Certain Expansion Formulae Involving a Basic Analogue of Fox s H-Function

Size: px
Start display at page:

Download "Certain Expansion Formulae Involving a Basic Analogue of Fox s H-Function"

Transcription

1 vlle t htt:vu.edu l. l. Mth. ISSN: Vol. 3 Iue Jue Pevouly Vol. 3 No. lcto d led Mthetc: Itetol Joul M Cet Exo Foule Ivolvg c logue o Fox -Fucto S.. Puoht etet o c-scece Mthetc College o Techology d Egeeg M.P. Uvety o gcultue d Techology Udu-33 Id ul uoht@yhoo.co R. K. Ydv etet o Mthetc d Stttc J. N. Vy Uvety Jodhu-345 Id dydv@yhoo.co. S.L. Kll etet o Mthetc d Coute Scece P.O. ox-5969 St 36 Kuwt hyll@yhoo.co Receved ecee 3 7 cceted My 7 8 tct Cet exo oule o c logue o the Fox -ucto hve ee deved y the lcto o the -Le ule o the Weyl tye -devtve o oduct o two ucto. Exo oule volvg c logue o Mee -ucto d McRoet E-ucto hve ee deved ecl ce o the eult. Keywod: -Le ule Weyl ctol -tegl oeto Fox -ucto MS Suect Clcto Nue: 336 d 633 8

2 M: Ite J. Vol. 3 Iue Jue 8 [Pevouly Vol. 3 No. ] 9. Itoducto Recetly Puoht 7 toduced ew -exteo o the Le ule o the devtve o oduct o two c ucto te o te -ee volvg Weyl tye -devtve o the ucto the ollowg e: V U V U whee U d V e two egul ucto d the ctol -deetl oeto. o Weyl tye gve y t d t t whee Re d x y x y x y x 3 the c tegto c. e d Rh 99 deed : t d t. 4 I vew o the elto 4 oeto c e exeed : 5 whee Re. I tcul o the euto 5 yeld to 6 whee Re.

3 3 Puoht et l. We hll e ue o the ollowg otto d deto the euel: Fo el o colex d the -hted ctol deed : 7... N. I te o the -g ucto 7 c e exeed 8 whee the -g ucto c. e d Rh 99 gve y 9 whee.... Sxe et l. 983 toduced c logue o the -ucto te o the Mell- e tye c cotou tegl the ollowg e: C d whee d d e ll otve tege. The cotou C le llel to Re w wth detto ecey uch e tht ll the ole o e to the ght d thoe o to the let o C. The tegl covege log log ] o lge vlue o o the cotou C tht g ww log whee log w w w w w w e dete utte. w d w eg el.

4 M: Ite J. Vol. 3 Iue Jue 8 [Pevouly Vol. 3 No. ] 3 Fo the deto educe to the -logue o the Mee' -ucto due to Sxe et l. 983 ely C d whee d ] log log. Futhe we et d the euto we get the c logue o McRoet' E-ucto due to gwl 96 ely ] : : [ E C d 3 whee ] log log. The Fox -ucto d Mee -ucto hve ee tuded detl y evel thetc o the theoetcl d lcto ot o vew. Thee ucto hve oud wde gg lcto thetcl hycl ologcl d tttcl cece. It would e teetg to oeve tht lot ll the clcl ecl ucto e the tcul ce o the Fox -ucto. detled ccout o vou clcl ecl ucto exele te o Mee -ucto o Fox -ucto log wth the lcto to the oeetoed eld c e oud the eech oogh y Mth et l ew geelto w codeed y Sxe et l. 983 the o o the -exteo o the Fox - ucto d Mee -ucto y e o the Mell- e tye o c tegl. The dvtge o thee ew exteo o the Fox d Mee -ucto le the ct tht ue o -ecl ucto cludg the c hyegeoetc ucto he to e the tcul ce o the. d. ucto thu wdeg the coe o uthe lcto. I e Sxe et l. 99 ede ovg oe teetg elto

5 3 Puoht et l. hve etlhed ott lt oul o the. ucto whe ted to. Vou c ucto exele te o the c logue o Fox -ucto o c Mee -ucto wth the lcto c e oud the eech e due to Sxe et l. 5 d Ydv et l. 6. I the eet e we hll exloe the olty o devto o oe exo oule volvg the c logue o the Fox -ucto y the lcto o the -Le ule o the Weyl tye -devtve o oduct o two ucto. We lo vetgte the exo oule volvg the c logue o Mee -ucto d McRoet E-ucto.. M Reult I th ecto we hll etlh cet eult octed wth the c logue o Fox' - ucto y gg utle vlue to the ucto V U d the -Le ule. The eult to e etlhed e ude: 4 whee ] log log d eg y colex utty. 5 whee ] log log d eg y colex utty. Poo o the eult: To ove the eult 4 d 5 we eg wth U d V

6 M: Ite J. Vol. 3 Iue Jue 8 [Pevouly Vol. 3 No. ] 33 the euto to ot. 6 vew o the deto the let-hd de o euto 6 ecoe d C. 7 O g ue o ctol -devtve oul 6 the ove euto 7 we ot ollowg teetg toto o the. ucto te cet lcto: 8 whee. g we te we ot the ollowg ctol -devtve oul o the. ucto ely. 9 We ow uttute d elce y d the y eectvely euto 8 to ot the ollowg toto o the. ucto:

7 34 Puoht et l.. Futhe vew o the eult 6 oe c ely ot the ollowg elto. O uttutg the vlue o the vou exeo volved the euto 6 o euto 8 d we ve t the eult 4. The oo o the eult 5 ollow lly whe d y the uge o the toto oul 9 d the elto. 3. Secl Ce I th ecto we hll code oe ecl ce o the eult d deduce cet exo oule volvg the c logue o Mee' -ucto d c logue o McRoet' E-ucto. I we et d the eult 4 we ot the ollowg teetg exo oul volvg Mee'. ucto ely whee ] log log d eg y colex utty. Slly o d the eult 5 educe to yet othe exo oul octed wth the c logue o Mee' -ucto ely

8 M: Ite J. Vol. 3 Iue Jue 8 [Pevouly Vol. 3 No. ] 35 3 whee log log ] d eg y colex utty. Flly we et d the eult yeld to exo oul volvg McRoet' E. ucto ely E [ : : ] E whee log log ] d eg y colex utty. [ : : ] 4 cowledgeet: The utho ceely cowledge the vlule uggeto de y oe o the eeee. REFERENCES gwl N logue o McRoet' geeled E-ucto t gwl R.P Fctol -devtve d -tegl d cet hyegeoetc toto t l-sl W Soe ctol -tegl d -devtve Poc. Ed. Mth. Soc e. M. Rh 99. c yegeoetc See Cdge Uvety Pe Cdge. Mth. M. R. K. Sxe 973. eeled yegeoetc Fucto Wth lcto Stttc d Phycl Scece Sge-Velg el. Mth. M. R. K. Sxe 978. The -ucto Wth lcto Stttc d Othe cle Joh Wley d So. Ic. New Yo. Puoht S.. 7. O -exteo o the Le ule v Weyl tye o -devtve oeto Coucted. Sxe R.K..C. Mod. S.L. Kll 983. c logue o Fox' -ucto Rev. Tec. Ig. Uv. Zul Sxe R.K. R. Ku 99. Recuece elto o the c logue o the -ucto J. Nt. cd. Mth Sxe R.K. R.K. Ydv S.. Puoht S.L. Kll 5. Koe ctol -tegl oeto o the c logue o the -ucto Rev. Tec. Ig. Uv. Zul Slte L.J eeled yegeoetc Fucto Cdge Uvety Pe Cdge Lodo d New Yo.

