Trace of Positive Integer Power of Adjacency Matrix
|
|
- Ethan Griffith
- 6 years ago
- Views:
Transcription
1 Global Joual of Pue ad Appled Mathematcs. IN Volume, Numbe 07), pp Reseach Ida Publcatos Tace of Postve Itege Powe of Adacecy Matx Jagdsh Kuma Pahade * ad Mao Jha Depatmet of Mathematcs, Maulaa Azad Natoal Isttute of Techology, Bhopal M.P.) Ida. Depatmet of Mathematcs, Maulaa Azad Natoal Isttute of Techology, Bhopal M.P.), Ida. Abstact Fdg the tace of postve tege powe of a matx s a mpotat poblem matx theoy. I the Gaph Theoy a mpotat applcato of the tace of postve tege powe of Adacecy matx s coutg the tagles coected gaph. I ths pape we peset a ew effcet fomula to fd the tace of postve tege powe of some specal Adacecy matx of coected smple gaph. The key dea of ou fomula s to multply the matx k tmes, whee k s postve tege. Keywods: Adacecy matx, Complete Gaph, Tace, Matx multplcato, Matx powe. INTRODUCTION Taces of powes of matces ase seveal felds of mathematcs. Moe specfcally Netwok Aalyss, Numbe theoy, Dyamcal systems, Matx theoy, ad Dffeetal equatos []. Thee ae may applcatos matx theoy ad umecal lea algeba. Fo example, ode to obta appoxmatos of the smallest ad the lagest Ege values of a symmetc matx A, a pocedue based o estmates of the tace of A ad A -, s atual, was poposed []. Whe aalyzg a complex etwok, a mpotat poblem s to compute the total umbe of tagles
2 080 Jagdsh Kuma Pahade ad Mao Jha of a coected smple gaph. Ths umbe s equal to TA )/ whee A s the adacecy matx of the gaph [].It s possble to solve tagle fdg ad coutg a gaph by adacecy matx epesetato of the gaph [9]. Fo ay tege matx M ad ay pme umbe p, the etes of the uque Wtt vecto cosstg of p-adc teges ae expessed fom the taces of powes of the tege matx M [].Taces of powes of tege matces ae coected wth the Eule coguece [] p TM p T M mod p ) Holds fo all tege matces M, all pmes p, ad all atual. Thee ae may applcatos of ths coguece to dyamcal systems, whch s atual studyg those vaats of dyamcal systems that ae descbed tems of the taces of powes of tege matces, fo example studyg the Lefschetz umbes [].oluto of Lyapuov matx equatos ca be solved by usg matx polyomals ad chaactestc polyomals whee the computato of the taces of matx powes ae eeded [].Thee s a questo [],ca tace k Awhee k A s the k-th symmetc powe of matx A) be wtte tems of some coeffcet of A k+ ad the coespodg coeffcet A? The computato of the tace of matx powes has eceved much atteto. I [], a algothm fo computg TA k ), k s tege, s poposed, whe A s a lowe Hessebeg matx wth a ut codagoal. I [7], a symbolc calculato of the tace of powes of Tdagoal matces s peseted. Tace of postve tege powe of eal matces s peseted [8].A fomula fo tace of ay symmetc powe of a matx s peseted [0] tems of the oday powe of matx. Let A be a symmetc postve defte matx, ad let {λk} deote ts Ege values. Fo q R, A q s also symmetc postve defte, ad t holds [] TA q =Ʃkλk q But fo hghe ode matx fdg Ege values λk s vey dffcult ad tme cosumg, theefoe othe fomula to compute tace of matx powe s eeded. Now we peset a ew theoem to compute tace of matx powe fo adacecy matx of a coected smple gaph wth ay umbe of vetces. Ou estmato fo the tace of A k s based o the multplcato of matx. Ths fomula wll deped oly o ode of the matx. Tace of a matx A = [a], s defed to be the sum of the elemets o the ma dagoal of A..e. TA = a + a +..+a A complete gaph s a smple udected gaph whch evey pa of dstct vetces s coected by a uque edge. Fo a gve umbe of vetces, thee's a
3 Tace of Postve Itege Powe of Adacecy Matx 08 uque complete gaph. The adacecy matx of the complete gaph takes the patculaly smple fom of all ˈs wth 0ˈs o the dagoal,.e., the ut matx mus the detty matx. MAIN REULT Theoem.Let A s a adacecy symmetc matx of a complete smple gaph wth vetces, the TA ad k / / s k, ) k k, fo eve postve tege k k TA s k, ), fo odd postve tege k. whee k, be a umbe depedg upo k ad, ad defed by k k,, k, k /, k, k /, ad, k, k, k, Poof: Cosde a adacecy symmetc matx A = a),, whee a = 0 f f Now A = a),, whee a = f f HeceTA = O TA. =, O TA = s, ) ) ).
