On Union and Intersection of Fuzzy Soft Set

Size: px
Start display at page:

Download "On Union and Intersection of Fuzzy Soft Set"

Transcription

1 Dusmanta Kumar Sut et al Int. J. omp. Teh. ppl. Vol ISSN:9-609 On Unon and Interseton of uzzy Soft Set Trdv Jyot Neog Dusmanta Kumar Sut. Researh Sholar Department of Mathemats MJ Unversty Shllong Meghalaya emal : trdvjyot@gmal.om. ssstant Professor Department of Mathemats Jorhat Insttute of Sene and Tehnology Jorhat ssam emal : sutdk00@yahoo.om bstrat Molodtsov ntrodued the theory of soft sets whh an be seen as a new mathematal approah to vagueness. Maj et al. have further ntated several bas notons of soft set theory. They have also ntrodued the onept of fuzzy soft set a more generalzed onept whh s a ombnaton of fuzzy set and soft set. They ntrodued some propertes regardng fuzzy soft unon nterseton omplement of a fuzzy soft set DeMorgan Laws et. These results were further revsed and mproved by hmad and Kharal. They defned arbtrary fuzzy soft unon and nterseton and proved DeMorgan Inlusons and DeMorgan Laws n uzzy Soft Set Theory. In ths paper we gve some propostons on fuzzy soft unon and nterseton wth proof and examples. Usng the defnton of arbtrary fuzzy soft unon and nterseton proposed by hmad and Kharal we are gvng two more propostons wth proof and examples. We further gve the proof of DeMorgan Laws for a famly of fuzzy soft sets n a fuzzy soft lass proposed by hmad and Kharal and verfy these laws wth examples. Key words: Soft Set uzzy Soft Set uzzy Soft lass.. Introduton. In order to deal wth many omplated problems n the felds of engneerng soal sene eonoms medal sene et nvolvng unertantes lassal methods are found to be nadequate n reent tmes. Molodstov [7] ponted out that the mportant exstng theores vz. Probablty Theory uzzy Set Theory Intutonst uzzy Set Theory Rough Set Theory et. whh an be onsdered as mathematal tools for dealng wth unertantes have ther own dffultes. e further ponted out that the reason for these dffultes s possbly the nadequay of the parameterzaton tool of the theory. In 999 he proposed a new mathematal tool for dealng wth unertantes whh s free of the dffultes present n these theores. e ntrodued the novel onept of Soft Sets and establshed the fundamental results of the new theory. e also showed how Soft Set Theory s free from parameterzaton nadequay syndrome of uzzy Set Theory Rough Set Theory Probablty Theory et. Many of the establshed paradgms appear as speal ases of Soft Set Theory. In 00 P.K.Maj R.Bswas and.r.roy [6] studed the theory of soft sets ntated by Molodstov. They defned equalty of two soft sets subset and super set of a soft set omplement of a soft set null soft set and absolute soft set wth examples. Soft bnary operatons lke ND OR and also the operatons of unon nterseton were also defned. In 005 Pe and Mao [8] and hen et al. [] mproved the work of Maj et al. [ 6]. In 008 M.Irfan l eng eng Xaoyan LuWon Keun Mn M.Shabr [] gave some new notons suh as the restrted nterseton the restrted unon the restrted dfferene and the extended nterseton of two soft sets along wth a new noton of omplement of a soft set. In reent tmes researhes have ontrbuted a lot towards fuzzfaton of Soft Set Theory. Maj et al. [5] ntrodued some propertes regardng fuzzy soft unon nterseton omplement of a fuzzy soft set DeMorgan Law et. These results were further revsed and mproved by hmad and Kharal []. They defned arbtrary fuzzy soft unon and nterseton and proved DeMorgan Inlusons and DeMorgan Laws n uzzy Soft Set Theory. IJT SPT-OT 0 valable onlne@ 60

2 Dusmanta Kumar Sut et al Int. J. omp. Teh. ppl. Vol ISSN:9-609 In ths paper we gve the proof of some propostons ntrodued by hmad and Kharal [] and support them wth examples. We further gve some more propostons regardng fuzzy soft unon and nterseton and support these propostons wth proof and examples. Defnton. [7] par E s alled a soft set over U f and only f s a mappng of E nto the set of all subsets of the set U. In other words the soft set s a parameterzed famly of subsets of the set U. Every set E from ths famly may be onsdered as the set of - elements of the soft set E or as the set of - approxmate elements of the soft set. Example. Let U { } be the set of four ars under onsderaton and E { e ostly e Beautful e uel Effent e ModernTehnology e 5 Luxurous} be the set of parameters and { e e e } E. Then { e { }e { }e { }} s the soft set representng the attratveness of the ar whh Mr. X s gong to buy. We an represent ths soft set n a tabular form as shown below [].Ths style of representaton wll be useful for storng a soft set n a omputer memory. U e e e Defnton. [5] par s alled a fuzzy soft set over U where : P U s a mappng from nto P U. Example. Let U { } be the set of four ars under onsderaton and E { e ostly e Beautful e uel Effent e ModernTehnology e 5 Luxurous} be the set of parameters and { e e e } E. Then { e { /0.7 /0. /0. /0.6} e { /0.8 /0.6 /0. /0.5} e { /0. /0. /0.7 /0.}} s the fuzzy soft set representng the attratveness of the ar whh Mr. X s gong to buy. Defnton. [] Let U be a unverse and E a set of attrbutes. Then the par U E denotes the olleton of all fuzzy soft sets on U wth attrbutes from E and s alled a fuzzy soft lass. Defnton. [5] or two fuzzy soft sets and G B n a fuzzy soft lass U E we say that s a fuzzy soft subset of G B f B or all G and s wrtten as G B. IJT SPT-OT 0 valable onlne@ 6