9 36 Puoht et l. Ydv R.K. S.. Puoht 6. O ctol -devtve d toto o the geeled c hyegeoetc ucto J. Id cd. Mth Ydv R.K. d S.. Puoht 6. O lcto o Weyl ctol -tegl oeto to geeled c hyegeoetc ucto Kyugoo Mth. J

Fredholm Type Integral Equations with Aleph-Function. and General Polynomials

Fredholm Type Integral Equations with Aleph-Function. and General Polynomials Iteto Mthetc Fou Vo. 8 3 o. 989-999 HIKI Ltd.-h.co Fedho Te Iteg uto th eh-fucto d Gee Poo u J K.J. o Ittute o Mgeet tude & eech Mu Id u5@g.co Kt e K.J. o Ittute o Mgeet tude & eech Mu Id dehuh_3@hoo.co

More information

The shifted Jacobi polynomial integral operational matrix for solving Riccati differential equation of fractional order

The shifted Jacobi polynomial integral operational matrix for solving Riccati differential equation of fractional order Avlble t htt://vuedu/ Al Al Mth SSN: 9-966 Vol ue Decebe 5 878-89 Alcto d Aled Mthetc: A tetol oul AAM he hted cob olyol tegl oetol t o olvg Rcct deetl euto o ctol ode A Nety B Aghel d R D Detet o Mthetc

More information

A Unified Formula for The nth Derivative and The nth Anti-Derivative of the Bessel Function of Real Orders

A Unified Formula for The nth Derivative and The nth Anti-Derivative of the Bessel Function of Real Orders Aec Joul of Aled Mthetc d Stttc 5 Vol 3 No 3-4 Avlble ole t htt://ubceubco/j/3/3/3 Scece d Educto Publhg DOI:69/j-3-3-3 A Ufed Foul fo The th Devtve d The th At-Devtve of the eel Fucto of Rel Ode Mhe M

More information

E-Companion: Mathematical Proofs

E-Companion: Mathematical Proofs E-omnon: Mthemtcl Poo Poo o emm : Pt DS Sytem y denton o t ey to vey tht t ncee n wth d ncee n We dene } ] : [ { M whee / We let the ttegy et o ech etle n DS e ]} [ ] [ : { M w whee M lge otve nume oth

More information

Moments of Generalized Order Statistics from a General Class of Distributions

Moments of Generalized Order Statistics from a General Class of Distributions ISSN 684-843 Jol of Sttt Vole 5 28. 36-43 Moet of Geelzed Ode Sttt fo Geel l of Dtto Att Mhd Fz d Hee Ath Ode ttt eod le d eel othe odel of odeed do le e ewed el e of geelzed ode ttt go K 995. I th e exlt

More information

NONDIFFERENTIABLE MATHEMATICAL PROGRAMS. OPTIMALITY AND HIGHER-ORDER DUALITY RESULTS

NONDIFFERENTIABLE MATHEMATICAL PROGRAMS. OPTIMALITY AND HIGHER-ORDER DUALITY RESULTS HE PUBLISHING HOUSE PROCEEDINGS OF HE ROMANIAN ACADEMY, See A, OF HE ROMANIAN ACADEMY Volue 9, Nube 3/8,. NONDIFFERENIABLE MAHEMAICAL PROGRAMS. OPIMALIY AND HIGHER-ORDER DUALIY RESULS Vale PREDA Uvety

More information

Some Integrals Pertaining Biorthogonal Polynomials and Certain Product of Special Functions

Some Integrals Pertaining Biorthogonal Polynomials and Certain Product of Special Functions Global Joual o Scece Fote Reeach atheatc ad Deco Scece Volue Iue Veo Te : Double Bld ee Reewed Iteatoal Reeach Joual ublhe: Global Joual Ic SA Ole ISSN: 49-466 & t ISSN: 975-5896 Soe Itegal etag Bothogoal

More information

A Dynamical Quasi-Boolean System

A Dynamical Quasi-Boolean System ULETNUL Uestăţ Petol Gze Ploeşt Vol LX No / - 9 Se Mtetă - otă - Fză l Qs-oole Sste Gel Mose Petole-Gs Uest o Ploest ots etet est 39 Ploest 68 o el: ose@-loesto stt Ths e oes the esto o ol theoetl oet:

More information

SOME REMARKS ON HORIZONTAL, SLANT, PARABOLIC AND POLYNOMIAL ASYMPTOTE

SOME REMARKS ON HORIZONTAL, SLANT, PARABOLIC AND POLYNOMIAL ASYMPTOTE D I D A C T I C S O F A T H E A T I C S No (4) 3 SOE REARKS ON HORIZONTAL, SLANT, PARABOLIC AND POLYNOIAL ASYPTOTE Tdeusz Jszk Abstct I the techg o clculus, we cosde hozotl d slt symptote I ths ppe the

More information

2. Elementary Linear Algebra Problems

2. Elementary Linear Algebra Problems . Eleety e lge Pole. BS: B e lge Suoute (Pog pge wth PCK) Su of veto opoet:. Coputto y f- poe: () () () (3) N 3 4 5 3 6 4 7 8 Full y tee Depth te tep log()n Veto updte the f- poe wth N : ) ( ) ( ) ( )

More information

X-Ray Notes, Part III

X-Ray Notes, Part III oll 6 X-y oe 3: Pe X-Ry oe, P III oe Deeo Coe oupu o x-y ye h look lke h: We efe ue of que lhly ffee efo h ue y ovk: Co: C ΔS S Sl o oe Ro: SR S Co o oe Ro: CR ΔS C SR Pevouly, we ee he SR fo ye hv pxel

More information

Analysis of torque cam mechanism

Analysis of torque cam mechanism Aly o toque c ech Iy He,*, Pet Hej, Šte Mch, Mt Svood, Joe Souku culty o Puducto Techology d Mgeet J Evgelt Pukyě Uvety Útí d Le, Detet o Mche d Mechc, 400 96, Puteov, Útí /L, Czech Reulc Atct: The tcle