4 08 Jagdsh Kuma Pahade ad Mao Jha Aga A = a),, whee a = f f Hece TA = O TA =., O TA =. ) ) ), Aga A = a),, whee a = f f O a = f f Hece TA = O TA =.. ) ),) ) ), s O TA =. ) ) ), Aga A = a),, whee a = f f
5 Tace of Postve Itege Powe of Adacecy Matx 08 O a = f f Hece TA = O TA =.. ) ),) ) ), O. ) ) ), T A Aga A = a),, whee a= f f O a = f f Hece TA = ) + ) ) + ) O TA =.. ) ),) ) ), +. ) ),) O TA =. ) ) ), Aga A 7 = a),, whee a= f f
6 08 Jagdsh Kuma Pahade ad Mao Jha O a f f Hece TA 7 = ) ) + ) ) ) + O TA 7 = , ) ) 7,) ) + 7,) ) ) 7. ) O TA 7 = 7, ) ) ) 7. Cotug ths pocess of multplcato of matx, we coclude that, TA k / s k, ) k, fo eve postve tege k ad / k TA whee k k k,, be a umbe depedg upo k ad, ad defed by k, fo odd postve tege k. k,, k, k /, k, k /, ad, k, k, k, Ths completes the poof.
7 Tace of Postve Itege Powe of Adacecy Matx 08 Example : Cosde a matx A = TA. 0 0 [ ] ad let we ae to fd Hee = ad k =.the by ou theoem, we have TA =, ) ) ). O TA =.., ) ),) ) O TA = + = 0 Example : How may tagles ae thee the followg gaph? ) We kow that the umbe of tagles the coected gaph s TA )/, whee A s the adacecy matx of the gaph. The adacecy matx of ths gaph s A = By ou theoem TA =, ) ) ) Hee =, TA =,) ) )..
8 08 Jagdsh Kuma Pahade ad Mao Jha O TA = = Numbe of tagles the gaph = TA )/ = / =,amely,,,. Example : How may tagles the followg gaph? 7 Hee adacecy matx of the gaph s A = a), 7, 7 whee a 0 f f By ou theoem TA =, ) ) ) Hee = 7, TA. =,)77 ) 7 ) O TA = 7 = 0 Numbe of tagles the gaph = TA )/ = 0/ =.. CONCLUION AND FUTURE WORK I ths pape,we exteded the ode of matx peseted [8] fo the tace of postve tege powe of eal matx to the tace of postve tege powe of some adacecy matx of ay ode.as explaed the pape such estmates have applcatos vaous baches of mathematcs. The deas peseted ths pape could be exteded to ay matx.
9 Tace of Postve Itege Powe of Adacecy Matx 087 ACKNOWLEDGMENT We would lke to hadly thakful wth geat atttude to Decto, Maulaa Azad Natoal Isttute of Techology, Bhopal fo facal suppot ad we also thakful to HOD, Depatmet of Mathematcs of ths sttute fo gvg me oppotuty to expose my eseach scetfc wold. REFERENCE [] B. N. Dattaad K. Datta, A algothm fo computg powes of a Hessebeg matx ad ts applcatos, Lea Algeba Appl., 97), pp [] H. Avo, Coutg tagles lage gaphs usg adomzed matx tace estmato, Poceedgs of kdd-ldmta 0, acm, 00. [] Claude Bezsk, Paaskev Fka, ad Malea Mtoul, Estmatos of the tace of powes of postve self-ado opeatos by extapolato of the momets, Electoc tasactos o umecal aalyss, Volume 9, pp. -, 0. [] V. Pa, Estmatg the extemal egevalues of a symmetc matx, Comput. Math. Appl.,0990), pp. 7. [] N. Hgham, Fuctos of Matces: Theoy ad Computato, IAM, Phladelpha, 008. [] A. V. Zaelua, O cogueces fo the taces of powes of some matces, Poc. teklovist. Math., 008), pp [7] M. T. Chu, ymbolc calculato of the tace of the powe of a tdagoal matx, Computg, 98),pp [8] Pahade, J. ad Jha, M. 0) Tace of Postve Itege Powe of Real Matces. Advaces Lea algeba & Matx Theoy,,0-. [9] Matheu Latapy, Ma-memoy tagle computatos fo vey lage gaph, Theoetcal Compute cece ) 8 7. [0] Cseos J.L.,Heea R. ad ataa N.,A fomula fo the tace of symmetc powe of matces, math DG 0,aXv:.0v. [] Cseos-Mola, J.L.,A vaat of matces, Electo.J.Lea Algeba 00),-.