3 Dusmanta Kumar Sut et al Int. J. omp. Teh. ppl. Vol ISSN:9-609 Example. Let { } the set of four ars under onsderaton and { e ostly e Beautful e uel Effent e ModernTehnology e Luxurous} U be E 5 be the set of parameters { e e e } E and B { e e e e 5 } E. Then { e { /0.7 /0. /0. /0.6} e { /0.8 /0.6 /0. /0.5} e { /0. /0. /0.7 /0.}} s the fuzzy soft set representng the attratveness of the ar whh Mr. X s gong to buy and G B { Ge { /0.7 /0. /0. /0.7} Ge { /0.9 /0.6 /0.5 /} Ge { /0. /0. /0.8 /0.} Ge 5 { /0. /0. /0.7 /0.}} s the fuzzy soft set representng the attratveness of the ar whh Mr. Y s gong to buy. ere B and for all G. Thus G B. Defnton 5. [5] The omplement of a fuzzy soft set s denoted by and s defned by where : P U s a mappng gven by σ σ for all σ. Example. Let U { } be the set of four ars under onsderaton and E { e ostly e Beautful e uel Effent e ModernTehnology e 5 Luxurous} be the set of parameters and { e e e } E. Then { e { /0.7 /0. /0. /0.6} e { /0.8 /0.6 /0. /0.5} e { /0. /0. /0.7 /0.}} s the fuzzy soft set representng the attratveness of the ar whh Mr. X s gong to buy. ere { e { /0. /0.9 /0.8 /0.} e { /0. /0. /0.9 /0.5} e { /0.9 /0.8 /0. /0.7}} Defnton 6. [5] Unon of two fuzzy soft sets and G B n a soft lass U E s a fuzzy soft set where B and f x B G f x B G f x B G B. and s wrtten as IJT SPT-OT 0 valable onlne@ 6

4 Dusmanta Kumar Sut et al Int. J. omp. Teh. ppl. Vol ISSN:9-609 Example 5. Let { } U be the set of four ars under onsderaton and { e ostly e Beautful e uel Effent e ModernTehnology e Luxurous} E 5 be the set of parameters { e e e } E and B { e e e e 5 } E. We onsder the fuzzy soft sets { e { /0.9 /0. /0. /0.6} e { / /0 /0.9 /0.5} e { /0.8 /0. /0.7 /0.6}} and G B { Ge { /0.7 /0. /0. /0.7} Ge { /0.9 /0.6 /0.5 /} Ge { /0. /0. /0.8 /0.} Ge 5 { /0. /0. /0.7 /0.}} G B where B {e e e e 5 } and Then { e { /0.9 /0. /0. /0.7} e { / /0.6 /0.9 /} e { /0.8 /0. /0.8 /0.6} e 5 { /0. /0. /0.7 /0.}} Defnton 7. [5] Interseton of two fuzzy soft sets and G B n a soft lass U E s a fuzzy soft set where B and or G as both are same fuzzy set and s wrtten as G B. hmad and Kharal [] ponted out that generally or G may not be dental. Moreover n order to avod the degenerate ase he proposed that defnton as follows. B must be non-empty and thus revsed the above Defnton 8. [] Let and G B be two fuzzy soft sets n a soft lass U E wth B φ.then Interseton of two fuzzy soft sets and G B n a soft lass U E s a fuzzy soft set where B and G. We wrte G B. Example 6. or the two fuzzy soft sets and G B gven n Example 5 G B where B { e e e } and { e { /0.7 /0. /0. /0.6} e { /0.9 /0 /0.5 /0.5} e { /0. /0. /0.7 /0.}}. Some Propostons on uzzy Soft Unon and Interseton. hmad and Kharal [] gave some propostons on fuzzy soft unon and nterseton. ere we gve the proof of those propostons along wth some addtonal propostons. Let and be three fuzzy soft sets n a soft lass U E. IJT SPT-OT 0 valable onlne@ 6

5 ommutatve Property. Proof. Let Where and gan let Where and learly and. Thus. Let Where and f f f gan let Where and f f f. Thus and ene. ssoatve Property. Proof. Let and Where and nd gan let and Where and nd Dusmanta Kumar Sut et al Int. J. omp. Teh. ppl. Vol IJT SPT-OT 0 valable onlne@ 6 ISSN:9-609

6 Dusmanta Kumar Sut et al Int. J. omp. Teh. ppl. Vol ISSN:9-609 It s lear that and Thus Let and and Where.. ase I. When.. ase II When f f.. f ase III When Now When by Thus.. When by Thus..5 When by Thus..6 gan Let and Where and..7 ase I When f f..8 f ase II When..9 IJT SPT-OT 0 valable onlne@ 65

7 Dusmanta Kumar Sut et al Int. J. omp. Teh. ppl. Vol ISSN:9-609 ase III When When by 8 Thus.e...0 When by 8 Thus.e... When by 8 Thus.e... Now when by nd by 8 When When by by 8 { ` } by by 9 When IJT SPT-OT 0 valable onlne@ 66

8 Dusmanta Kumar Sut et al Int. J. omp. Teh. ppl. Vol ISSN:9-609 { } When { } by by When When by and by 8 When by 5 by 0 When by 6 nd by Thus Idempotent Property. IJT SPT-OT 0 valable onlne@ 67

9 Dusmanta Kumar Sut et al Int. J. omp. Teh. ppl. Vol ISSN:9-609 Proof. Let Where and Thus Let Where and Thus v bsorpton Property. Proof. Let and f Where and f f lso and Now f nd f Thus Let and Where and lso and Thus v Dstrbutve Property. Proof. Let and Where Let where IJT SPT-OT 0 valable onlne@ 68

10 Dusmanta Kumar Sut et al Int. J. omp. Teh. ppl. Vol ISSN:9-609 ase I. When ase - II When ase - III When Let and 5 5 Where 5 When ase I. 5 When 5 When ase II. 5 When 5 When ase III. 5 When 5 When IJT SPT-OT 0 valable onlne@ 69

11 Dusmanta Kumar Sut et al Int. J. omp. Teh. ppl. Vol ISSN:9-609 It s lear from above that Ths an be proved n a smlar way. v Proof. Let where and Now and Thus. The other result an also be proved n a smlar way. Let where f nd f f f - Now and f Thus Thus. The other result an also be proved n a smlar way. v Proof. Let. Then Now let and. Then as nd as Thus Let. Then and Now let. Then as nd as Thus IJT SPT-OT 0 valable onlne@ 70