More information

The use of linear parametric approximation in numerical solving of nonlinear non-smooth Fuzzy equations

The use of linear parametric approximation in numerical solving of nonlinear non-smooth Fuzzy equations vlle ole t www.choleechl.co chve o ppled Scece Reech 5 6:49-6 http://choleechl.co/chve.htl ISSN 975-58X CODEN US SRC9 The ue o le petc ppoto uecl olvg o ole o-ooth uzz equto Mjd Hllj e Ze d l Vhd Kd Nehu

More information

African Journal of Science and Technology (AJST) Science and Engineering Series Vol. 4, No. 2, pp GENERALISED DELETION DESIGNS

African Journal of Science and Technology (AJST) Science and Engineering Series Vol. 4, No. 2, pp GENERALISED DELETION DESIGNS Af Joul of See Tehology (AJST) See Egeeg See Vol. 4, No.,. 7-79 GENERALISED DELETION DESIGNS Mhel Ku Gh Joh Wylff Ohbo Dee of Mhe, Uvey of Nob, P. O. Bo 3097, Nob, Key ABSTRACT:- I h e yel gle ele fol

More information

Lecture 9-3/8/10-14 Spatial Description and Transformation

Lecture 9-3/8/10-14 Spatial Description and Transformation Letue 9-8- tl Deton nd nfomton Homewo No. Due 9. Fme ngement onl. Do not lulte...8..7.8 Otonl et edt hot oof tht = - Homewo No. egned due 9 tud eton.-.. olve oblem:.....7.8. ee lde 6 7. e Mtlb on. f oble.

More information

Elastic-Plastic Transition of Transversely. Isotropic Thin Rotating Disc

Elastic-Plastic Transition of Transversely. Isotropic Thin Rotating Disc otempoy Egeeg Sceces, Vol., 9, o. 9, 4-44 Elstc-Plstc sto o svesely Isotopc h ottg Dsc Sjeev Shm d Moj Sh Deptmet o Mthemtcs JII Uvesty, -, Secto 6 Nod-7, UP, Id sjt@edml.com, moj_sh7@edml.com stct Elstc-plstc

More information

On Almost Increasing Sequences For Generalized Absolute Summability

On Almost Increasing Sequences For Generalized Absolute Summability Joul of Applied Mthetic & Bioifotic, ol., o., 0, 43-50 ISSN: 79-660 (pit), 79-6939 (olie) Itetiol Scietific Pe, 0 O Alot Iceig Sequece Fo Geelized Abolute Subility W.. Suli Abtct A geel eult coceig bolute

More information

FRACTIONAL MELLIN INTEGRAL TRANSFORM IN (0, 1/a)

FRACTIONAL MELLIN INTEGRAL TRANSFORM IN (0, 1/a) Ieol Jol o Se Reeh Pblo Volme Ie 5 y ISSN 5-5 FRACTIONAL ELLIN INTEGRAL TRANSFOR IN / S.. Kh R..Pe* J.N.Slke** Deme o hem hh Aemy o Egeeg Al-45 Pe I oble No.: 98576F No.: -785759 Eml-mkh@gml.om Deme o

More information

International Mathematical Forum, Vol. 9, 2014, no. 13, HIKARI Ltd,

International Mathematical Forum, Vol. 9, 2014, no. 13, HIKARI Ltd, Ieol Mhemcl oum Vol. 9 4 o. 3 65-6 HIKARI Ld www.m-h.com hp//d.do.o/.988/m.4.43 Some Recuece Relo ewee he Sle Doule d Tple Mome o Ode Sc om Iveed mm Duo d hceo S. M. Ame * ollee o Scece d Hume Quwh Shq

More information

Nonlocal Boundary Value Problem for Nonlinear Impulsive q k Symmetric Integrodifference Equation

Nonlocal Boundary Value Problem for Nonlinear Impulsive q k Symmetric Integrodifference Equation OSR ol o Mec OSR-M e-ssn: 78-578 -SSN: 9-765X Vole e Ve M - A 7 PP 95- wwwojolog Nolocl Bo Vle Poble o Nole lve - Sec egoeece Eo Log Ceg Ceg Ho * Yeg He ee o Mec Yb Uve Yj PR C Abc: A oe ole lve egoeece

More information

Difference Sets of Null Density Subsets of

Difference Sets of Null Density Subsets of dvces Pue Mthetcs 95-99 http://ddoog/436/p37 Pulshed Ole M (http://wwwscrpog/oul/p) Dffeece Sets of Null Dest Susets of Dwoud hd Dsted M Hosse Deptet of Mthetcs Uvest of Gul Rsht I El: hd@gulc h@googlelco

More information

ECONOMETRIC ANALYSIS ON EFFICIENCY OF ESTIMATOR ABSTRACT

ECONOMETRIC ANALYSIS ON EFFICIENCY OF ESTIMATOR ABSTRACT ECOOMETRIC LYSIS O EFFICIECY OF ESTIMTOR M. Khohev, Lectue, Gffth Uvet, School of ccoutg d Fce, utl F. K, tt Pofeo, Mchuett Ittute of Techolog, Deptet of Mechcl Egeeg, US; cuetl t Shf Uvet, I. Houl P.

More information

AN ALGEBRAIC APPROACH TO M-BAND WAVELETS CONSTRUCTION

AN ALGEBRAIC APPROACH TO M-BAND WAVELETS CONSTRUCTION AN ALGEBRAIC APPROACH TO -BAN WAELETS CONSTRUCTION Toy L Qy S Pewe Ho Ntol Lotoy o e Peeto Pe Uety Be 8 P. R. C Att T e eet le o to ott - otool welet e. A yte of ott eto ote fo - otool flte te olto e o

More information

2.Decision Theory of Dependence

2.Decision Theory of Dependence .Deciio Theoy of Depedece Theoy :I et of vecto if thee i uet which i liely depedet the whole et i liely depedet too. Coolly :If the et i liely idepedet y oepty uet of it i liely idepedet. Theoy : Give

More information

Studying the Problems of Multiple Integrals with Maple Chii-Huei Yu

Studying the Problems of Multiple Integrals with Maple Chii-Huei Yu Itetol Joul of Resech (IJR) e-issn: 2348-6848, - ISSN: 2348-795X Volume 3, Issue 5, Mch 26 Avlble t htt://tetoljoulofesechog Studyg the Poblems of Multle Itegls wth Mle Ch-Hue Yu Detmet of Ifomto Techology,

More information

ANOTHER INTEGER NUMBER ALGORITHM TO SOLVE LINEAR EQUATIONS (USING CONGRUENCY)

