Abteilung für Stadt und Regionalentwicklung Department of Urban and Regional Development


 Paulina Ellis
 1 years ago
 Views:
Transcription
1 Abtelung für Stadt und Regonalentwcklung Department of Urban and Regonal Development Gunther Maer, Alexander Kaufmann The Development of Computer Networks Frst Results from a Mcroeconomc Model SREDscusson
2 The Development of ComputerNetworks: Frst Results from a Mcroeconomc Model Gunther Maer, Alexander Kaufmann Insttute for Urban and Regonal Studes, Venna Unversty of Economcs and Busness Admnstraton Augasse 26 A1090 Venna Austra Abstract Computer networks lke the Internet are ganng mportance n socal and economc lfe. The acceleratng pace of the adopton of network technologes for busness purposes s a rather recent phenomenon. Many applcatons are stll n the early, sometmes even expermental phase. Nevertheless, t seems to be certan that networks wll change the socoeconomc structures we know today. Ths s the background for our specal nterest n the development of networks, n the role of spatal factors nfluencng the formaton of networks and consequences of networks on spatal structures, and n the role of externaltes. Ths paper dscusses a smple economc model based on a mcroeconomc calculus that ncorporates the man factors that generate the growth of computer networks. The paper provdes frst analytc results about the generaton of computer networks. The paper dscusses (1) under what condtons economc factors wll ntate the process of network formaton, (2) the relatonshp between ndvdual and socal evaluaton, and (3) the effcency of a network that s generated based on economc mechansms.
3 1. Introducton The development of computer technologes and ts applcatons has been extremely rapd n the eghtes and nnetes. Computer networks belong to the most sgnfcant felds of techncal development. Ths s a consequence of two development paths: 1. The growng mportance of PCs due to the rapdly ncreasng computng capacty. 2. The organzatonal and communcatve advantages of electronc networks have led to the wdespread use of prvate networks, not only wthn companes and ts subsdares but also n customersupplerrelatons. The man mpulse came from a publc network  the Internet. It s generally beleved that computer networks lke the Internet wll fundamentally change economy and socety (see e.g., Castells, 1996, MacLuhan, 1992, Gllespe, 1991). Castells (1996) even compares ths new development wth the Industral Revoluton. In order to understand what consequences computer networks wll have on socety and economy t seems necessary to frst understand why and how such networks develop. In ths paper we try to take a step n ths drecton. We attempt to fnd key economc factors that may have drven the rapd nternatonal dffuson of networkng over the past years, and to dentfy the condtons that may stmulate or hamper ths development. We wll do ths by developng a conceptual framework and a smple economc model that captures the key factors. In ths paper we apply a mcroeconomc perspectve. Ratonal agents are assumed to decde about whether to connect to another agent through a network lnk or not based on a comparson of ther costs and benefts of ths step. In order to keep the analyss manageable we use relatvely smple concepts of costs and benefts n ths context. Most mportantly, we assume that all the costs and benefts materalze n the current perod so that we don t have to take nto account dscountng and expectatons about the future development of the network. 2
4 Of course, n realty there are dfferent components of the costs of a network lnk: nstallaton costs, fxed and varable telecommuncaton costs, provder fees, etc. In our analyss we assume only the costs of establshng the network lnk. A smlar argument holds for benefts as well. Here we assume that the man effect of a computer network lnk les n the reducton of dstance frcton. Ths, n turn, allows for an ncreased level of nteracton between actors. The actors are assumed to derve utlty from ths nteracton. A maor economc element of any network nfrastructure les n the exstence of network externaltes (Capello, 1994). In our smple model network externaltes orgnate from the fact that when an actor connects to another actor who s already on a network, dstance frcton between all actors already on the network and the new member s reduced. As we wll see, these network externaltes are the man drvng force behnd network development. They also rase the queston of optmalty and ndvdual vs. socal valuaton. 2. The Model In order to gan some nsght nto the development of computer networks, we now develop a model that allows us to talk about the above mentoned mechansms and relatonshps n more precse terms. We start by descrbng the ntal condton of the problem,.e. the stuaton wthout any computer network at all, by a complete graph G = ( V, E) (1) wth V beng a set of n vertces and E the set of all n( n 1) 2 possble connectons between these vertces. The weghts of the graph are gven by a weght or dstance matrx D. Economc actors are located at the vertces of the graph G. Ths weght matrx represents the general dstances between each par of actors. 3
5 The computer network s descrbed by another graph N = ( V, L) wth the same set of vertces as G and a set of edges L that s a subset of E and represents exstng computer lnks. Intally, we set L = {} 0 and denote ths graph as N (, 0 = V L0 ). The graph N may consst of a number of components,.e. the subgraphs formed of connected vertces and the correspondng edges. Snce unconnected vertces are defned as components, the number of components may be between 1 (when all vertces are connected by the same network) and n (when no network connectons exst). We wll denote the components of graph N as where C (N) s the number of components of graph N. c ( N), = 1,, C( N) (2) Wth these defntons, each vertex must belong to exactly one of the components of N. We wll wrte the component that contans vertex V as c. Note that when V and V are drectly or ndrectly connected by a network lnk,.e. by network lnks n L, they belong to the same component and c = c. The actors are assumed to beneft from nteracton. They can ether nteract along the edges of the underlyng graph G, or along the network lnks n N. Of course, they can nteract along N only wth those actors that belong to the same component;.e. those who are on the same physcal network. Network lnks ease nteracton and are therefore benefcal for the actors. We defne the beneft of nteracton as a standard nteracton potental. For N 0, the case wth no network lnks, the beneft for actor s therefore B ( N 0) = exp( α D) (3) Now, what s the effect of a network lnk on the benefts of a certan actor? It can be argued that n today s computer networks dstance frcton s neglgble. Delays n the communcaton over those networks orgnate from other factors lke lmted capacty of a server, lmted capacty of the fnal 4
