CEM-1 Single-Layer Printed Circuit Board Using Experimental Modal Analysis

Modal Characteristics study of CEM-1 Single-Layer Printed Circuit Board Using Experimental Modal Analysis Available online at www.sciencediect.com Pocedia Engineeing 41 (2012 ) 1360 1366 Intenational Symposium on Robotics and Intelligent Sensos 2012 (IRIS 2012) Modal Chaacteistics study of CEM-1 Single-Laye

More information

Uncertain Version Control in Open Collaborative Editing of Tree-Structured Documents

Uncertain Version Control in Open Collaborative Editing of Tree-Structured Documents Uncetain Vesion Contol in Open Collaboative Editing of Tee-Stuctued Documents M. Lamine Ba Institut Mines Télécom; Télécom PaisTech; LTCI Pais, Fance mouhamadou.ba@ telecom-paistech.f Talel Abdessalem

More information

YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH

YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH nd INTERNATIONAL TEXTILE, CLOTHING & ESIGN CONFERENCE Magic Wold of Textiles Octobe 03 d to 06 th 004, UBROVNIK, CROATIA YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH Jana VOBOROVA; Ashish GARG; Bohuslav

More information

UNIT CIRCLE TRIGONOMETRY

UNIT CIRCLE TRIGONOMETRY UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + = - - -

More information

BA 351 CORPORATE FINANCE LECTURE 4 TAXES AND THE MARGINAL INVESTOR. John R. Graham Adapted from S. Viswanathan FUQUA SCHOOL OF BUSINESS

BA 351 CORPORATE FINANCE LECTURE 4 TAXES AND THE MARGINAL INVESTOR. John R. Graham Adapted from S. Viswanathan FUQUA SCHOOL OF BUSINESS BA 351 CORPORATE FINANCE LECTURE 4 TAXES AND THE MARGINAL INVESTOR John R. Gaham Adapted fom S. Viswanathan FUQUA SCHOOL OF BUSINESS DUKE UNIVERSITY 1 In this lectue we conside the effect of govenment

More information

The Supply of Loanable Funds: A Comment on the Misconception and Its Implications

The Supply of Loanable Funds: A Comment on the Misconception and Its Implications JOURNL OF ECONOMICS ND FINNCE EDUCTION Volume 7 Numbe 2 Winte 2008 39 The Supply of Loanable Funds: Comment on the Misconception and Its Implications. Wahhab Khandke and mena Khandke* STRCT Recently Fields-Hat

More information

SUPPORT VECTOR MACHINE FOR BANDWIDTH ANALYSIS OF SLOTTED MICROSTRIP ANTENNA

SUPPORT VECTOR MACHINE FOR BANDWIDTH ANALYSIS OF SLOTTED MICROSTRIP ANTENNA Intenational Jounal of Compute Science, Systems Engineeing and Infomation Technology, 4(), 20, pp. 67-7 SUPPORT VECTOR MACHIE FOR BADWIDTH AALYSIS OF SLOTTED MICROSTRIP ATEA Venmathi A.R. & Vanitha L.

More information

Efficient Redundancy Techniques for Latency Reduction in Cloud Systems

Efficient Redundancy Techniques for Latency Reduction in Cloud Systems Efficient Redundancy Techniques fo Latency Reduction in Cloud Systems 1 Gaui Joshi, Emina Soljanin, and Gegoy Wonell Abstact In cloud computing systems, assigning a task to multiple seves and waiting fo

More information

International Monetary Economics Note 1

International Monetary Economics Note 1 36-632 Intenational Monetay Economics Note Let me biefly ecap on the dynamics of cuent accounts in small open economies. Conside the poblem of a epesentative consume in a county that is pefectly integated

More information

Spirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project

Spirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project Spiotechnics! Septembe 7, 2011 Amanda Zeingue, Michael Spannuth and Amanda Zeingue Dieential Geomety Poject 1 The Beginning The geneal consensus of ou goup began with one thought: Spiogaphs ae awesome.

More information

I = Prt. = P(1+i) n. A = Pe rt

I = Prt. = P(1+i) n. A = Pe rt 11 Chapte 6 Matheatcs of Fnance We wll look at the atheatcs of fnance. 6.1 Sple and Copound Inteest We wll look at two ways nteest calculated on oney. If pncpal pesent value) aount P nvested at nteest

More information

Design and Analysis of a Classical Controller to the Residual Oil in a Small Scale Semibatch Extractor

Design and Analysis of a Classical Controller to the Residual Oil in a Small Scale Semibatch Extractor Euopean Symposium on Compute Aded Aided Pocess Engineeing 15 L. Puigjane and A. Espuña (Editos) 25 Elsevie Science B.V. All ights eseved. Design and Analysis of a Classical Contolle to the Residual Oil

More information