12 Dusmanta Kumar Sut et al Int. J. omp. Teh. ppl. Vol ISSN:9-609 Defnton 9. [] Let I { I} be a famly of fuzzy soft sets n a fuzzy soft lass U E.Then the unon of fuzzy soft sets n I s a fuzzy soft set where and for all f Where ϕ f Example 7. Let U { } be the set of four ars under onsderaton and E { e ostly e Beautful e uel Effent e ModernTehnology e 5 Luxurous} be the set of parameters and { e e e } E { e e } E { e e e e } E. We onsder three fuzzy soft sets and as follows. { e { /0.7 /0. /0. /0.6} e { /0.8 /0.6 /0. /0.5} e { /0. /0. /0.7 /0.}} { e { /0. /0.6 /0. /0.6} e { /0.8 /0. /0. /0.5}} { e { /0. /0. /0.5 /0} e { /0. /0.9 /0.5 /0.5} e { /0. /0. /0.6 /0.} e { /0.8 /0. /0.5 /0.}} Thus where { e e e e } and { e { /0.7 /0.6 /0.5 /0.6} e { /0.8 /0.9 /0.5 /0.5} e { /0. /0. /0.7 /0.} e { /0.8 /0. /0.5 /0.5}} Defnton 0. [] Let I { I} be a famly of fuzzy soft sets n a fuzzy soft lass U Ewth ϕ.then the nterseton of fuzzy soft sets n I s a fuzzy soft set where and for all IJT SPT-OT 0 valable onlne@ 7

13 Dusmanta Kumar Sut et al Int. J. omp. Teh. ppl. Vol ISSN:9-609 Example 8. U Let { } be the set of four ars under onsderaton and { e ostly e Beautful e uel Effent e ModernTehnology e Luxurous} E 5 be the set of parameters and { e e e } E { e e } E { e e e e } E. We onsder three fuzzy soft sets and as follows. { e { /0.7 /0. /0. /0.6} e { /0.8 /0.6 /0. /0.5} e { /0. /0. /0.7 /0.}} { e { /0. /0.6 /0. /0.6} e { /0.8 /0. /0. /0.5}} { e { /0. /0. /0.5 /0} e { /0. /0.9 /0.5 /0.5} e { /0. /0. /0.6 /0.} e { /0.8 /0. /0.5 /0.}} Thus where { e } and { e { /0. /0. /0. /0}} ollowng the defntons 9 and 0 we now propose the followng two propostons. Proposton. Let I { I} be a famly of fuzzy soft sets n a fuzzy soft lass U E.Then I Proof. Let where and α I α α where α f α α ϕ f α learly.e and α I α α.e. α α Thus I Example 9. or the three fuzzy soft sets and gven n Example 7 we see that where { e e e e } and { e { /0.7 /0.6 /0.5 /0.6} e { /0.8 /0.9 /0.5 /0.5} e { /0. /0. /0.7 /0.} e { /0.8 /0. /0.5 /0.5}} Thus and for IJT SPT-OT 0 valable onlne@ 7

14 Dusmanta Kumar Sut et al Int. J. omp. Teh. ppl. Vol ISSN:9-609 Proposton 5. Let I { I} be a famly of fuzzy soft sets n a fuzzy soft lass U E.Then I Proof. Suppose that where and α I α α Now and α I α α α Thus α α α and hene the result follows. Example 0. or the three fuzzy soft sets and gven n Example 8 we see that where { e } and { e { /0. /0. /0. /0}. Thus and for. hmad and Kharal [] proved DeMorgan Laws for soft sets and G n a soft lass U E. e further generalzed DeMorgan Laws for a famly of fuzzy soft sets n a fuzzy soft lass U E as follows- Theorem. [] Let I { I} be a famly of fuzzy soft sets n a fuzzy soft lass U E.Then one has the followng -.. ere we gve the proof of ths theorem. Proof..We have say Where α α α... gan suppose that I.Then I I where IJT SPT-OT 0 valable onlne@ 7

15 Dusmanta Kumar Sut et al Int. J. omp. Teh. ppl. Vol ISSN:9-609 I α [ I α ] α α we have I α α α... rom and we get the desred result.. We have say where α α α gan suppose that I.Then I I where I α [ I α ] α α we have I α α α rom and we get the desred result. Example. Let U { } be the set of four ars under onsderaton and E { e ostly e Beautful e uel Effent e ModernTehnology e 5 Luxurous} be the set of parameters and { e e } E We onsder three fuzzy soft sets and as follows. { e { /0.7 /0. /0. /0.6} e { /0.8 /0.6 /0. /0.5}} { e { /0. /0.9 /0.8 /0.} e { /0. /0. /0.9 /0.5}} { e { /0. /0.6 /0. /0.6} e { /0.8 /0. /0. /0.5}} { e { /0.6 /0. /0.9 /0.} e { /0. /0.9 /0.6 /0.5}} IJT SPT-OT 0 valable onlne@ 7

16 Dusmanta Kumar Sut et al Int. J. omp. Teh. ppl. Vol ISSN:9-609 { e { /0. /0. /0.5 /0} e { /0.8 /0. /0.5 /0.}} { e { /0.8 /0.7 /0.5 /} e { /0. /0.7 /0.5 /0.9}} Thus where { e { /0.7 /0.6 /0.5 /0.6} e { /0.8 /0.6 /0.5 /0.5}} { e { /0. /0. /0.5 /0.} e { /0. /0. /0.5 /0.5}} and where { e { /0. /0. /0. /0} e { /0.8 /0. /0. /0.}} { e { /0.8 /0.9 /0.9 /} e { /0. /0.9 /0.9 /0.9}} Now I { I e { /0.8 /0.9 /0.9 /} I e { /0. /0.9 /0.9 /0.9}} nd J {J e { /0. /0. /0.5 /0.} J e { /0. /0. /0.5 /0.5}} It s lear that. onluson. The Soft Set Theory of Molodstov [7] offers a general mathematal tool for dealng wth unertan and vague objets. t present work on the extenson of soft set theory s progressng rapdly. Maj et al. [5] proposed the onept of fuzzy soft set and developed some propertes of fuzzy soft sets and n reent years the researhers have ontrbuted a lot towards the fuzzfaton of Soft Set Theory. Ths paper ontrbutes some more propertes regardng fuzzy soft unon and nterseton and support these propostons wth proof and examples. We further gve the proof of some propostons ntrodued by hmad and Kharal [] and support them wth examples. We hope that our fndngs wll help enhanng ths study on fuzzy soft sets. and IJT SPT-OT 0 valable onlne@ 75