6 lnk, a general level of congeston, etc. that are not related to dstance. Therefore, t can be argued that dstance frcton s completely elmnated by network lnks. The benefts for an actor on the network would therefore become D c B ( N) = exp( α ) + exp(0) (4) Ths, of course, s an extreme poston that may hold only for pure communcaton. As soon as there are other forms of nteracton nvolved, lke the shpment of products or personal vstatons, dstance frcton s agan mportant. Therefore, a more moderate formulaton would be to allow the network lnks to reduce dstance frcton by a certan factor δ ( 0 δ 1). The benefts for an actor would therefore become c c B ( N) = exp( α D) + exp[ α(1 δ ) D ]. (5) Ths s the most general formulaton. It contans the two others as specal cases (δ = 0 and δ = 1, respectvely). For any δ > 0 the actors nvolved benefts from a network connecton. But, of course, there may also be costs nvolved n establshng and operatng a network lnk. These costs are probably proportonal to the length of the network lnk. If we denote a drect network connecton between vertex and vertex as c L, the costs for ths lnk can be wrtten as C(. (6) L ) = γd Note that wth the establshment of a lnk from to we also establsh a lnk from to. Therefore, the queston arses, who wll bear the costs of ths network lnk. In the worst case, one of the two actors that set up a new network lnk wll have to bear all the costs. Therefore, n hs/her decson makng every actor wll have to assume that he/she wll have to bear all the costs of the network lnk. Consequently, we can wrte for C ( ), the costs the lnk may create for actor as L C ( L ) = C( L ) = γd. (7) 5
7 Smlarly, C (N) s the costs network N generates for actor. The queston of our paper s, how N evolves over tme, when the decsons about whether to establsh a certan network lnk or not are based upon the economc calculus of the actors. For each par of graphs G and N we can compute the benefts and costs for each actor. Ths yelds vectors of benefts and costs Snce G s a constant, we wll use the smplfed notaton B = B(N,G) and C = C(N,G). (8) B = B(N); C = C(N). (9) Gven these benefts and costs, the actors are, of course, nterested n maxmzng ther profts: Π ( N) = B ( N) C ( N) (10) As mentoned above, we assume throughout that all the costs and benefts occur only n the current perod. That means that actors look only at the current stuaton and do not make any nvestmenttype decsons where they trade off current expendtures for future benefts. Also, we assume that there are no capacty constrants. Therefore, the addton of a network connecton cannot lower the beneft of actors already on the network. These two assumptons smplfy the problem consderably, but at the same tme severely lmt the potental value of the analyss. We hope to be able to remove these assumptons n future work. + Let us wrte as N = ( V, L + L ) the graph that we get when addng the network connecton L to a base graph N. Smlarly, N = ( V, L L ) s the graph that we get when we remove the network connecton L from the base graph N. But, snce we do not allow for capacty constrants, network lnks wll only be added n our analyss, never removed. At every tme perod each actor can choose from n dfferent strateges. She can stay wth the current stuaton, drop the network lnk to any of the say k other actors he/she s currently connected to, or establsh a lnk to any one of the nk1 actors she s currently not connected to. 6
8 The margnal profts of these strateges can be derved drectly from the above defntons: Π ( N ) Π ( N) = [ B ( N ) B ( N)] [ C ( N ) C ( N)] Π ( N ) Π ( N) = [ B ( N ) B ( N)] [ C ( N ) C ( N)] (11) (12) The margnal proft of no change at all s zero, of course. At every tme perod a ratonal actor wll try to mplement the strategy that provdes hm/her the maxmum margnal proft. However, mplementng such a strategy has mplcatons for other actors as well. It can well be that addng lnk L yelds the hghest margnal proft for actor, but does not yeld the hghest margnal proft for actor. A number of mechansms are concevable that decde such stuatons. For example, we may assume that only the strategy wth the hghest margnal proft of all actors wll be mplemented. The most meanngful mechansm from a mcroeconomc pont of few s what we call the mutual best strategy. Ths means that only those network lnks wll be establshed that yeld the hghest margnal proft for both actors nvolved. 3. Some Results 3.1. Network Generaton We can derve some nterestng frst results even from ths very smple structure. The frst queston we wll ask s, under what condtons the economc forces wll be suffcent to generate a network. More formally: Under what condtons wll economcally ratonal actors establsh at least one network lnk. A related queston that we can answer wth the frst one s whch one of the possble connectons wll be establshed frst. From (5) we know that the followng holds: + 0 ] exp( αd B ( N ) B ( N0) = exp[ α(1 δ ) D ) (13) The margnal costs for actor are smply a lnear functon of dstance: C + ( N ) C ( N0 0 ) = γd (14) 7