10 088 Jagdsh Kuma Pahade ad Mao Jha
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= y and Normed Linear Spaces
304-50 LINER SYSTEMS Lectue 8: Solutos to = ad Nomed Lea Spaces 73 Fdg N To fd N, we eed to chaacteze all solutos to = 0 Recall that ow opeatos peseve N, so that = 0 = 0 We ca solve = 0 ecusvel backwads
More information( m is the length of columns of A ) spanned by the columns of A : . Select those columns of B that contain a pivot; say those are Bi
Assgmet /MATH 47/Wte Due: Thusday Jauay The poblems to solve ae umbeed [] to [] below Fst some explaatoy otes Fdg a bass of the colum-space of a max ad povg that the colum ak (dmeso of the colum space)
More informationMinimum Hyper-Wiener Index of Molecular Graph and Some Results on Szeged Related Index
Joual of Multdscplay Egeeg Scece ad Techology (JMEST) ISSN: 359-0040 Vol Issue, Febuay - 05 Mmum Hype-Wee Idex of Molecula Gaph ad Some Results o eged Related Idex We Gao School of Ifomato Scece ad Techology,
More informationInequalities for Dual Orlicz Mixed Quermassintegrals.
Advaces Pue Mathematcs 206 6 894-902 http://wwwscpog/joual/apm IN Ole: 260-0384 IN Pt: 260-0368 Iequaltes fo Dual Olcz Mxed Quemasstegals jua u chool of Mathematcs ad Computatoal cece Hua Uvesty of cece
More informationXII. Addition of many identical spins
XII. Addto of may detcal sps XII.. ymmetc goup ymmetc goup s the goup of all possble pemutatos of obects. I total! elemets cludg detty opeato. Each pemutato s a poduct of a ceta fte umbe of pawse taspostos.
More informationFairing of Parametric Quintic Splines
ISSN 46-69 Eglad UK Joual of Ifomato ad omputg Scece Vol No 6 pp -8 Fag of Paametc Qutc Sples Yuau Wag Shagha Isttute of Spots Shagha 48 ha School of Mathematcal Scece Fuda Uvesty Shagha 4 ha { P t )}
More informationProfessor Wei Zhu. 1. Sampling from the Normal Population
AMS570 Pofesso We Zhu. Samplg fom the Nomal Populato *Example: We wsh to estmate the dstbuto of heghts of adult US male. It s beleved that the heght of adult US male follows a omal dstbuto N(, ) Def. Smple
More informationOn EPr Bimatrices II. ON EP BIMATRICES A1 A Hence x. is said to be EP if it satisfies the condition ABx
Iteatoal Joual of Mathematcs ad Statstcs Iveto (IJMSI) E-ISSN: 3 4767 P-ISSN: 3-4759 www.jms.og Volume Issue 5 May. 4 PP-44-5 O EP matces.ramesh, N.baas ssocate Pofesso of Mathematcs, ovt. ts College(utoomous),Kumbakoam.