17 Dusmanta Kumar Sut et al Int. J. omp. Teh. ppl. Vol ISSN:9-609 Referenes. hmad B and Kharal thar On uzzy Soft Sets dvanes n uzzy Systems Volume l M.I eng Lu XY Mn WK Shabr M 009 On some new operatons n soft set theory. omputers and Mathemats wth pplatons 57: hen D Tsang E Yeung D S and Wang X The parameterzaton reduton of soft sets and ts applatons omputers & Mathemats wth pplatons vol. 9 no.5-6 pp Maj P K and Roy R n pplaton of Soft Sets n Deson Makng Problem omputers and Mathemats wth pplatons Maj P K Bswas R and Roy R uzzy Soft Sets Journal of uzzy Mathemats Vol 9 no.pp Maj P K and Roy R Soft Set Theory omputers and Mathemats wth pplatons Molodstov D Soft Set Theory - rst Result omputers and Mathemats wth pplatons Pe D and Mao D rom soft sets to nformaton systems n Proeedngs of the IEEE Internatonal onferene on Granular omputng vol. pp IJT SPT-OT 0 valable onlne@ 76

Data Analysis with Fuzzy Measure on Intuitionistic Fuzzy Sets

Data Analysis with Fuzzy Measure on Intuitionistic Fuzzy Sets Proeedngs of the Internatonal MultConferene of Engneers and Computer Sentsts 2016 Vol II Marh 16-18 2016 Hong Kong Data nalyss wth Fuzzy Measure on Intutonst Fuzzy Sets Sanghyuk Lee * Ka Lok Man Eng Gee

More information

Series Solutions of ODEs 2 the Frobenius method. The basic idea of the Frobenius method is to look for solutions of the form 3

Series Solutions of ODEs 2 the Frobenius method. The basic idea of the Frobenius method is to look for solutions of the form 3 Royal Holloway Unversty of London Department of Physs Seres Solutons of ODEs the Frobenus method Introduton to the Methodology The smple seres expanson method works for dfferental equatons whose solutons

More information

v a 1 b 1 i, a 2 b 2 i,..., a n b n i.

v a 1 b 1 i, a 2 b 2 i,..., a n b n i. SECTION 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS 455 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS All the vector spaces we have studed thus far n the text are real vector spaces snce the scalars are

More information

Extending Probabilistic Dynamic Epistemic Logic

Extending 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 σ-algebra: a set

More information

8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by

8.5 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 information

What is Candidate Sampling

What 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 information

Luby s Alg. for Maximal Independent Sets using Pairwise Independence

Luby 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 information

Recurrence. 1 Definitions and main statements

Recurrence. 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 information

Behavior Coordination in E-commerce Supply Chains

Behavior Coordination in E-commerce Supply Chains Assoaton for Informaton ystems AI Eletron Lbrary AIeL) WHICEB 25 Proeedngs Wuhan Internatonal Conferene on e-busness ummer 6-9-25 Behavor Coordnaton n E-ommere upply Chans Yanhong Zhang Insttute of system

More information

We are now ready to answer the question: What are the possible cardinalities for finite fields?

We are now ready to answer the question: What are the possible cardinalities for finite fields? Chapter 3 Fnte felds We have seen, n the prevous chapters, some examples of fnte felds. For example, the resdue class rng Z/pZ (when p s a prme) forms a feld wth p elements whch may be dentfed wth the

More information

BERNSTEIN POLYNOMIALS

BERNSTEIN POLYNOMIALS On-Lne 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 information

Generalizing the degree sequence problem

Generalizing 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 information

Figure 1. Inventory Level vs. Time - EOQ Problem

Figure 1. Inventory Level vs. Time - EOQ Problem IEOR 54 Sprng, 009 rof Leahman otes on Eonom Lot Shedulng and Eonom Rotaton Cyles he Eonom Order Quantty (EOQ) Consder an nventory tem n solaton wth demand rate, holdng ost h per unt per unt tme, and replenshment

More information

A Probabilistic Theory of Coherence

A 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 information

How To Understand The Results Of The German Meris Cloud And Water Vapour Product

How To Understand The Results Of The German Meris Cloud And Water Vapour Product Ttel: Project: Doc. No.: MERIS level 3 cloud and water vapour products MAPP MAPP-ATBD-ClWVL3 Issue: 1 Revson: 0 Date: 9.12.1998 Functon Name Organsaton Sgnature Date Author: Bennartz FUB Preusker FUB Schüller

More information

1 Example 1: Axis-aligned rectangles

1 Example 1: Axis-aligned 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 information

On the Algebraic Structures of Soft Sets in Logic

On the Algebraic Structures of Soft Sets in Logic Applied Mathematical Sciences, Vol. 8, 2014, no. 38, 1873-1881 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.43127 On the Algebraic Structures of Soft Sets in Logic Burak Kurt Department

More information

Vision Mouse. Saurabh Sarkar a* University of Cincinnati, Cincinnati, USA ABSTRACT 1. INTRODUCTION

Vision Mouse. Saurabh Sarkar a* University of Cincinnati, Cincinnati, USA ABSTRACT 1. INTRODUCTION Vson Mouse Saurabh Sarkar a* a Unversty of Cncnnat, Cncnnat, USA ABSTRACT The report dscusses a vson based approach towards trackng of eyes and fngers. The report descrbes the process of locatng the possble

More information

Loop Parallelization

Loop Parallelization - - Loop Parallelzaton C-52 Complaton steps: nested loops operatng on arrays, sequentell executon of teraton space DECLARE B[..,..+] FOR I :=.. FOR J :=.. I B[I,J] := B[I-,J]+B[I-,J-] ED FOR ED FOR analyze

More information

An Interest-Oriented Network Evolution Mechanism for Online Communities

An Interest-Oriented Network Evolution Mechanism for Online Communities An Interest-Orented 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 information

A hybrid global optimization algorithm based on parallel chaos optimization and outlook algorithm

A 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):1884-1889 Research Artcle ISSN : 0975-7384 CODEN(USA) : JCPRC5 A hybrd global optmzaton algorthm based on parallel

More information

Cyber-Security Via Computing With Words

Cyber-Security Via Computing With Words Cyber-Seurty Va Computng Wth Words John. Rkard Dstrbuted Infnty, In. 4637 Shoshone Drve Larkspur, CO 808 Emal: trkard@dstrbutednfnty.om ABSRAC Cyber-seurty systems must deal wth a hgh rate of observable

More information

21 Vectors: The Cross Product & Torque

21 Vectors: The Cross Product & Torque 21 Vectors: The Cross Product & Torque Do not use our left hand when applng ether the rght-hand rule for the cross product of two vectors dscussed n ths chapter or the rght-hand rule for somethng curl