ANOTHER INTEGER NUMBER ALGORITHM TO SOLVE LINEAR EQUATIONS (USING CONGRUENCY) ANOTHER INTEGER NUMBER ALGORITHM TO SOLVE LINEAR EQUATIONS (USING CONGRUENCY) Floet Smdche, Ph D Aocte Pofeo Ch of Deptmet of Mth & Scece Uvety of New Mexco 2 College Rod Gllup, NM 873, USA E-ml: md@um.edu

More information

On Some Hadamard-Type Inequalıtıes for Convex Functıons

On Some Hadamard-Type Inequalıtıes for Convex Functıons Aville t htt://vuedu/ Al Al Mth ISSN: 93-9466 Vol 9, Issue June 4, 388-4 Alictions nd Alied Mthetics: An Intentionl Jounl AAM On Soe Hdd-Tye Inequlıtıes o, Convex Functıons M Ein Özdei Detent o Mthetics

More information

Numerical Solution of Fractional Telegraph Equation Using the Second Kind Chebyshev Wavelets Method

Numerical Solution of Fractional Telegraph Equation Using the Second Kind Chebyshev Wavelets Method J App Evo Bo Sc 59S64-74 5 5 etrod Pucto SSN: 9-474 Jou o Apped Evoet d Boogc Scece tetodco Nuec Souto o cto eegph Equto Ug the Secod d Cheyhev Wveet ethod A Sdegh * H Heyd R Hoohd d S 4 4 eptet o thetc

More information

On the k-lucas Numbers of Arithmetic Indexes

On the k-lucas Numbers of Arithmetic Indexes Alied Mthetics 0 3 0-06 htt://d.doi.og/0.436/.0.307 Published Olie Octobe 0 (htt://www.scirp.og/oul/) O the -ucs Nubes of Aithetic Idees Segio lco Detet of Mthetics d Istitute fo Alied Micoelectoics (IUMA)

More information

-HYBRID LAPLACE TRANSFORM AND APPLICATIONS TO MULTIDIMENSIONAL HYBRID SYSTEMS. PART II: DETERMINING THE ORIGINAL

-HYBRID LAPLACE TRANSFORM AND APPLICATIONS TO MULTIDIMENSIONAL HYBRID SYSTEMS. PART II: DETERMINING THE ORIGINAL UPB Sc B See A Vo 72 I 3 2 ISSN 223-727 MUTIPE -HYBRID APACE TRANSORM AND APPICATIONS TO MUTIDIMENSIONA HYBRID SYSTEMS PART II: DETERMININ THE ORIINA Ve PREPEIŢĂ Te VASIACHE 2 Ace co copeeă oă - pce he

More information

Bayesian Credibility for Excess of Loss Reinsurance Rating. By Mark Cockroft 1 Lane Clark & Peacock LLP

Bayesian Credibility for Excess of Loss Reinsurance Rating. By Mark Cockroft 1 Lane Clark & Peacock LLP By Cly o c o Lo Rc Rg By M Coco L Cl & Pcoc LLP GIRO coc 4 Ac Th pp c how o v cly wgh w po- pc-v o c o lo c. Th po co o Poo-Po ol ch wh po G o. Kywo c o lo c g By cly Poo Po G po Acowlg cl I wol l o h

More information

such that for 1 From the definition of the k-fibonacci numbers, the firsts of them are presented in Table 1. Table 1: First k-fibonacci numbers F 1

such that for 1 From the definition of the k-fibonacci numbers, the firsts of them are presented in Table 1. Table 1: First k-fibonacci numbers F 1 Scholas Joual of Egeeg ad Techology (SJET) Sch. J. Eg. Tech. 0; (C):669-67 Scholas Academc ad Scetfc Publshe (A Iteatoal Publshe fo Academc ad Scetfc Resouces) www.saspublshe.com ISSN -X (Ole) ISSN 7-9

More information

A Study on New Sequence of Functions Involving the Generalized Contour Integral

A Study on New Sequence of Functions Involving the Generalized Contour Integral Globl Jourl of Scece Froter Reerch Mthetc d Deco Scece Volue 3 Iue Vero. Yer 23 Type : Double Bld Peer Revewed Itertol Reerch Jourl Publher: Globl Jourl Ic. (USA Ole ISS: 2249-4626 & Prt ISS: 975-5896

More information

10.2 Series. , we get. which is called an infinite series ( or just a series) and is denoted, for short, by the symbol. i i n

10.2 Series. , we get. which is called an infinite series ( or just a series) and is denoted, for short, by the symbol. i i n 0. Sere I th ecto, we wll troduce ere tht wll be dcug for the ret of th chpter. Wht ere? If we dd ll term of equece, we get whch clled fte ere ( or jut ere) d deoted, for hort, by the ymbol or Doe t mke

More information

Chapter 2: Descriptive Statistics

Chapter 2: Descriptive Statistics Chapte : Decptve Stattc Peequte: Chapte. Revew of Uvaate Stattc The cetal teecy of a oe o le yetc tbuto of a et of teval, o hghe, cale coe, ofte uaze by the athetc ea, whch efe a We ca ue the ea to ceate

More information

176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s

176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps

More information

THE WEIBULL NEGATIVE BINOMIAL DISTRIBUTION

THE WEIBULL NEGATIVE BINOMIAL DISTRIBUTION Advce d Alcto Stttc Volue Nue Pge 5-55 Th e vlle ole t htt://hco/oul/dht Puh Pulhg Houe THE WEIBULL NEGATIVE BINOMIAL DISTRIBUTION CRISTIANE RODRIGUES GAUSS M CORDEIRO CLARICE G B DEMÉTRIO d EDWIN M M

More information

University of Pavia, Pavia, Italy. North Andover MA 01845, USA

University of Pavia, Pavia, Italy. North Andover MA 01845, USA Iteatoal Joual of Optmzato: heoy, Method ad Applcato 27-5565(Pt) 27-6839(Ole) wwwgph/otma 29 Global Ifomato Publhe (HK) Co, Ltd 29, Vol, No 2, 55-59 η -Peudoleaty ad Effcecy Gogo Gog, Noma G Rueda 2 *

More information

Asymptotic Dominance Problems. is not constant but for n 0, f ( n) 11. 0, so that for n N f

Asymptotic Dominance Problems. is not constant but for n 0, f ( n) 11. 0, so that for n N f Asymptotc Domce Prolems Dsply ucto : N R tht s Ο( ) ut s ot costt 0 = 0 The ucto ( ) = > 0 s ot costt ut or 0, ( ) Dee the relto " " o uctos rom N to R y g d oly = Ο( g) Prove tht s relexve d trstve (Recll:

More information

Chapter Linear Regression

Chapter Linear Regression Chpte 6.3 Le Regesso Afte edg ths chpte, ou should be ble to. defe egesso,. use sevel mmzg of esdul cte to choose the ght cteo, 3. deve the costts of le egesso model bsed o lest sques method cteo,. use

More information

ICS141: Discrete Mathematics for Computer Science I

ICS141: Discrete Mathematics for Computer Science I Uversty o Hw ICS: Dscrete Mthemtcs or Computer Scece I Dept. Iormto & Computer Sc., Uversty o Hw J Stelovsy bsed o sldes by Dr. Be d Dr. Stll Orgls by Dr. M. P. Fr d Dr. J.L. Gross Provded by McGrw-Hll

More information

Numerical Methods for Eng [ENGR 391] [Lyes KADEM 2007] Direct Method; Newton s Divided Difference; Lagrangian Interpolation; Spline Interpolation.