More informationRecent Advances in Computers, Communications, Applied Social Science and Mathematics
Recet Advaces Computes, Commucatos, Appled ocal cece ad athematcs Coutg Roots of Radom Polyomal Equatos mall Itevals EFRAI HERIG epatmet of Compute cece ad athematcs Ael Uvesty Cete of amaa cece Pa,Ael,4487
More informationSOME ARITHMETIC PROPERTIES OF OVERPARTITION K -TUPLES
#A17 INTEGERS 9 2009), 181-190 SOME ARITHMETIC PROPERTIES OF OVERPARTITION K -TUPLES Deick M. Keiste Depatmet of Mathematics, Pe State Uivesity, Uivesity Pak, PA 16802 dmk5075@psu.edu James A. Selles Depatmet
More informationAn Unconstrained Q - G Programming Problem and its Application
Joual of Ifomato Egeeg ad Applcatos ISS 4-578 (pt) ISS 5-0506 (ole) Vol.5, o., 05 www.ste.og A Ucostaed Q - G Pogammg Poblem ad ts Applcato M. He Dosh D. Chag Tved.Assocate Pofesso, H L College of Commece,
More informationFIBONACCI-LIKE SEQUENCE ASSOCIATED WITH K-PELL, K-PELL-LUCAS AND MODIFIED K-PELL SEQUENCES
Joual of Appled Matheatcs ad Coputatoal Mechacs 7, 6(), 59-7 www.ac.pcz.pl p-issn 99-9965 DOI:.75/jac.7..3 e-issn 353-588 FIBONACCI-LIKE SEQUENCE ASSOCIATED WITH K-PELL, K-PELL-LUCAS AND MODIFIED K-PELL
More informationGREEN S FUNCTION FOR HEAT CONDUCTION PROBLEMS IN A MULTI-LAYERED HOLLOW CYLINDER
Joual of ppled Mathematcs ad Computatoal Mechacs 4, 3(3), 5- GREE S FUCTIO FOR HET CODUCTIO PROBLEMS I MULTI-LYERED HOLLOW CYLIDER Stasław Kukla, Uszula Sedlecka Isttute of Mathematcs, Czestochowa Uvesty
More informationExponential 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 informationHarmonic Curvatures in Lorentzian Space
BULLETIN of the Bull Malaya Math Sc Soc Secod See 7-79 MALAYSIAN MATEMATICAL SCIENCES SOCIETY amoc Cuvatue Loetza Space NEJAT EKMEKÇI ILMI ACISALIOĞLU AND KĀZIM İLARSLAN Aaa Uvety Faculty of Scece Depatmet
More informationON THE CONVERGENCE THEOREMS OF THE McSHANE INTEGRAL FOR RIESZ-SPACES-VALUED FUNCTIONS DEFINED ON REAL LINE
O The Covegece Theoems... (Muslm Aso) ON THE CONVERGENCE THEOREMS OF THE McSHANE INTEGRAL FOR RIESZ-SPACES-VALUED FUNCTIONS DEFINED ON REAL LINE Muslm Aso, Yosephus D. Sumato, Nov Rustaa Dew 3 ) Mathematcs
More informationRECAPITULATION & CONDITIONAL PROBABILITY. Number of favourable events n E Total number of elementary events n S
Fomulae Fo u Pobablty By OP Gupta [Ida Awad We, +91-9650 350 480] Impotat Tems, Deftos & Fomulae 01 Bascs Of Pobablty: Let S ad E be the sample space ad a evet a expemet espectvely Numbe of favouable evets
More informationHyper-wiener index of gear fan and gear wheel related graph
Iteatoal Joual of Chemcal Studes 015; (5): 5-58 P-ISSN 49 858 E-ISSN 1 490 IJCS 015; (5): 5-58 014 JEZS Receed: 1-0-015 Accepted: 15-0-015 We Gao School of Ifomato Scece ad Techology, Yua Nomal Uesty,
More informationThe Exponentiated Lomax Distribution: Different Estimation Methods
Ameca Joual of Appled Mathematcs ad Statstcs 4 Vol. No. 6 364-368 Avalable ole at http://pubs.scepub.com/ajams//6/ Scece ad Educato Publshg DOI:.69/ajams--6- The Expoetated Lomax Dstbuto: Dffeet Estmato
More informationThe calculation of the characteristic and non-characteristic harmonic current of the rectifying system
The calculato of the chaactestc a o-chaactestc hamoc cuet of the ectfyg system Zhag Ruhua, u Shagag, a Luguag, u Zhegguo The sttute of Electcal Egeeg, Chese Acaemy of Sceces, ejg, 00080, Cha. Zhag Ruhua,