9 When we plot the margnal benefts as a functon of dstance we see that for 0 < δ < 1 the functon s postve, but approaches zero as dstance ncreases. The maxmum of the functon s where 1 1 D = ln( ). (15) αδ 1 δ For δ = 1,.e. the case where dstance frcton s elmnated completely, the margnal beneft ncreases monotoncally and approaches 1. Snce δ = 0 represents the case when dstance frcton s not changed at all by network lnks, the margnal beneft s always zero n ths case. Snce the margnal beneft s postve for all meanngful values of δ, the answer to the queston we have posed depends upon the slope of the cost functon. When the slope of the cost functon s lower than that of the margnal beneft at dstance zero, there wll be a range of dstances where the creaton of a network lnk s benefcal. Snce the slope of the margnal beneft functon at dstance zero s αδ, we fnd that only when αδ > γ (16) a network lnk may be created by ratonal economc agents. When ths condton holds, the range of dstances at whch establshng a network lnk s economcal always begns at dstance zero. For δ < 1 and γ > 0 there must be a maxmum dstance beyond whch the margnal proft s negatve. The optmum dstance, the dstance for whch the margnal proft s hghest, must be somewhere between zero and ths upper bound. Because of the dfference of exponental functons n (5) we cannot calculate an exact soluton for the upper bound and the optmum dstance. When we approxmate the beneft functon by a Taylor seres expanson, we fnd that the upper bound and the optmum dstance are approxmately 2( γ + αδ ) 2 α δ ( δ 2) and ( γ + αδ ). (17) 2 α δ ( δ 2) When the parameters are such that for a certan range of dstances n D postve margnal profts exst, wll there always be a network lnk establshed? Under our set of assumptons the answer s 8
10 yes. The reason s that the network lnk that yelds the hghest margnal proft of all possble network lnks must also yeld the hghest margnal proft for the actors at both ts ends. Therefore, whenever at least one dstance exsts that provdes a postve margnal proft, a network lnk wll be establshed for economc reasons. Because of (16) and the condton that δ s at most equal one, both nomnators and the denomnator n (17) are less than zero. Therefore, when γ ncreases, the optmum dstance and the upper bound decrease. Ths mples, for example, that n a country where telecommuncaton costs are hgh, computer networks wll start off wth shorter connectons than n a country where telecommuncaton costs are low. The argument that we have made so far also holds when network lnks can be establshed for free ( γ = 0 ). Although the margnal proft s postve for all dstances, the maxmum margnal proft s at the dstance gven by (15) above. So, even when network lnks are free, the network wll begn wth that connecton that s closest n dstance to the optmum dstance gven n (15). The reason s that nteracton partners that are further away than ths optmum dstance contrbute less to the beneft of the actor. Only when n addton to free network lnks (γ = 0) also dstance frcton s perfectly elmnated (δ = 1), then actors wll want to start the network by establshng the longest possble network lnk Indvdual vs. Socal Proft The next queston we can dscuss s that of the ndvdual evaluaton n relaton to a socal one. We can pose ths queston n the context of the above dscussed problem and ask ourselves, whether there mght be stuatons when based on the ndvdual evaluaton no frst network lnk wll be created although t would be desrable from a socal pont of vew. A dfference between ndvdual and socal evaluaton may result from two sources: 1. There mght be benefts to other actors that are not taken nto account by the decson maker, and 9
11 2. the costs to socety may dffer from those that the decson maker takes nto account. As mentoned above, both sources exst n our problem. Establshng a network lnk from to not only mproves the nteracton potental of actor, but also that of and all the other actors that are already connected to or. As far as costs are concerned, we have argued above that apror t s unclear who wll have to bear the costs of a network lnk and that therefore each actor should base her decson upon the assumpton that she wll have to bear all the costs by herself. As stated n (7), the ndvdual costs of an addtonal lnk are equal to the socal costs. Therefore, on each sde the margnal beneft of the network lnk must be hgher than the total margnal costs. From a socal pont of vew, however, the margnal benefts to all actors together have to exceed the margnal costs of the lnk. We can derve the socal beneft of a certan network N drectly from (5) above by summng the benefts for all actors n the system. So, the socal beneft can be wrtten as: B ( N) = B ( N) (18) Ths allows us to derve a drect measure of the network externalty at the beneft sde, whch s the sum of all the benefts that are not been taken nto account by the decson maker. When s the decson maker, the network externalty s B ( N) B ( N) = B ( N) (19) Based on these arguments, we can derve the socal margnal proft of the frst network lnk between and as: + + Π( N 0 ) Π( N 0 ) = [ B ( N 0 ) B ( N 0 )] [ C ( N 0 ) C ( N 0 )] (20) k k k k + k = 2 {exp[ α(1 δ ) D ] exp( αd )} γd (21) 10
12 When we compare (21) to (13) and (14), we see that the socal margnal proft dffers from the ndvdual one by the ndvdual margnal beneft of the lnk. Ths s the beneft that actor enoys, but whch s not consdered by actor n the decson makng. When we do the same calculatons as above, we fnd that the equvalent to (16), the condton that a network lnk may be socally desrable, s 2αδ > γ. (22) Obvously, the costs for the network lnk could be twce as hgh when socal costs and benefts are taken nto account than n the case of an ndvdual calculaton. So, when 2αδ > γ > αδ (23) a socally desrable network lnk may be possble, but wll not be created based on the actors mcroeconomc calculus. We can also derve approxmate solutons for the upper bound of the dstance range and the optmum dstance under a socal calculus. They turn out to be ( γ + 2αδ ) 2 α δ ( δ 2) and ( γ + 2αδ ). (24) 2 2α δ ( δ 2) When we compare these results to (17), we fnd that both the upper bound and the optmum dstance s hgher under socal evaluaton. So, from a socal pont of vew, the range of dstances for whch a network lnk may be created s too narrow, and when a network lnk s created based on the ndvdual calculus, t wll tend to be too short from a socal pont of vew Network Structure Another queston we may ask s, whether a network that emerges step by step from ths mcroeconomc mechansm wll be effcently servng the system of actors. In order to answer ths queston, we wll have to look at the end pont of the process. Suppose that the spatal constellaton and parameter values are such that based on the decson process n the end all actors are connected 11