Numerical Methods for Eng [ENGR 391] [Lyes KADEM 2007] Direct Method; Newton s Divided Difference; Lagrangian Interpolation; Spline Interpolation. Nuecl Methods o Eg [ENGR 39 [Les KADEM 7 CHAPTER V Itepolto d Regesso Topcs Itepolto Regesso Dect Method; Newto s Dvded Deece; Lgg Itepolto; ple Itepolto Le d o-le Wht s tepolto? A ucto s ote gve ol t

More information

P a g e 5 1 of R e p o r t P B 4 / 0 9

P a g e 5 1 of R e p o r t P B 4 / 0 9 P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e

More information

Three Phase Asymmetrical Load Flow for Four-Wire Distribution Networks

Three Phase Asymmetrical Load Flow for Four-Wire Distribution Networks T Aytl Lo Flow o Fou-W Dtuto Ntwo M. Mo *, A. M. Dy. M. A Dtt o Eltl E, A Uvty o Toloy Hz Av., T 59, I * El: o8@yoo.o Att-- Mjoty o tuto two ul u to ul lo, yty to l two l ut. T tt o tuto yt ult y o ovt

More information

SUBSEQUENCE CHARACTERIZAT ION OF UNIFORM STATISTICAL CONVERGENCE OF DOUBLE SEQUENCE

SUBSEQUENCE CHARACTERIZAT ION OF UNIFORM STATISTICAL CONVERGENCE OF DOUBLE SEQUENCE Reseach ad Coucatos atheatcs ad atheatcal ceces Vol 9 Issue 7 Pages 37-5 IN 39-6939 Publshed Ole o Novebe 9 7 7 Jyot cadec Pess htt//yotacadecessog UBEQUENCE CHRCTERIZT ION OF UNIFOR TTITIC CONVERGENCE

More information

The formulae in this booklet have been arranged according to the unit in which they are first

The formulae in this booklet have been arranged according to the unit in which they are first Fomule Booklet Fomule Booklet The fomule ths ooklet hve ee ge og to the ut whh the e fst toue. Thus te sttg ut m e eque to use the fomule tht wee toue peeg ut e.g. tes sttg C mght e epete to use fomule

More information

Occurrences of ordered patterns in rectangular space filling curve through homomorphism

Occurrences of ordered patterns in rectangular space filling curve through homomorphism AUSTRALIAN JOURNAL OF BASI AND APPLIED SIENES ISSN:99- EISSN: 9- Jo hoe ge: www.bweb.co Occece o odeed tte ectg ce g cve thogh hoooh K.Nveeth K. Thg S. Jeybhth Po Nt Reech cho Ph.D-B JUL-69 Detet o Mthetc

More information

Describes techniques to fit curves (curve fitting) to discrete data to obtain intermediate estimates.

Describes techniques to fit curves (curve fitting) to discrete data to obtain intermediate estimates. CURVE FITTING Descbes techques to ft cuves (cuve fttg) to dscete dt to obt temedte estmtes. Thee e two geel ppoches fo cuve fttg: Regesso: Dt ehbt sgfct degee of sctte. The stteg s to deve sgle cuve tht

More information

Chapter 17. Least Square Regression

Chapter 17. Least Square Regression The Islmc Uvest of Gz Fcult of Egeeg Cvl Egeeg Deptmet Numecl Alss ECIV 336 Chpte 7 Lest que Regesso Assocte Pof. Mze Abultef Cvl Egeeg Deptmet, The Islmc Uvest of Gz Pt 5 - CURVE FITTING Descbes techques

More information

Theory of Finsler spaces with ( λβ, ) Metric

Theory of Finsler spaces with ( λβ, ) Metric Theoy of Fsle sces wth ( λβ ) Metc Dhed Thu Kll Multle us Thuv Uvesty Kll DhdhNel E-l: dhedthuc@lco ABTRAT The of ths e s to toduce d study the cocet of ( ) theoes hve ee woout fo ( ) etc whee (x)y s oe

More information

Keywords: Heptic non-homogeneous equation, Pyramidal numbers, Pronic numbers, fourth dimensional figurate numbers.

Keywords: Heptic non-homogeneous equation, Pyramidal numbers, Pronic numbers, fourth dimensional figurate numbers. [Gol 5: M 0] ISSN: 77-9655 IJEST INTENTIONL JOUNL OF ENGINEEING SCIENCES & ESECH TECHNOLOGY O the Hetc No-Hoogeeous Euto th Four Ukos z 6 0 M..Gol * G.Suth S.Vdhlksh * Dertet of MthetcsShrt Idr Gdh CollegeTrch

More information

TWO INTERFACIAL COLLINEAR GRIFFITH CRACKS IN THERMO- ELASTIC COMPOSITE MEDIA

TWO INTERFACIAL COLLINEAR GRIFFITH CRACKS IN THERMO- ELASTIC COMPOSITE MEDIA WO INERFIL OLLINER GRIFFIH RS IN HERMO- ELSI OMOSIE MEDI h m MISHR S DS * Deme o Mheml See I Ie o eholog BHU V-5 I he oee o he le o he e e o eeg o o olle Gh e he ee o he wo ohoo mel e e e emee el. he olem

More information

Fractional Integrals Involving Generalized Polynomials And Multivariable Function

Fractional Integrals Involving Generalized Polynomials And Multivariable Function IOSR Joual of ateatcs (IOSRJ) ISSN: 78-578 Volue, Issue 5 (Jul-Aug 0), PP 05- wwwosoualsog Factoal Itegals Ivolvg Geealzed Poloals Ad ultvaable Fucto D Neela Pade ad Resa Ka Deatet of ateatcs APS uvest

More information

Efficient Estimator for Population Variance Using Auxiliary Variable

Efficient Estimator for Population Variance Using Auxiliary Variable Amec Joul o Opetol eech 6 6): 9-5 DOI:.59/j.jo.66. Ecet Etmto o Populto Vce Ug Aul Vble ubhh Kum Yv heel M.. Mh * Deptmet o Mthemtc tttc A Cete o Ecellece) D. ML Avh Uvet Fzb U.P. I Deptmet o tttc Uvet