More informationCouncil for Innovative Research
Geometc-athmetc Idex ad Zageb Idces of Ceta Specal Molecula Gaphs efe X, e Gao School of Tousm ad Geogaphc Sceces, Yua Nomal Uesty Kumg 650500, Cha School of Ifomato Scece ad Techology, Yua Nomal Uesty
More informationQuasi-Rational Canonical Forms of a Matrix over a Number Field
Avace Lea Algeba & Matx Theoy, 08, 8, -0 http://www.cp.og/joual/alamt ISSN Ole: 65-3348 ISSN Pt: 65-333X Qua-Ratoal Caocal om of a Matx ove a Numbe el Zhueg Wag *, Qg Wag, Na Q School of Mathematc a Stattc,
More informationNon-axial symmetric loading on axial symmetric. Final Report of AFEM
No-axal symmetc loadg o axal symmetc body Fal Repot of AFEM Ths poject does hamoc aalyss of o-axal symmetc loadg o axal symmetc body. Shuagxg Da, Musket Kamtokat 5//009 No-axal symmetc loadg o axal symmetc
More informationThe 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 informationUniversity 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 informationIterative Algorithm for a Split Equilibrium Problem and Fixed Problem for Finite Asymptotically Nonexpansive Mappings in Hilbert Space
Flomat 31:5 (017), 143 1434 DOI 10.98/FIL170543W Publshed by Faculty of Sceces ad Mathematcs, Uvesty of Nš, Seba Avalable at: http://www.pmf..ac.s/flomat Iteatve Algothm fo a Splt Equlbum Poblem ad Fxed
More informationLecture 10: Condensed matter systems
Lectue 0: Codesed matte systems Itoducg matte ts codesed state.! Ams: " Idstgushable patcles ad the quatum atue of matte: # Cosequeces # Revew of deal gas etopy # Femos ad Bosos " Quatum statstcs. # Occupato
More informationGreatest term (numerically) in the expansion of (1 + x) Method 1 Let T
BINOMIAL THEOREM_SYNOPSIS Geatest tem (umeically) i the epasio of ( + ) Method Let T ( The th tem) be the geatest tem. Fid T, T, T fom the give epasio. Put T T T ad. Th will give a iequality fom whee value
More informationApplication Of Alternating Group Explicit Method For Parabolic Equations
WSEAS RANSACIONS o INFORMAION SCIENCE ad APPLICAIONS Qghua Feg Applcato Of Alteatg oup Explct Method Fo Paabolc Equatos Qghua Feg School of Scece Shadog uvesty of techology Zhagzhou Road # Zbo Shadog 09
More informationRANDOM SYSTEMS WITH COMPLETE CONNECTIONS AND THE GAUSS PROBLEM FOR THE REGULAR CONTINUED FRACTIONS
RNDOM SYSTEMS WTH COMPETE CONNECTONS ND THE GUSS PROBEM FOR THE REGUR CONTNUED FRCTONS BSTRCT Da ascu o Coltescu Naval cademy Mcea cel Bata Costata lascuda@gmalcom coltescu@yahoocom Ths pape peset the
More informationBINOMIAL THEOREM An expression consisting of two terms, connected by + or sign is called a
BINOMIAL THEOREM hapte 8 8. Oveview: 8.. A epessio cosistig of two tems, coected by + o sig is called a biomial epessio. Fo eample, + a, y,,7 4 5y, etc., ae all biomial epessios. 8.. Biomial theoem If
More informationCounting Functions and Subsets
CHAPTER 1 Coutig Fuctios ad Subsets This chapte of the otes is based o Chapte 12 of PJE See PJE p144 Hee ad below, the efeeces to the PJEccles book ae give as PJE The goal of this shot chapte is to itoduce
More informationComparing Different Estimators of three Parameters for Transmuted Weibull Distribution
Global Joural of Pure ad Appled Mathematcs. ISSN 0973-768 Volume 3, Number 9 (207), pp. 55-528 Research Ida Publcatos http://www.rpublcato.com Comparg Dfferet Estmators of three Parameters for Trasmuted
More informationChapter 7 Varying Probability Sampling