13 to the network. Let us denote ths network as are actually lnked, ths network wll yeld a vector of benefts wth The socal beneft s N n. It s easy to see that rrespectve of how the actors B ( N ) = exp[ α (1 δ ) D ]. (25) n B ( N n ) = exp[ α (1 δ ) D ]. (26) The proft of the network therefore depends only upon the costs. The network N n wll be optmal when the actors are connected such that the sum of the costs of these connectons s mnmal. In graph theoretc terms ths means that the vertces V must be connected by a mnmumweght spannng tree (see e.g. Gbbons, 1985). Prm (1957) has shown that a mnmumweght spannng tree can be constructed by always fndng the shortest dstance between a vertex n the tree and one not n the tree and connectng the two. So, when we want to construct a network that serves the system at least costs, we should begn by selectng an arbtrary vertex and connect t to that vertex whch s nearest to t. Ths provdes the bass for answerng the queston we have rased above. As we have seen, nether based on the ndvdual nor based on the socal calculus wll want to establsh a network lnk to her nearest neghbor. Instead, she wll want to establsh a lnk to that actor that s nearest to the optmum dstance, where the latter dffers from zero when there exsts a range of dstances for whch a network lnk s desrable. So, the network that emerges from a mcroeconomc calculus rrespectve of whether t s based on ndvdual or socal costs and benefts wll not connect the actors at least costs. There mght always exst another set of connectons that yelds the same level of benefts at lower costs. As some expermentaton shows, the mutual best mechansm that we have dscussed may not even connect the actors by a tree. The resultng network may even dsplay loops. 4. Conclusons 12
14 Ths paper represents a frst step toward an economc analyss of the queston of the formaton of computer networks. Stmulated by the tremendous growth of the Internet, we try to nvestgate whch economc factors drve ths development toward global connectvty and how these factors nfluence the process of network formaton. In a frst part (secton 2) we develop a formal model of the key economc mechansms that drve network formaton. The model focuses on ndvdual mcroeconomc decsons based upon a comparson of costs of network lnks and benefts n the form of an ncrease n the nteracton potental. The model s stll farly smple, and there s room for mprovement. For example, the model does not take nto account capacty constrants, dfferences between actors, dfferent decson strateges, etc. In secton 3 we analyze the behavor of ths model and the mplcatons t has for the process of network formaton. We show under what condtons the economc ncentve s suffcent to ntate the process of network formaton, that there mght be constellatons where a network would be socally desrable, but the economc ncentves are nsuffcent to generate any network lnks, and that the economc process of network formaton does not lead to an optmal network topology. As has been mentoned above, we vew ths paper as a frst step n the drecton of the topc and ntend to develop more elaborated versons of the model later. Because of the complex relatonshps between the varous actors n the process of network formaton and because of network externaltes and capacty constrants, we wll probably have to use smulaton experments when analyzng these more complex model versons. 13
15 References Capello, Roberta, 1994: Spatal Economc Analyss of Telecommuncatons Network Externaltes. Avebury Castells, Manuel, 1996: The Rse of the Network Socety. Blackwell Gbbons, Alan, Algorthmc Graph Theory, Cambrdge, Cambrdge Unversty Press Gllespe, Andrew: Advanced communcatons networks, terrtoral ntegraton and local development. In: Camagn, Roberto (ed.), 1991: Innovaton networks  spatal perspectves. Belhaven Press; p MacLuhan, Marshall and Powers, Bruce R., 1992: The global vllage  transformatons n world lfe and meda n the 21st century. Oxford Unversty Press Prm, R. C., Shortest connecton networks and some generalzatons, Bell System Tech. Journal, Vol. 36, pp
16 Abtelung für Stadt und Regonalentwcklung Wrtschaftsunverstät Wen Abtelungsleter: o.unv.prof. Edward M. Bergman, PhD Roßauer Lände 23/3 A1090 Wen, Austra Tel.: /4777 Fax: /705 EMal:
benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationLuby s Alg. for Maximal Independent Sets using Pairwise Independence
Lecture Notes for Randomzed Algorthms Luby s Alg. for Maxmal Independent Sets usng Parwse Independence Last Updated by Erc Vgoda on February, 006 8. Maxmal Independent Sets For a graph G = (V, E), an ndependent
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationGraph Theory and Cayley s Formula
Graph Theory and Cayley s Formula Chad Casarotto August 10, 2006 Contents 1 Introducton 1 2 Bascs and Defntons 1 Cayley s Formula 4 4 Prüfer Encodng A Forest of Trees 7 1 Introducton In ths paper, I wll
More informationWeek 6 Market Failure due to Externalities
Week 6 Market Falure due to Externaltes 1. Externaltes n externalty exsts when the acton of one agent unavodably affects the welfare of another agent. The affected agent may be a consumer, gvng rse to
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationAn InterestOriented Network Evolution Mechanism for Online Communities
An InterestOrented Network Evoluton Mechansm for Onlne Communtes Cahong Sun and Xaopng Yang School of Informaton, Renmn Unversty of Chna, Bejng 100872, P.R. Chna {chsun,yang}@ruc.edu.cn Abstract. Onlne
More informationCan Auto Liability Insurance Purchases Signal Risk Attitude?
Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? ChuShu L Department of Internatonal Busness, Asa Unversty, Tawan ShengChang
More informationMoment of a force about a point and about an axis
3. STATICS O RIGID BODIES In the precedng chapter t was assumed that each of the bodes consdered could be treated as a sngle partcle. Such a vew, however, s not always possble, and a body, n general, should
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMISP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationOn the Optimal Control of a Cascade of HydroElectric Power Stations
On the Optmal Control of a Cascade of HydroElectrc Power Statons M.C.M. Guedes a, A.F. Rbero a, G.V. Smrnov b and S. Vlela c a Department of Mathematcs, School of Scences, Unversty of Porto, Portugal;
More informationThe Greedy Method. Introduction. 0/1 Knapsack Problem
The Greedy Method Introducton We have completed data structures. We now are gong to look at algorthm desgn methods. Often we are lookng at optmzaton problems whose performance s exponental. For an optmzaton
More informationLecture 3: Force of Interest, Real Interest Rate, Annuity
Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annutymmedate, and ts present value Study annutydue, and
More informationCommunication Networks II Contents
8 / 1  Communcaton Networs II (Görg)  www.comnets.unbremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP
More informationPROFIT RATIO AND MARKET STRUCTURE
POFIT ATIO AND MAKET STUCTUE By Yong Yun Introducton: Industral economsts followng from Mason and Ban have run nnumerable tests of the relaton between varous market structural varables and varous dmensons
More informationNonlinear data mapping by neural networks
Nonlnear data mappng by neural networks R.P.W. Dun Delft Unversty of Technology, Netherlands Abstract A revew s gven of the use of neural networks for nonlnear mappng of hgh dmensonal data on lower dmensonal
More informationEconomic Models for Cloud Service Markets
Economc Models for Cloud Servce Markets Ranjan Pal and Pan Hu 2 Unversty of Southern Calforna, USA, rpal@usc.edu 2 Deutsch Telekom Laboratores, Berln, Germany, pan.hu@telekom.de Abstract. Cloud computng
More informationBERNSTEIN POLYNOMIALS
OnLne Geometrc Modelng Notes BERNSTEIN POLYNOMIALS Kenneth I. Joy Vsualzaton and Graphcs Research Group Department of Computer Scence Unversty of Calforna, Davs Overvew Polynomals are ncredbly useful
More informationIntroduction: Analysis of Electronic Circuits
/30/008 ntroducton / ntroducton: Analyss of Electronc Crcuts Readng Assgnment: KVL and KCL text from EECS Just lke EECS, the majorty of problems (hw and exam) n EECS 3 wll be crcut analyss problems. Thus,
More informationThe Development of Web Log Mining Based on ImproveKMeans Clustering Analysis
The Development of Web Log Mnng Based on ImproveKMeans Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.
More information9 Arithmetic and Geometric Sequence
AAU  Busness Mathematcs I Lecture #5, Aprl 4, 010 9 Arthmetc and Geometrc Sequence Fnte sequence: 1, 5, 9, 13, 17 Fnte seres: 1 + 5 + 9 + 13 +17 Infnte sequence: 1,, 4, 8, 16,... Infnte seres: 1 + + 4
More informationJ. Parallel Distrib. Comput.
J. Parallel Dstrb. Comput. 71 (2011) 62 76 Contents lsts avalable at ScenceDrect J. Parallel Dstrb. Comput. journal homepage: www.elsever.com/locate/jpdc Optmzng server placement n dstrbuted systems n
More information7.5. Present Value of an Annuity. Investigate
7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 MultpleChoce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multplechoce questons. For each queston, only one of the answers s correct.
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More information"Research Note" APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES *
Iranan Journal of Scence & Technology, Transacton B, Engneerng, ol. 30, No. B6, 789794 rnted n The Islamc Republc of Iran, 006 Shraz Unversty "Research Note" ALICATION OF CHARGE SIMULATION METHOD TO ELECTRIC
More informationTrafficlight a stress test for life insurance provisions
MEMORANDUM Date 006097 Authors Bengt von Bahr, Göran Ronge Traffclght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax
More informationb) The mean of the fitted (predicted) values of Y is equal to the mean of the Y values: c) The residuals of the regression line sum up to zero: = ei
Mathematcal Propertes of the Least Squares Regresson The least squares regresson lne obeys certan mathematcal propertes whch are useful to know n practce. The followng propertes can be establshed algebracally:
More information+ + +   This circuit than can be reduced to a planar circuit
MeshCurrent Method The meshcurrent s analog of the nodeoltage method. We sole for a new set of arables, mesh currents, that automatcally satsfy KCLs. As such, meshcurrent method reduces crcut soluton to
More informationEvolution of Internet Infrastructure in the 21 st century: The Role of Private Interconnection Agreements
Evoluton of Internet Infrastructure n the 21 st century: The Role of Prvate Interconnecton Agreements Rajv Dewan*, Marshall Fremer, and Pavan Gundepud {dewan, fremer, gundepudpa}@ssb.rochester.edu Smon
More informationQuestions that we may have about the variables
Antono Olmos, 01 Multple Regresson Problem: we want to determne the effect of Desre for control, Famly support, Number of frends, and Score on the BDI test on Perceved Support of Latno women. Dependent
More informationState function: eigenfunctions of hermitian operators> normalization, orthogonality completeness
Schroednger equaton Basc postulates of quantum mechancs. Operators: Hermtan operators, commutators State functon: egenfunctons of hermtan operators> normalzaton, orthogonalty completeness egenvalues and
More informationHow Sets of Coherent Probabilities May Serve as Models for Degrees of Incoherence
1 st Internatonal Symposum on Imprecse Probabltes and Ther Applcatons, Ghent, Belgum, 29 June 2 July 1999 How Sets of Coherent Probabltes May Serve as Models for Degrees of Incoherence Mar J. Schervsh
More informationMultivariate EWMA Control Chart
Multvarate EWMA Control Chart Summary The Multvarate EWMA Control Chart procedure creates control charts for two or more numerc varables. Examnng the varables n a multvarate sense s extremely mportant
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More informationMaster s Thesis. Configuring robust virtual wireless sensor networks for Internet of Things inspired by brain functional networks
Master s Thess Ttle Confgurng robust vrtual wreless sensor networks for Internet of Thngs nspred by bran functonal networks Supervsor Professor Masayuk Murata Author Shnya Toyonaga February 10th, 2014
More informationSection B9: Zener Diodes
Secton B9: Zener Dodes When we frst talked about practcal dodes, t was mentoned that a parameter assocated wth the dode n the reverse bas regon was the breakdown voltage, BR, also known as the peaknverse
More informationThe Magnetic Field. Concepts and Principles. Moving Charges. Permanent Magnets
. The Magnetc Feld Concepts and Prncples Movng Charges All charged partcles create electrc felds, and these felds can be detected by other charged partcles resultng n electrc force. However, a completely
More informationNasdaq Iceland Bond Indices 01 April 2015
Nasdaq Iceland Bond Indces 01 Aprl 2015 Fxed duraton Indces Introducton Nasdaq Iceland (the Exchange) began calculatng ts current bond ndces n the begnnng of 2005. They were a response to recent changes
More informationThe impact of hard discount control mechanism on the discount volatility of UK closedend funds
Investment Management and Fnancal Innovatons, Volume 10, Issue 3, 2013 Ahmed F. Salhn (Egypt) The mpact of hard dscount control mechansm on the dscount volatlty of UK closedend funds Abstract The mpact
More informationFinancial Mathemetics
Fnancal Mathemetcs 15 Mathematcs Grade 12 Teacher Gude Fnancal Maths Seres Overvew In ths seres we am to show how Mathematcs can be used to support personal fnancal decsons. In ths seres we jon Tebogo,
More informationLecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression.