More information

Beechwood Music Department Staff

Beechwood Music Department Staff Beechwood Music Department Staff MRS SARAH KERSHAW - HEAD OF MUSIC S a ra h K e rs h a w t r a i n e d a t t h e R oy a l We ls h C o l le g e of M u s i c a n d D ra m a w h e re s h e ob t a i n e d

More information

On Certain Classes of Analytic and Univalent Functions Based on Al-Oboudi Operator

On Certain Classes of Analytic and Univalent Functions Based on Al-Oboudi Operator Boig Itetiol Joul o t Miig, Vol, No, Jue 0 6 O Ceti Clsses o Alytic d Uivlet Fuctios Bsed o Al-Oboudi Opeto TV Sudhs d SP Viylkshmi Abstct--- Followig the woks o [, 4, 7, 9] o lytic d uivlet uctios i this

More information

The Solution of Heat Conduction Equation with Mixed Boundary Conditions

The Solution of Heat Conduction Equation with Mixed Boundary Conditions Joul of Mhec d Sc (: 346-35, 6 ISSN 549-3644 6 Scece Publco The Soluo of He Coduco Equo wh Mxed Bou Codo Ne Abdelzq Dee of Bc d Aled Scece, Tfl Techcl Uvey PO Box 79, Tfl, Jod Abc: The u devoed o deee

More information

Exponential Generating Functions - J. T. Butler

Exponential Generating Functions - J. T. Butler Epoetal Geeatg Fuctos - J. T. Butle Epoetal Geeatg Fuctos Geeatg fuctos fo pemutatos. Defto: a +a +a 2 2 + a + s the oday geeatg fucto fo the sequece of teges (a, a, a 2, a, ). Ep. Ge. Fuc.- J. T. Butle

More information

The formulae in this booklet have been arranged according to the unit in which they are first

The formulae in this booklet have been arranged according to the unit in which they are first Fomule Booklet Fomule Booklet The fomule ths ooklet hve ee ge ccog to the ut whch the e fst touce. Thus cte sttg ut m e eque to use the fomule tht wee touce peceg ut e.g. ctes sttg C mght e epecte to use

More information

Observations on the transcendental Equation

Observations on the transcendental Equation IOSR Jourl o Mecs IOSR-JM e-issn: 78-78-ISSN: 9-7 Volue 7 Issue Jul. - u. -7 www.osrjourls.or Oservos o e rscedel Euo M..Gol S.Vds T.R.Us R Dere o Mecs Sr Idr Gd Collee Trucrll- src: Te rscedel euo w ve

More information

The Geometric Proof of the Hecke Conjecture

The Geometric Proof of the Hecke Conjecture The Geometc Poof of the Hecke Cojectue Kada Sh Depatmet of Mathematc Zhejag Ocea Uvety Zhouha Cty 6 Zhejag Povce Cha Atact Begg fom the eoluto of Dchlet fucto ug the e poduct fomula of two fte-dmeoal vecto

More information

Two kurtosis measures in a simulation study

Two kurtosis measures in a simulation study Two kuto meue n multon tudy Ann M Fo Deptment o Quntttve Method o Economc nd Bune Scence Unvety o Mlno-Bcocc nn.o@unmb.t CNAM, P COMPSTAT 00 Augut 3, 00 Ovevew The IF (SIF) nd t ole n kuto tude Fom nequlty

More information

Sensorless A.C. Drive with Vector Controlled Synchronous Motor

Sensorless A.C. Drive with Vector Controlled Synchronous Motor Seole A.C. Dve wth Vecto Cotolle Sychoo Moto Ořej Fše VŠB-echcal Uvety of Otava, Faclty of Electcal Egeeg a Ifomatc, Deatmet of Powe Electoc a Electcal Dve, 17.ltoa 15, 78 33 Otava-Poba, Czech eblc oej.fe@vb.cz

More information

Trignometric Inequations and Fuzzy Information Theory

Trignometric Inequations and Fuzzy Information Theory Iteratoal Joural of Scetfc ad Iovatve Mathematcal Reearch (IJSIMR) Volume, Iue, Jauary - 0, PP 00-07 ISSN 7-07X (Prt) & ISSN 7- (Ole) www.arcjoural.org Trgometrc Iequato ad Fuzzy Iformato Theory P.K. Sharma,

More information

In Calculus I you learned an approximation method using a Riemann sum. Recall that the Riemann sum is

In Calculus I you learned an approximation method using a Riemann sum. Recall that the Riemann sum is Mth Sprg 08 L Approxmtg Dete Itegrls I Itroducto We hve studed severl methods tht llow us to d the exct vlues o dete tegrls However, there re some cses whch t s ot possle to evlute dete tegrl exctly I

More information

Parametric Methods. Autoregressive (AR) Moving Average (MA) Autoregressive - Moving Average (ARMA) LO-2.5, P-13.3 to 13.4 (skip

Parametric Methods. Autoregressive (AR) Moving Average (MA) Autoregressive - Moving Average (ARMA) LO-2.5, P-13.3 to 13.4 (skip Pmeti Methods Autoegessive AR) Movig Avege MA) Autoegessive - Movig Avege ARMA) LO-.5, P-3.3 to 3.4 si 3.4.3 3.4.5) / Time Seies Modes Time Seies DT Rdom Sig / Motivtio fo Time Seies Modes Re the esut

More information

Spectral Continuity: (p, r) - Α P And (p, k) - Q

Spectral Continuity: (p, r) - Α P And (p, k) - Q IOSR Joul of Mthemtcs (IOSR-JM) e-issn: 2278-5728, p-issn: 2319-765X Volume 11, Issue 1 Ve 1 (J - Feb 215), PP 13-18 wwwosjoulsog Spectl Cotuty: (p, ) - Α P Ad (p, k) - Q D Sethl Kum 1 d P Mhesw Nk 2 1

More information

On Fractional Operational Calculus pertaining to the product of H- functions

On Fractional Operational Calculus pertaining to the product of H- functions nenonl eh ounl of Enneen n ehnolo RE e-ssn: 2395-56 Volume: 2 ue: 3 une-25 wwwene -SSN: 2395-72 On Fonl Oeonl Clulu enn o he ou of - funon D VBL Chu, C A 2 Demen of hem, Unve of Rhn, u-3255, n E-ml : vl@hooom

More information

Chapter #2 EEE State Space Analysis and Controller Design

Chapter #2 EEE State Space Analysis and Controller Design Chpte EEE8- Chpte # EEE8- Stte Spce Al d Cotolle Deg Itodcto to tte pce Obevblt/Cotollblt Modle ede: D D Go - d.go@cl.c.k /4 Chpte EEE8-. Itodcto Ae tht we hve th ode te: f, ', '',.... Ve dffclt to td