More information

Using Series to Analyze Financial Situations: Present Value

Using 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 information

CONSIDER a connected network of n nodes that all wish

CONSIDER a connected network of n nodes that all wish 36 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 60, NO. 2, FEBRUARY 204 Coded Cooperatve Data Exhange n Multhop Networks Thomas A. Courtade, Member, IEEE, and Rhard D. Wesel, Senor Member, IEEE Abstrat

More information

On Lockett pairs and Lockett conjecture for π-soluble Fitting classes

On Lockett pairs and Lockett conjecture for π-soluble Fitting classes On Lockett pars and Lockett conjecture for π-soluble Fttng classes Lujn Zhu Department of Mathematcs, Yangzhou Unversty, Yangzhou 225002, P.R. Chna E-mal: ljzhu@yzu.edu.cn Nanyng Yang School of Mathematcs

More information

A Novel Methodology of Working Capital Management for Large. Public Constructions by Using Fuzzy S-curve Regression

A Novel Methodology of Working Capital Management for Large. Public Constructions by Using Fuzzy S-curve Regression Novel Methodology of Workng Captal Management for Large Publc Constructons by Usng Fuzzy S-curve Regresson Cheng-Wu Chen, Morrs H. L. Wang and Tng-Ya Hseh Department of Cvl Engneerng, Natonal Central Unversty,

More information

Computer Administering of the Psychological Investigations: Set-Relational Representation

Computer Administering of the Psychological Investigations: Set-Relational Representation Open Journal of Appled Senes 2012 2 110-114 do:10.4236/ojapps.2012.22015 Publshed Onlne June 2012 (http://www.srp.org/journal/ojapps) Coputer Adnsterng of the Psyhologal Investgatons: Set-Relatonal Representaton

More information

The Greedy Method. Introduction. 0/1 Knapsack Problem

The 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 information

A Secure Password-Authenticated Key Agreement Using Smart Cards

A Secure Password-Authenticated Key Agreement Using Smart Cards A Secure Password-Authentcated Key Agreement Usng Smart Cards Ka Chan 1, Wen-Chung Kuo 2 and Jn-Chou Cheng 3 1 Department of Computer and Informaton Scence, R.O.C. Mltary Academy, Kaohsung 83059, Tawan,

More information

1.1 The University may award Higher Doctorate degrees as specified from time-to-time in UPR AS11 1.

1.1 The University may award Higher Doctorate degrees as specified from time-to-time 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 information

Hollinger Canadian Publishing Holdings Co. ( HCPH ) proceeding under the Companies Creditors Arrangement Act ( CCAA )

Hollinger 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 information

benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).

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 information

How To Calculate The Accountng Perod Of Nequalty

How To Calculate The Accountng Perod Of Nequalty 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 information

Project Networks With Mixed-Time Constraints

Project Networks With Mixed-Time Constraints Project Networs Wth Mxed-Tme 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 information

1. Measuring association using correlation and regression

1. 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 information

Performance Management and Evaluation Research to University Students

Performance Management and Evaluation Research to University Students 631 A publcaton of CHEMICAL ENGINEERING TRANSACTIONS VOL. 46, 2015 Guest Edtors: Peyu Ren, Yancang L, Hupng Song Copyrght 2015, AIDIC Servz S.r.l., ISBN 978-88-95608-37-2; ISSN 2283-9216 The Italan Assocaton

More information

Chapter 6. Demand Relationships Among Goods

Chapter 6. Demand Relationships Among Goods Chapter 6 Demand Relatonshps Among Goods Up to ths pont, we have held the pre of other goods onstant. Now we onsder how hanges n p affet n a two-good world. I p I p I p I p p p ( ) ( ) then I p then (

More information

"Research Note" APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES *

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, 789-794 rnted n The Islamc Republc of Iran, 006 Shraz Unversty "Research Note" ALICATION OF CHARGE SIMULATION METHOD TO ELECTRIC

More information

Forecasting the Direction and Strength of Stock Market Movement

Forecasting 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 information

International Journal of Mathematical Archive-7(5), 2016, 193-198 Available online through www.ijma.info ISSN 2229 5046

International Journal of Mathematical Archive-7(5), 2016, 193-198 Available online through www.ijma.info ISSN 2229 5046 Inernaonal Journal of Mahemacal rchve-75), 06, 9-98 valable onlne hrough wwwjmanfo ISSN 9 506 NOTE ON FUZZY WEKLY OMPLETELY PRIME - IDELS IN TERNRY SEMIGROUPS U NGI REDDY *, Dr G SHOBHLTH Research scholar,

More information

+ + + - - This circuit than can be reduced to a planar circuit

+ + + - - 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 information

Use of Multi-attribute Utility Functions in Evaluating Security Systems

Use of Multi-attribute Utility Functions in Evaluating Security Systems LLNL-TR-405048 Use of Mult-attrbute Utlty Funtons n Evaluatng Seurty Systems C. Meyers, A. Lamont, A. Sherman June 30, 2008 Ths doument was prepared as an aount of work sponsored by an ageny of the Unted

More information

CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol

CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL

More information

Conversion between the vector and raster data structures using Fuzzy Geographical Entities

Conversion between the vector and raster data structures using Fuzzy Geographical Entities Converson between the vector and raster data structures usng Fuzzy Geographcal Enttes Cdála Fonte Department of Mathematcs Faculty of Scences and Technology Unversty of Combra, Apartado 38, 3 454 Combra,

More information

Canon NTSC Help Desk Documentation

Canon NTSC Help Desk Documentation Canon NTSC Help Desk Documentaton READ THIS BEFORE PROCEEDING Before revewng ths documentaton, Canon Busness Solutons, Inc. ( CBS ) hereby refers you, the customer or customer s representatve or agent

More information

When can bundling help adoption of network technologies or services?