Lecture 3: Annuty Goals: Learn contnuous annuty and perpetuty. Study annutes whose payments form a geometrc progresson or a arthmetc progresson. Dscuss yeld rates. Introduce Amortzaton Suggested Textbook
More informationMultiplePeriod Attribution: Residuals and Compounding
MultplePerod Attrbuton: Resduals and Compoundng Our revewer gave these authors full marks for dealng wth an ssue that performance measurers and vendors often regard as propretary nformaton. In 1994, Dens
More informationStaff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall
SP 200502 August 2005 Staff Paper Department of Appled Economcs and Management Cornell Unversty, Ithaca, New York 148537801 USA Farm Savngs Accounts: Examnng Income Varablty, Elgblty, and Benefts Brent
More informationTHE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek
HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More information9.1 The Cumulative Sum Control Chart
Learnng Objectves 9.1 The Cumulatve Sum Control Chart 9.1.1 Basc Prncples: Cusum Control Chart for Montorng the Process Mean If s the target for the process mean, then the cumulatve sum control chart s
More informationGeneralizing the degree sequence problem
Mddlebury College March 2009 Arzona State Unversty Dscrete Mathematcs Semnar The degree sequence problem Problem: Gven an nteger sequence d = (d 1,...,d n ) determne f there exsts a graph G wth d as ts
More informationSolution of Algebraic and Transcendental Equations
CHAPTER Soluton of Algerac and Transcendental Equatons. INTRODUCTION One of the most common prolem encountered n engneerng analyss s that gven a functon f (, fnd the values of for whch f ( = 0. The soluton
More information8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by
6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng
More informationA Computer Technique for Solving LP Problems with Bounded Variables
Dhaka Unv. J. Sc. 60(2): 163168, 2012 (July) A Computer Technque for Solvng LP Problems wth Bounded Varables S. M. Atqur Rahman Chowdhury * and Sanwar Uddn Ahmad Department of Mathematcs; Unversty of
More information1 Approximation Algorithms
CME 305: Dscrete Mathematcs and Algorthms 1 Approxmaton Algorthms In lght of the apparent ntractablty of the problems we beleve not to le n P, t makes sense to pursue deas other than complete solutons
More informationProject Networks With MixedTime Constraints
Project Networs Wth MxedTme Constrants L Caccetta and B Wattananon Western Australan Centre of Excellence n Industral Optmsaton (WACEIO) Curtn Unversty of Technology GPO Box U1987 Perth Western Australa
More informationU.C. Berkeley CS270: Algorithms Lecture 4 Professor Vazirani and Professor Rao Jan 27,2011 Lecturer: Umesh Vazirani Last revised February 10, 2012
U.C. Berkeley CS270: Algorthms Lecture 4 Professor Vazran and Professor Rao Jan 27,2011 Lecturer: Umesh Vazran Last revsed February 10, 2012 Lecture 4 1 The multplcatve weghts update method The multplcatve
More informationRing structure of splines on triangulations
www.oeaw.ac.at Rng structure of splnes on trangulatons N. Vllamzar RICAMReport 201448 www.rcam.oeaw.ac.at RING STRUCTURE OF SPLINES ON TRIANGULATIONS NELLY VILLAMIZAR Introducton For a trangulated regon
More informationAryabhata s Root Extraction Methods. Abhishek Parakh Louisiana State University Aug 31 st 2006
Aryabhata s Root Extracton Methods Abhshek Parakh Lousana State Unversty Aug 1 st 1 Introducton Ths artcle presents an analyss of the root extracton algorthms of Aryabhata gven n hs book Āryabhatīya [1,
More informationIntrayear Cash Flow Patterns: A Simple Solution for an Unnecessary Appraisal Error
Intrayear Cash Flow Patterns: A Smple Soluton for an Unnecessary Apprasal Error By C. Donald Wggns (Professor of Accountng and Fnance, the Unversty of North Florda), B. Perry Woodsde (Assocate Professor
More informationMAPP. MERIS level 3 cloud and water vapour products. Issue: 1. Revision: 0. Date: 9.12.1998. Function Name Organisation Signature Date
Ttel: Project: Doc. No.: MERIS level 3 cloud and water vapour products MAPP MAPPATBDClWVL3 Issue: 1 Revson: 0 Date: 9.12.1998 Functon Name Organsaton Sgnature Date Author: Bennartz FUB Preusker FUB Schüller
More information17 Capital tax competition
17 Captal tax competton 17.1 Introducton Governments would lke to tax a varety of transactons that ncreasngly appear to be moble across jursdctonal boundares. Ths creates one obvous problem: tax base flght.