More information

OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9

OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9 OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at

More information

On Stability of a Class of Fractional Differential Equations

On Stability of a Class of Fractional Differential Equations Proceedgs of the Pkst Acdey of Sceces 49 (: 39-43 (0 Coyrght Pkst Acdey of Sceces SSN: 0377-969 Pkst Acdey of Sceces Orgl Artcle O Stblty of Clss of Frctol Dfferetl Equtos Rbh W. brh* sttute of Mthetcl

More information

Control of industrial robots. Robot dynamics

Control of industrial robots. Robot dynamics Coto of dut oot Root dy of. oo Roo (oo.oo@o.t) oteo d Mo Dteto d Eetto, Ifozoe e Bogege Itoduto Wth thee de we w deve the dy ode of the uto he dy ode out fo the eto etwee the oue of oto (foe d oet) d the

More information

THE PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Series A, OF THE ROMANIAN ACADEMY Volume 6, Number 1/2005, pp

THE PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Series A, OF THE ROMANIAN ACADEMY Volume 6, Number 1/2005, pp THE PUBLISHING HOUSE PROCEEDINGS OF THE ROANIAN ACADEY, Sere A, OF THE ROANIAN ACADEY Volume 6, Number /005,. 000-000 ON THE TRANSCENDENCE OF THE TRACE FUNCTION Vctor ALEXANDRU Faculty o athematc, Uverty

More information

I. Exponential Function

I. Exponential Function MATH & STAT Ch. Eoetil Fuctios JCCSS I. Eoetil Fuctio A. Defiitio f () =, whee ( > 0 ) d is the bse d the ideedet vible is the eoet. [ = 1 4 4 4L 4 ] ties (Resf () = is owe fuctio i which the bse is the

More information

«A first lesson on Mathematical Induction»

«A first lesson on Mathematical Induction» Bcgou ifotio: «A fist lesso o Mtheticl Iuctio» Mtheticl iuctio is topic i H level Mthetics It is useful i Mtheticl copetitios t ll levels It hs bee coo sight tht stuets c out the poof b theticl iuctio,

More information

fur \ \,,^N/ D7,,)d.s) 7. The champion and Runner up of the previous year shall be allowed to play directly in final Zone.

fur \ \,,^N/ D7,,)d.s) 7. The champion and Runner up of the previous year shall be allowed to play directly in final Zone. OUL O GR SODRY DUTO, ODS,RT,SMTUR,USWR.l ntuctin f cnuct f Kbi ( y/gil)tunent f 2L-Lg t. 2.. 4.. 6. Mtche hll be lye e K ule f ene f tie t tie Dutin f ech tch hll be - +0 (Rece)+ = M The ticint f ech Te

More information

3. REVIEW OF PROPERTIES OF EIGENVALUES AND EIGENVECTORS

3. REVIEW OF PROPERTIES OF EIGENVALUES AND EIGENVECTORS . REVIEW OF PROPERTIES OF EIGENVLUES ND EIGENVECTORS. EIGENVLUES ND EIGENVECTORS We hll ow revew ome bc fct from mtr theory. Let be mtr. clr clled egevlue of f there et ozero vector uch tht Emle: Let 9

More information

SOLVING SYSTEMS OF EQUATIONS, DIRECT METHODS

SOLVING SYSTEMS OF EQUATIONS, DIRECT METHODS ELM Numecl Alyss D Muhem Mecmek SOLVING SYSTEMS OF EQUATIONS DIRECT METHODS ELM Numecl Alyss Some of the cotets e dopted fom Luee V. Fusett Appled Numecl Alyss usg MATLAB. Petce Hll Ic. 999 ELM Numecl

More information

The linear system. The problem: solve

The linear system. The problem: solve The ler syste The prole: solve Suppose A s vertle, the there ests uue soluto How to effetly opute the soluto uerlly??? A A A evew of dret ethods Guss elto wth pvotg Meory ost: O^ Coputtol ost: O^ C oly

More information

Mean Cordial Labeling of Certain Graphs

Mean Cordial Labeling of Certain Graphs J Comp & Math Sc Vol4 (4), 74-8 (03) Mea Cordal Labelg o Certa Graphs ALBERT WILLIAM, INDRA RAJASINGH ad S ROY Departmet o Mathematcs, Loyola College, Chea, INDIA School o Advaced Sceces, VIT Uversty,

More information

SYSTEMS OF NON-LINEAR EQUATIONS. Introduction Graphical Methods Close Methods Open Methods Polynomial Roots System of Multivariable Equations

SYSTEMS OF NON-LINEAR EQUATIONS. Introduction Graphical Methods Close Methods Open Methods Polynomial Roots System of Multivariable Equations SYSTEMS OF NON-LINEAR EQUATIONS Itoduto Gaphal Method Cloe Method Ope Method Polomal Root Stem o Multvaale Equato Chapte Stem o No-Lea Equato /. Itoduto Polem volvg o-lea equato egeeg lude optmato olvg

More information

On The Circulant K Fibonacci Matrices

On The Circulant K Fibonacci Matrices IOSR Jou of Mthetcs (IOSR-JM) e-issn: 78-578 p-issn: 39-765X. Voue 3 Issue Ve. II (M. - Ap. 07) PP 38-4 www.osous.og O he Ccut K bocc Mtces Sego co (Deptet of Mthetcs Uvesty of Ls Ps de G C Sp) Abstct:

More information

are positive, and the pair A, B is controllable. The uncertainty in is introduced to model control failures.

are positive, and the pair A, B is controllable. The uncertainty in is introduced to model control failures. Lectue 4 8. MRAC Desg fo Affe--Cotol MIMO Systes I ths secto, we cosde MRAC desg fo a class of ult-ut-ult-outut (MIMO) olea systes, whose lat dyacs ae lealy aaetezed, the ucetates satsfy the so-called

More information

On the Oscillation of Solutions of Fractional Vector Partial Differential Equations with Deviating Arguments

On the Oscillation of Solutions of Fractional Vector Partial Differential Equations with Deviating Arguments Aec evew o Mhec d Sc Je 7 ol 5 No 5-57 ISSN: 7-8 7-56 Ole Cogh The AhoAll gh eeved blhed b Aec eech Ie o olc eveloe OI: 56/v55 : h://doog/56/v55 O he Ocllo o Solo o Fcol eco l eel Eqo wh evg Age Sdhv d

More information

Numerical Methods using the Successive Approximations for the Solution of a Fredholm Integral Equation