When can bundling help adoption of network technologies or services? When an bundlng help adopton of network tehnologes or serves? Steven Weber Dept. of ECE, Drexel U. sweber@oe.drexel.edu Roh Guérn Dept. of CSE, WUSTL guern@wustl.edu Jaudele C. de Olvera Dept. of ECE,

More information

Application of Fuzzy Soft Set Theory in Day to Day Problems

Application of Fuzzy Soft Set Theory in Day to Day Problems pplication of uzzy Soft Set Theory in Day to Day Problems Krishna ogoi Devicharan Barua irls College, Jorhat, ssam lock Kr. Dutta Bahona College, Bahona, Jorhat, ssam Chandra Chutia Jorhat Institute of

More information

Implementation of Deutsch's Algorithm Using Mathcad

Implementation of Deutsch's Algorithm Using Mathcad Implementaton of Deutsch's Algorthm Usng Mathcad Frank Roux The followng s a Mathcad mplementaton of Davd Deutsch's quantum computer prototype as presented on pages - n "Machnes, Logc and Quantum Physcs"

More information

Embedding lattices in the Kleene degrees

Embedding lattices in the Kleene degrees F U N D A M E N T A MATHEMATICAE 62 (999) Embeddng lattces n the Kleene degrees by Hsato M u r a k (Nagoya) Abstract. Under ZFC+CH, we prove that some lattces whose cardnaltes do not exceed ℵ can be embedded

More information

Study on Model of Risks Assessment of Standard Operation in Rural Power Network

Study on Model of Risks Assessment of Standard Operation in Rural Power Network Study on Model of Rsks Assessment of Standard Operaton n Rural Power Network Qngj L 1, Tao Yang 2 1 Qngj L, College of Informaton and Electrcal Engneerng, Shenyang Agrculture Unversty, Shenyang 110866,

More information

An Alternative Way to Measure Private Equity Performance

An 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 information

Peer-to-peer systems have attracted considerable attention

Peer-to-peer systems have attracted considerable attention Reputaton Aggregaton n Peer-to-Peer etwork Usng Dfferental Gossp Algorthm Ruhr Gupta, Yatndra ath Sngh, Senor Member, IEEE, arxv:20.430v4 [s.i] 28 Jan 204 Abstrat Reputaton aggregaton n peer to peer networks

More information

Forecasting the Demand of Emergency Supplies: Based on the CBR Theory and BP Neural Network

Forecasting the Demand of Emergency Supplies: Based on the CBR Theory and BP Neural Network 700 Proceedngs of the 8th Internatonal Conference on Innovaton & Management Forecastng the Demand of Emergency Supples: Based on the CBR Theory and BP Neural Network Fu Deqang, Lu Yun, L Changbng School

More information

Pricing System Security in Electricity Markets. latter might lead to high prices as a result of unrealistic

Pricing System Security in Electricity Markets. latter might lead to high prices as a result of unrealistic 1 Pro. Bulk Power Systems Dynams and Control{V, Onomh, Japan, August 2001. Prng System Seurty n Eletrty Markets Claudo A. Ca~nzares Hong Chen Wllam Rosehart UnverstyofWaterloo Unversty of Calgary Dept.

More information

Ring structure of splines on triangulations

Ring structure of splines on triangulations www.oeaw.ac.at Rng structure of splnes on trangulatons N. Vllamzar RICAM-Report 2014-48 www.rcam.oeaw.ac.at RING STRUCTURE OF SPLINES ON TRIANGULATIONS NELLY VILLAMIZAR Introducton For a trangulated regon

More information

FLASH POINT DETERMINATION OF BINARY MIXTURES OF ALCOHOLS, KETONES AND WATER. P.J. Martínez, E. Rus and J.M. Compaña

FLASH POINT DETERMINATION OF BINARY MIXTURES OF ALCOHOLS, KETONES AND WATER. P.J. Martínez, E. Rus and J.M. Compaña FLASH POINT DETERMINATION OF BINARY MIXTURES OF ALCOHOLS, KETONES AND WATER Abstract P.J. Martínez, E. Rus and J.M. Compaña Departamento de Ingenería Químca. Facultad de Cencas. Unversdad de Málaga. 29071

More information

`Will it snow tomorrow?' `What are our chances of winning the lottery?' What is the time between emission of alpha particles by a radioactive source?

`Will it snow tomorrow?' `What are our chances of winning the lottery?' What is the time between emission of alpha particles by a radioactive source? Notes for Chapter of DeGroot and Schervsh The world s full of random events that we seek to understand. x. `Wll t snow tomorrow?' `What are our chances of wnnng the lottery?' What s the tme between emsson

More information

The OC Curve of Attribute Acceptance Plans

The 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

1 De nitions and Censoring

1 De nitions and Censoring De ntons and Censorng. Survval Analyss We begn by consderng smple analyses but we wll lead up to and take a look at regresson on explanatory factors., as n lnear regresson part A. The mportant d erence

More information

PERRON FROBENIUS THEOREM

PERRON FROBENIUS THEOREM PERRON FROBENIUS THEOREM R. CLARK ROBINSON Defnton. A n n matrx M wth real entres m, s called a stochastc matrx provded () all the entres m satsfy 0 m, () each of the columns sum to one, m = for all, ()

More information

Research Article Enhanced Two-Step Method via Relaxed Order of α-satisfactory Degrees for Fuzzy Multiobjective Optimization

Research Article Enhanced Two-Step Method via Relaxed Order of α-satisfactory Degrees for Fuzzy Multiobjective Optimization Hndaw Publshng Corporaton Mathematcal Problems n Engneerng Artcle ID 867836 pages http://dxdoorg/055/204/867836 Research Artcle Enhanced Two-Step Method va Relaxed Order of α-satsfactory Degrees for Fuzzy

More information

The Development of Web Log Mining Based on Improve-K-Means Clustering Analysis

The Development of Web Log Mining Based on Improve-K-Means Clustering Analysis The Development of Web Log Mnng Based on Improve-K-Means Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.

More information

Module 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur

Module 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 information

Piecewise affine approximation of nonlinear systems a case study of a benchmark nonlinear boiler

Piecewise affine approximation of nonlinear systems a case study of a benchmark nonlinear boiler Proeedngs of the 8th WSEAS Internatonal Conferene on SYSTEM SCIENCE and SIMULATION n ENGINEERING Peewse affne approxmaton of nonlnear sstems a ase std of a benhmark nonlnear boler RADEK HORÁLEK* AND JAROSLAV

More information

PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 12

PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 12 14 The Ch-squared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304-C) 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 information

Partner Choice and the Marital College Premium: Analyzing Marital Patterns Over Several Decades

Partner Choice and the Marital College Premium: Analyzing Marital Patterns Over Several Decades Partner Choe and the Martal College Premum: Analyzng Martal Patterns Over Several Deades Perre-André Chappor Bernard Salané Yoram Wess January 31, 2015 Abstrat We onstrut a strutural model of household

More information

Product Approximate Reasoning of Online Reviews Applying to Consumer Affective and Psychological Motives Research