More informationSupport Vector Machines
Support Vector Machnes Max Wellng Department of Computer Scence Unversty of Toronto 10 Kng s College Road Toronto, M5S 3G5 Canada wellng@cs.toronto.edu Abstract Ths s a note to explan support vector machnes.
More informationInequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.
Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.
More informationANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING
ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING Matthew J. Lberatore, Department of Management and Operatons, Vllanova Unversty, Vllanova, PA 19085, 6105194390,
More informationWhat is Candidate Sampling
What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble
More informationSmall pots lump sum payment instruction
For customers Small pots lump sum payment nstructon Please read these notes before completng ths nstructon About ths nstructon Use ths nstructon f you re an ndvdual wth Aegon Retrement Choces Self Invested
More informationCHAPTER 14 MORE ABOUT REGRESSION
CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp
More informationA Probabilistic Theory of Coherence
A Probablstc Theory of Coherence BRANDEN FITELSON. The Coherence Measure C Let E be a set of n propostons E,..., E n. We seek a probablstc measure C(E) of the degree of coherence of E. Intutvely, we want
More informationOptimal Transfers and Participation Decisions in International Environmental Agreements 1
Optmal Transfers and Partcpaton Decsons n Internatonal Envronmental Agreements 1 by Carlo Carraro 2, Johan Eyckmans 3 and Mchael Fnus 4 Abstract The lterature on nternatonal envronmental agreements has
More informationEnergy Conserving Routing in Wireless Adhoc Networks
Energy Conservng Routng n Wreless Adhoc Networks JaeHwan Chang and Leandros Tassulas Department of Electrcal and Computer Engneerng & Insttute for Systems Research Unversty of Maryland at College ark
More informationHÜCKEL MOLECULAR ORBITAL THEORY
1 HÜCKEL MOLECULAR ORBITAL THEORY In general, the vast maorty polyatomc molecules can be thought of as consstng of a collecton of two electron bonds between pars of atoms. So the qualtatve pcture of σ
More informationNetwork Security Situation Evaluation Method for Distributed Denial of Service
Network Securty Stuaton Evaluaton Method for Dstrbuted Denal of Servce Jn Q,2, Cu YMn,2, Huang MnHuan,2, Kuang XaoHu,2, TangHong,2 ) Scence and Technology on Informaton System Securty Laboratory, Bejng,
More informationPassive Filters. References: Barbow (pp 265275), Hayes & Horowitz (pp 3260), Rizzoni (Chap. 6)
Passve Flters eferences: Barbow (pp 6575), Hayes & Horowtz (pp 360), zzon (Chap. 6) Frequencyselectve or flter crcuts pass to the output only those nput sgnals that are n a desred range of frequences (called
More informationNumber of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000
Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from
More informationFINANCIAL MATHEMATICS. A Practical Guide for Actuaries. and other Business Professionals
FINANCIAL MATHEMATICS A Practcal Gude for Actuares and other Busness Professonals Second Edton CHRIS RUCKMAN, FSA, MAAA JOE FRANCIS, FSA, MAAA, CFA Study Notes Prepared by Kevn Shand, FSA, FCIA Assstant
More information1. Measuring association using correlation and regression
How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a
More information1.1 The University may award Higher Doctorate degrees as specified from timetotime in UPR AS11 1.
HIGHER DOCTORATE DEGREES SUMMARY OF PRINCIPAL CHANGES General changes None Secton 3.2 Refer to text (Amendments to verson 03.0, UPR AS02 are shown n talcs.) 1 INTRODUCTION 1.1 The Unversty may award Hgher
More informationExtending Probabilistic Dynamic Epistemic Logic
Extendng Probablstc Dynamc Epstemc Logc Joshua Sack May 29, 2008 Probablty Space Defnton A probablty space s a tuple (S, A, µ), where 1 S s a set called the sample space. 2 A P(S) s a σalgebra: a set
More informationx f(x) 1 0.25 1 0.75 x 1 0 1 1 0.04 0.01 0.20 1 0.12 0.03 0.60
BIVARIATE DISTRIBUTIONS Let be a varable that assumes the values { 1,,..., n }. Then, a functon that epresses the relatve frequenc of these values s called a unvarate frequenc functon. It must be true
More informationEE201 Circuit Theory I 2015 Spring. Dr. Yılmaz KALKAN
EE201 Crcut Theory I 2015 Sprng Dr. Yılmaz KALKAN 1. Basc Concepts (Chapter 1 of Nlsson  3 Hrs.) Introducton, Current and Voltage, Power and Energy 2. Basc Laws (Chapter 2&3 of Nlsson  6 Hrs.) Voltage
More informationA hybrid global optimization algorithm based on parallel chaos optimization and outlook algorithm
Avalable onlne www.ocpr.com Journal of Chemcal and Pharmaceutcal Research, 2014, 6(7):18841889 Research Artcle ISSN : 09757384 CODEN(USA) : JCPRC5 A hybrd global optmzaton algorthm based on parallel
More informationVLSI Technology Dr. Nandita Dasgupta Department of Electrical Engineering Indian Institute of Technology, Madras
VLI Technology Dr. Nandta Dasgupta Department of Electrcal Engneerng Indan Insttute of Technology, Madras Lecture  11 Oxdaton I netcs of Oxdaton o, the unt process step that we are gong to dscuss today