Numerical Methods using the Successive Approximations for the Solution of a Fredholm Integral Equation ece Advce Appled d eorecl ec uercl eod u e Succeve Approo or e Soluo o Fredol Ierl Equo AIA OBIŢOIU epre o ec d opuer Scece Uvery o Peroş Uvery Sree 6 Peroş OAIA rdorou@yoo.co Arc: pper pree wo eod or

More information

On Several Inequalities Deduced Using a Power Series Approach

On Several Inequalities Deduced Using a Power Series Approach It J Cotemp Mth Sceces, Vol 8, 203, o 8, 855-864 HIKARI Ltd, wwwm-hrcom http://dxdoorg/02988/jcms2033896 O Severl Iequltes Deduced Usg Power Seres Approch Lored Curdru Deprtmet of Mthemtcs Poltehc Uversty

More information

Review of Linear Algebra

Review of Linear Algebra PGE 30: Forulto d Soluto Geosstes Egeerg Dr. Blhoff Sprg 0 Revew of Ler Alger Chpter 7 of Nuercl Methods wth MATLAB, Gerld Recktewld Vector s ordered set of rel (or cople) uers rrged s row or colu sclr

More information

An Analysis of Brand Selection

An Analysis of Brand Selection (IJCS) Itetol Joul of dvced Comute Scece d lctos Vol. o. 8 lss of Bd Selecto Kuho Tkesu College of Busess dmstto Tokoh Uvest 5 Oouch Fuj Ct Shuok -8 J uk Hguch Fcult of Busess dmstto Setsu Uvest -8 Iked-kmch

More information

Java Applets / Flash Java Applet vs. Flash

Java Applets / Flash Java Applet vs. Flash ava Alet / Flah ava Alet v. Flah oltal oblem wth Mooft hhl otable moe dfflt develomet ot a oblem le o exellet val develomet tool Alet / Flah ood fo tato volv omlex e t whee XTML t elemet ae ot adeqate

More information

Regularization of the Divergent Integrals I. General Consideration

Regularization of the Divergent Integrals I. General Consideration Zozuly / Electoc Joul o Bouy Eleets ol 4 No pp 49-57 6 Reulzto o the Dveet Itels I Geel Coseto Zozuly Ceto e Ivestco Cetc e Yuct AC Clle 43 No 3 Colo Chubuá e Hlo C 97 Mé Yuctá Méco E-l: zozuly@ccy Abstct

More information

Physics 232 Exam II Mar. 28, 2005

Physics 232 Exam II Mar. 28, 2005 Phi 3 M. 8, 5 So. Se # Ne. A piee o gl, ide o eio.5, h hi oig o oil o i. The oil h ide o eio.4.d hike o. Fo wh welegh, i he iile egio, do ou ge o eleio? The ol phe dieee i gie δ Tol δ PhDieee δ i,il δ

More information

SGN Audio and Speech Processing. Linear Prediction

SGN Audio and Speech Processing. Linear Prediction SGN-46 Audo d Seech Poceg Le Pedcto Slde fo th lectue e bed o thoe ceted by Kt Mhoe fo TUT coue Puheeättely meetelmät Sg 3. Othe ouce: K. Koe: Puheeättely meetelmät, lectue mtel, TUT, htt://www.c.tut.f/coue/sgn-4/g4.df

More information

PARAMETRIC STUDY ON PARETO, NASH MIN- MAX DIFFERENTIAL GAME

PARAMETRIC STUDY ON PARETO, NASH MIN- MAX DIFFERENTIAL GAME Euopea Scetc Joual Jauay 5 edto vol., No.3 ISSN: 857 788 (t) e - ISSN 857-743 ARAETRIC STUDY ON ARETO, NASH IN- AX DIFFERENTIAL GAE.S.Oma, o. th o Ramada Uvety, Egypt N.A. El-Kholy, D. Tata Uvety, Faculty

More information

H STO RY OF TH E SA NT

H STO RY OF TH E SA NT O RY OF E N G L R R VER ritten for the entennial of th e Foundin g of t lair oun t y on ay 8 82 Y EEL N E JEN K RP O N! R ENJ F ] jun E 3 1 92! Ph in t ed b y h e t l a i r R ep u b l i c a n O 4 1922

More information

Week 10: DTMC Applications Ranking Web Pages & Slotted ALOHA. Network Performance 10-1

Week 10: DTMC Applications Ranking Web Pages & Slotted ALOHA. Network Performance 10-1 Week : DTMC Alictions Rnking Web ges & Slotted ALOHA etwok efonce - Outline Aly the theoy of discete tie Mkov chins: Google s nking of web-ges Wht ge is the use ost likely seching fo? Foulte web-gh s Mkov

More information

GCE AS and A Level MATHEMATICS FORMULA BOOKLET. From September Issued WJEC CBAC Ltd.

GCE AS and A Level MATHEMATICS FORMULA BOOKLET. From September Issued WJEC CBAC Ltd. GCE AS d A Level MATHEMATICS FORMULA BOOKLET Fom Septeme 07 Issued 07 Pue Mthemtcs Mesuto Suce e o sphee = 4 Ae o cuved suce o coe = heght slt Athmetc Sees S = + l = [ + d] Geometc Sees S = S = o < Summtos

More information

Journal of Engineering and Natural Sciences Mühendislik ve Fen Bilimleri Dergisi SOME PROPERTIES CONCERNING THE HYPERSURFACES OF A WEYL SPACE

Journal of Engineering and Natural Sciences Mühendislik ve Fen Bilimleri Dergisi SOME PROPERTIES CONCERNING THE HYPERSURFACES OF A WEYL SPACE Jou of Eee d Ntu Scece Mühed e Fe Be De S 5/4 SOME PROPERTIES CONCERNING THE HYPERSURFACES OF A EYL SPACE N KOFOĞLU M S Güze St Üete, Fe-Edeyt Füte, Mtet Böüü, Beştş-İSTANBUL Geş/Receed:..4 Ku/Accepted:

More information

On Signed Product Cordial Labeling

On Signed Product Cordial Labeling Appled Mathematcs 55-53 do:.436/am..6 Publshed Ole December (http://www.scrp.or/joural/am) O Sed Product Cordal Label Abstract Jayapal Baskar Babujee Shobaa Loaatha Departmet o Mathematcs Aa Uversty Chea

More information

Some Equivalent Forms of Bernoulli s Inequality: A Survey *

Some Equivalent Forms of Bernoulli s Inequality: A Survey * Ale Mthets 3 4 7-93 htt://oog/436/34746 Pulshe Ole Jul 3 (htt://wwwsog/joul/) Soe Euvlet Fos of Beoull s Ieult: A Suve * u-chu L Cheh-Chh eh 3 Detet of Ale Mthets Ntol Chug-Hsg Uvest Tw Detet of Mthets

More information

T h e C S E T I P r o j e c t

T h e C S E T I P r o j e c t T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T

More information