Product Approximate Reasoning of Online Reviews Applying to Consumer Affective and Psychological Motives Research Appled Mathematcs & Informaton Scences An Internatonal Journal 2011 NSP 5 (2) (2011), 45S-51S Product Approxmate Reasonng of Onlne Revews Applyng to Consumer Affectve and Psychologcal Motves Research Narsa

More information

Chapter 31B - Transient Currents and Inductance

Chapter 31B - Transient Currents and Inductance Chapter 31B - Transent Currents and Inductance A PowerPont Presentaton by Paul E. Tppens, Professor of Physcs Southern Polytechnc State Unversty 007 Objectves: After completng ths module, you should be

More information

Section C2: BJT Structure and Operational Modes

Section C2: BJT Structure and Operational Modes Secton 2: JT Structure and Operatonal Modes Recall that the semconductor dode s smply a pn juncton. Dependng on how the juncton s based, current may easly flow between the dode termnals (forward bas, v

More information

NON-CONSTANT SUM RED-AND-BLACK GAMES WITH BET-DEPENDENT WIN PROBABILITY FUNCTION LAURA PONTIGGIA, University of the Sciences in Philadelphia

NON-CONSTANT SUM RED-AND-BLACK GAMES WITH BET-DEPENDENT WIN PROBABILITY FUNCTION LAURA PONTIGGIA, University of the Sciences in Philadelphia To appear n Journal o Appled Probablty June 2007 O-COSTAT SUM RED-AD-BLACK GAMES WITH BET-DEPEDET WI PROBABILITY FUCTIO LAURA POTIGGIA, Unversty o the Scences n Phladelpha Abstract In ths paper we nvestgate

More information

POLYSA: A Polynomial Algorithm for Non-binary Constraint Satisfaction Problems with and

POLYSA: A Polynomial Algorithm for Non-binary Constraint Satisfaction Problems with and POLYSA: A Polynomal Algorthm for Non-bnary Constrant Satsfacton Problems wth and Mguel A. Saldo, Federco Barber Dpto. Sstemas Informátcos y Computacón Unversdad Poltécnca de Valenca, Camno de Vera s/n

More information

The Application of Qubit Neural Networks for Time Series Forecasting with Automatic Phase Adjustment Mechanism

The Application of Qubit Neural Networks for Time Series Forecasting with Automatic Phase Adjustment Mechanism The Applaton of Qubt Neural Networks for Tme Seres Foreastng wth Automat Phase Adjustment Mehansm arlos R. B. Azevedo 1 and Tago. A. E. Ferrera 1 1 entro de ênas e Tenologa Unversdade atóla de Pernambuo

More information

Section 5.4 Annuities, Present Value, and Amortization

Section 5.4 Annuities, Present Value, and Amortization Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today

More information

n + d + q = 24 and.05n +.1d +.25q = 2 { n + d + q = 24 (3) n + 2d + 5q = 40 (2)

n + d + q = 24 and.05n +.1d +.25q = 2 { n + d + q = 24 (3) n + 2d + 5q = 40 (2) MATH 16T Exam 1 : Part I (In-Class) Solutons 1. (0 pts) A pggy bank contans 4 cons, all of whch are nckels (5 ), dmes (10 ) or quarters (5 ). The pggy bank also contans a con of each denomnaton. The total

More information

MINIMISING INVENTORY COSTS BY PROPERLY CHOOSING THE LEVEL OF SAFETY STOCK

MINIMISING INVENTORY COSTS BY PROPERLY CHOOSING THE LEVEL OF SAFETY STOCK ECONOMIC AND BUSINESS REVIEW VOL. No. 2 2009 09 7 09 MINIMISING INVENTORY COSTS BY PROPERLY CHOOSING THE LEVEL OF SAFETY STOCK LILJANA FERBAR TRATAR* ABSTRACT: Markets are everyday becomng ever more demandng

More information

Logical Development Of Vogel s Approximation Method (LD-VAM): An Approach To Find Basic Feasible Solution Of Transportation Problem

Logical Development Of Vogel s Approximation Method (LD-VAM): An Approach To Find Basic Feasible Solution Of Transportation Problem INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME, ISSUE, FEBRUARY ISSN 77-866 Logcal Development Of Vogel s Approxmaton Method (LD- An Approach To Fnd Basc Feasble Soluton Of Transportaton

More information

Inter-Ing 2007. INTERDISCIPLINARITY IN ENGINEERING SCIENTIFIC INTERNATIONAL CONFERENCE, TG. MUREŞ ROMÂNIA, 15-16 November 2007.

Inter-Ing 2007. INTERDISCIPLINARITY IN ENGINEERING SCIENTIFIC INTERNATIONAL CONFERENCE, TG. MUREŞ ROMÂNIA, 15-16 November 2007. Inter-Ing 2007 INTERDISCIPLINARITY IN ENGINEERING SCIENTIFIC INTERNATIONAL CONFERENCE, TG. MUREŞ ROMÂNIA, 15-16 November 2007. UNCERTAINTY REGION SIMULATION FOR A SERIAL ROBOT STRUCTURE MARIUS SEBASTIAN

More information

REGULAR MULTILINEAR OPERATORS ON C(K) SPACES

REGULAR MULTILINEAR OPERATORS ON C(K) SPACES REGULAR MULTILINEAR OPERATORS ON C(K) SPACES FERNANDO BOMBAL AND IGNACIO VILLANUEVA Abstract. The purpose of ths paper s to characterze the class of regular contnuous multlnear operators on a product of

More information

Implementation of Boolean Functions through Multiplexers with the Help of Shannon Expansion Theorem

Implementation of Boolean Functions through Multiplexers with the Help of Shannon Expansion Theorem Internatonal Journal o Computer pplcatons (975 8887) Volume 62 No.6, January 23 Implementaton o Boolean Functons through Multplexers wth the Help o Shannon Expanson Theorem Saurabh Rawat Graphc Era Unversty.