More informationHedging InterestRate Risk with Duration
FIXEDINCOME SECURITIES Chapter 5 Hedgng InterestRate Rsk wth Duraton Outlne Prcng and Hedgng Prcng certan cashflows Interest rate rsk Hedgng prncples DuratonBased Hedgng Technques Defnton of duraton
More informationSPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:
SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and
More informationSIX WAYS TO SOLVE A SIMPLE PROBLEM: FITTING A STRAIGHT LINE TO MEASUREMENT DATA
SIX WAYS TO SOLVE A SIMPLE PROBLEM: FITTING A STRAIGHT LINE TO MEASUREMENT DATA E. LAGENDIJK Department of Appled Physcs, Delft Unversty of Technology Lorentzweg 1, 68 CJ, The Netherlands Emal: e.lagendjk@tnw.tudelft.nl
More informationAPPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT
APPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT Toshhko Oda (1), Kochro Iwaoka (2) (1), (2) Infrastructure Systems Busness Unt, Panasonc System Networks Co., Ltd. Saedocho
More informationNew bounds in BalogSzemerédiGowers theorem
New bounds n BalogSzemerédGowers theorem By Tomasz Schoen Abstract We prove, n partcular, that every fnte subset A of an abelan group wth the addtve energy κ A 3 contans a set A such that A κ A and A
More informationHollinger Canadian Publishing Holdings Co. ( HCPH ) proceeding under the Companies Creditors Arrangement Act ( CCAA )
February 17, 2011 Andrew J. Hatnay ahatnay@kmlaw.ca Dear Sr/Madam: Re: Re: Hollnger Canadan Publshng Holdngs Co. ( HCPH ) proceedng under the Companes Credtors Arrangement Act ( CCAA ) Update on CCAA Proceedngs
More informationAN APPROACH TO WIRELESS SCHEDULING CONSIDERING REVENUE AND USERS SATISFACTION
The Medterranean Journal of Computers and Networks, Vol. 2, No. 1, 2006 57 AN APPROACH TO WIRELESS SCHEDULING CONSIDERING REVENUE AND USERS SATISFACTION L. Bada 1,*, M. Zorz 2 1 Department of Engneerng,
More informationInequity Aversion and Individual Behavior in Public Good Games: An Experimental Investigation
Dscusson Paper No. 07034 Inequty Averson and Indvdual Behavor n Publc Good Games: An Expermental Investgaton Astrd Dannenberg, Thomas Rechmann, Bodo Sturm, and Carsten Vogt Dscusson Paper No. 07034 Inequty
More information1 Example 1: Axisaligned rectangles
COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture # 6 Scrbe: Aaron Schld February 21, 2013 Last class, we dscussed an analogue for Occam s Razor for nfnte hypothess spaces that, n conjuncton
More informationIDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS
IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS Chrs Deeley* Last revsed: September 22, 200 * Chrs Deeley s a Senor Lecturer n the School of Accountng, Charles Sturt Unversty,
More informationJoe Pimbley, unpublished, 2005. Yield Curve Calculations
Joe Pmbley, unpublshed, 005. Yeld Curve Calculatons Background: Everythng s dscount factors Yeld curve calculatons nclude valuaton of forward rate agreements (FRAs), swaps, nterest rate optons, and forward
More informationForecasting the Direction and Strength of Stock Market Movement
Forecastng the Drecton and Strength of Stock Market Movement Jngwe Chen Mng Chen Nan Ye cjngwe@stanford.edu mchen5@stanford.edu nanye@stanford.edu Abstract  Stock market s one of the most complcated systems
More informationThus, if the two coffee shops collude, then they will produce a level of output q m
Introductory Mcroeconomcs (ES10001) Exercse 9: Suggested Solutons 1. There are two coffee shops on campus facng an aggregate demand functon for cups of coffee of q d = 00 0 p. The coffee s dentcal and
More informationLogical Development Of Vogel s Approximation Method (LDVAM): An Approach To Find Basic Feasible Solution Of Transportation Problem
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME, ISSUE, FEBRUARY ISSN 77866 Logcal Development Of Vogel s Approxmaton Method (LD An Approach To Fnd Basc Feasble Soluton Of Transportaton
More informationGeneral Auction Mechanism for Search Advertising
General Aucton Mechansm for Search Advertsng Gagan Aggarwal S. Muthukrshnan Dávd Pál Martn Pál Keywords game theory, onlne auctons, stable matchngs ABSTRACT Internet search advertsng s often sold by an
More informationFREQUENCY OF OCCURRENCE OF CERTAIN CHEMICAL CLASSES OF GSR FROM VARIOUS AMMUNITION TYPES
FREQUENCY OF OCCURRENCE OF CERTAIN CHEMICAL CLASSES OF GSR FROM VARIOUS AMMUNITION TYPES Zuzanna BRO EKMUCHA, Grzegorz ZADORA, 2 Insttute of Forensc Research, Cracow, Poland 2 Faculty of Chemstry, Jagellonan
More informationPSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 12
14 The Chsquared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed
More informationLaddered Multilevel DC/AC Inverters used in Solar Panel Energy Systems
Proceedngs of the nd Internatonal Conference on Computer Scence and Electroncs Engneerng (ICCSEE 03) Laddered Multlevel DC/AC Inverters used n Solar Panel Energy Systems Fang Ln Luo, Senor Member IEEE
More informationIMPACT ANALYSIS OF A CELLULAR PHONE
4 th ASA & μeta Internatonal Conference IMPACT AALYSIS OF A CELLULAR PHOE We Lu, 2 Hongy L Bejng FEAonlne Engneerng Co.,Ltd. Bejng, Chna ABSTRACT Drop test smulaton plays an mportant role n nvestgatng
More information