More information

Institute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic

Institute 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 information

PRE COURSE ASSIGNMENT ALT COURSE ( This should be prepared in separate sheets bounded in one booklet presentable manner )

PRE COURSE ASSIGNMENT ALT COURSE ( This should be prepared in separate sheets bounded in one booklet presentable manner ) . THE BHARAT SCOUTS AND GUIDES, NATIONAL TRAINING CENTRE PACHMARHI { M.P. } 461881. Ph. No. 07578 252026 (O), 252153(R), Fax No. 07578 252541 E-Mal ntc@bsgnda.org ********************************************************************************************

More information

VOLTAGE stability issue remains a major concern in

VOLTAGE stability issue remains a major concern in Impacts of Mert Order Based Dspatch on Transfer Capablty and Statc Voltage Stablty Cuong P. guyen, Student Member, IEEE, and Alexander J. Flueck, Member, IEEE Abstract In ths paper, the goal s to nvestgate

More information

Rotation Kinematics, Moment of Inertia, and Torque

Rotation Kinematics, Moment of Inertia, and Torque Rotaton Knematcs, Moment of Inerta, and Torque Mathematcally, rotaton of a rgd body about a fxed axs s analogous to a lnear moton n one dmenson. Although the physcal quanttes nvolved n rotaton are qute

More information

24. Impact of Piracy on Innovation at Software Firms and Implications for Piracy Policy

24. Impact of Piracy on Innovation at Software Firms and Implications for Piracy Policy 4. mpat of Pray on nnovaton at Software Frms and mplatons for Pray Poly Jeevan Jasngh Department of nformaton & Systems Management, HKUST Clear Water Bay, Kowloon Hong Kong jeevan@ust.h Abstrat A Busness

More information

Pricing Model of Cloud Computing Service with Partial Multihoming

Pricing Model of Cloud Computing Service with Partial Multihoming Prcng Model of Cloud Computng Servce wth Partal Multhomng Zhang Ru 1 Tang Bng-yong 1 1.Glorous Sun School of Busness and Managment Donghua Unversty Shangha 251 Chna E-mal:ru528369@mal.dhu.edu.cn Abstract

More information

Energies of Network Nastsemble

Energies of Network Nastsemble Supplementary materal: Assessng the relevance of node features for network structure Gnestra Bancon, 1 Paolo Pn,, 3 and Matteo Marsl 1 1 The Abdus Salam Internatonal Center for Theoretcal Physcs, Strada

More information

Calculation of Sampling Weights

Calculation of Sampling Weights Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a two-stage stratfed cluster desgn. 1 The frst stage conssted of a sample

More information

Hedging Interest-Rate Risk with Duration

Hedging Interest-Rate Risk with Duration FIXED-INCOME SECURITIES Chapter 5 Hedgng Interest-Rate Rsk wth Duraton Outlne Prcng and Hedgng Prcng certan cash-flows Interest rate rsk Hedgng prncples Duraton-Based Hedgng Technques Defnton of duraton

More information

University of Crete Computer Science Department QUERY ORDERING BASED TOP-K ALGORITHMS FOR QUALITATIVELY SPECIFIED PREFERENCES IOANNIS KAPANTAIDAKIS

University of Crete Computer Science Department QUERY ORDERING BASED TOP-K ALGORITHMS FOR QUALITATIVELY SPECIFIED PREFERENCES IOANNIS KAPANTAIDAKIS Unversty of Crete Computer Scence Department QUERY ORDERING BASED TOP-K ALGORITHMS FOR QUALITATIVELY SPECIFIED PREFERENCES by IOANNIS KAPANTAIDAKIS Master s Thess Heraklon, January 27 Unversty of Crete

More information

The descriptive complexity of the family of Banach spaces with the π-property

The descriptive complexity of the family of Banach spaces with the π-property Arab. J. Math. (2015) 4:35 39 DOI 10.1007/s40065-014-0116-3 Araban Journal of Mathematcs Ghadeer Ghawadrah The descrptve complexty of the famly of Banach spaces wth the π-property Receved: 25 March 2014

More information

To Fill or not to Fill: The Gas Station Problem

To Fill or not to Fill: The Gas Station Problem To Fll or not to Fll: The Gas Staton Problem Samr Khuller Azarakhsh Malekan Julán Mestre Abstract In ths paper we study several routng problems that generalze shortest paths and the Travelng Salesman Problem.

More information

Form-finding of grid shells with continuous elastic rods

Form-finding of grid shells with continuous elastic rods Page of 0 Form-fndng of grd shells wth contnuous elastc rods Jan-Mn L PhD student Insttute of Buldng Structures and Structural Desgn (tke), Unversty Stuttgart Stuttgar, Germany quantumamn@gmal.com Jan

More information

The Distribution of Eigenvalues of Covariance Matrices of Residuals in Analysis of Variance

The Distribution of Eigenvalues of Covariance Matrices of Residuals in Analysis of Variance JOURNAL OF RESEARCH of the Natonal Bureau of Standards - B. Mathem atca l Scence s Vol. 74B, No.3, July-September 1970 The Dstrbuton of Egenvalues of Covarance Matrces of Resduals n Analyss of Varance

More information

Laddered Multilevel DC/AC Inverters used in Solar Panel Energy Systems

Laddered 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 information

Traffic-light a stress test for life insurance provisions

Traffic-light a stress test for life insurance provisions MEMORANDUM Date 006-09-7 Authors Bengt von Bahr, Göran Ronge Traffc-lght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE-113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax

More information

ERP Software Selection Using The Rough Set And TPOSIS Methods

ERP Software Selection Using The Rough Set And TPOSIS Methods ERP Software Selecton Usng The Rough Set And TPOSIS Methods Under Fuzzy Envronment Informaton Management Department, Hunan Unversty of Fnance and Economcs, No. 139, Fengln 2nd Road, Changsha, 410205, Chna

More information

Performance Analysis of Energy Consumption of Smartphone Running Mobile Hotspot Application

Performance Analysis of Energy Consumption of Smartphone Running Mobile Hotspot Application Internatonal Journal of mart Grd and lean Energy Performance Analyss of Energy onsumpton of martphone Runnng Moble Hotspot Applcaton Yun on hung a chool of Electronc Engneerng, oongsl Unversty, 511 angdo-dong,

More information

The University of Texas at Austin. Austin, Texas 78712. December 1987. Abstract. programs in which operations of dierent processes mayoverlap.

The University of Texas at Austin. Austin, Texas 78712. December 1987. Abstract. programs in which operations of dierent processes mayoverlap. Atomc Semantcs of Nonatomc Programs James H. Anderson Mohamed G. Gouda Department of Computer Scences The Unversty of Texas at Austn Austn, Texas 78712 December 1987 Abstract We argue that t s possble,

More information

Capacity-building and training

Capacity-building and training 92 Toolkt to Combat Traffckng n Persons Tool 2.14 Capacty-buldng and tranng Overvew Ths tool provdes references to tranng programmes and materals. For more tranng materals, refer also to Tool 9.18. Capacty-buldng

More information