Chapte 7 Vayg Pobablty Samplg The smple adom samplg scheme povdes a adom sample whee evey ut the populato has equal pobablty of selecto. Ude ceta ccumstaces, moe effcet estmatos ae obtaed by assgg uequal
More informationBINOMIAL THEOREM NCERT An expression consisting of two terms, connected by + or sign is called a
8. Oveview: 8.. A epessio cosistig of two tems, coected by + o sig is called a biomial epessio. Fo eample, + a, y,,7 4, etc., ae all biomial 5y epessios. 8.. Biomial theoem BINOMIAL THEOREM If a ad b ae
More informationStability Analysis for Linear Time-Delay Systems. Described by Fractional Parameterized. Models Possessing Multiple Internal. Constant Discrete Delays
Appled Mathematcal Sceces, Vol. 3, 29, o. 23, 5-25 Stablty Aalyss fo Lea me-delay Systems Descbed by Factoal Paametezed Models Possessg Multple Iteal Costat Dscete Delays Mauel De la Se Isttuto de Ivestgacó
More informationOn Eigenvalues of Nonlinear Operator Pencils with Many Parameters
Ope Scece Joual of Matheatc ad Applcato 5; 3(4): 96- Publhed ole Jue 5 (http://wwwopececeoleco/oual/oa) O Egevalue of Nolea Opeato Pecl wth May Paaete Rakhhada Dhabaadeh Guay Salaova Depatet of Fuctoal
More informationPermutations that Decompose in Cycles of Length 2 and are Given by Monomials
Poceedgs of The Natoa Cofeece O Udegaduate Reseach (NCUR) 00 The Uvesty of Noth Caoa at Asheve Asheve, Noth Caoa Ap -, 00 Pemutatos that Decompose Cyces of Legth ad ae Gve y Moomas Lous J Cuz Depatmet
More informationLecture 9 Multiple Class Models
Lectue 9 Multple Class Models Multclass MVA Appoxmate MVA 8.4.2002 Copyght Teemu Keola 2002 1 Aval Theoem fo Multple Classes Wth jobs the system, a job class avg to ay seve sees the seve as equlbum wth
More informationBy the end of this section you will be able to prove the Chinese Remainder Theorem apply this theorem to solve simultaneous linear congruences
Chapte : Theoy of Modula Aithmetic 8 Sectio D Chiese Remaide Theoem By the ed of this sectio you will be able to pove the Chiese Remaide Theoem apply this theoem to solve simultaeous liea cogueces The
More informationThe Linear Probability Density Function of Continuous Random Variables in the Real Number Field and Its Existence Proof
MATEC Web of Cofeeces ICIEA 06 600 (06) DOI: 0.05/mateccof/0668600 The ea Pobablty Desty Fucto of Cotuous Radom Vaables the Real Numbe Feld ad Its Estece Poof Yya Che ad Ye Collee of Softwae, Taj Uvesty,
More informationMATH 247/Winter Notes on the adjoint and on normal operators.
MATH 47/Wter 00 Notes o the adjot ad o ormal operators I these otes, V s a fte dmesoal er product space over, wth gve er * product uv, T, S, T, are lear operators o V U, W are subspaces of V Whe we say
More informationFULLY RIGHT PURE GROUP RINGS (Gelanggang Kumpulan Tulen Kanan Penuh)
Joual of Qualty Measuemet ad Aalyss JQMA 3(), 07, 5-34 Jual Pegukua Kualt da Aalss FULLY IGHT PUE GOUP INGS (Gelaggag Kumpula Tule Kaa Peuh) MIKHLED ALSAAHEAD & MOHAMED KHEI AHMAD ABSTACT I ths pape, we
More informationEstimation of Stress- Strength Reliability model using finite mixture of exponential distributions
Iteratoal Joural of Computatoal Egeerg Research Vol, 0 Issue, Estmato of Stress- Stregth Relablty model usg fte mxture of expoetal dstrbutos K.Sadhya, T.S.Umamaheswar Departmet of Mathematcs, Lal Bhadur
More informationDANIEL YAQUBI, MADJID MIRZAVAZIRI AND YASIN SAEEDNEZHAD
MIXED -STIRLING NUMERS OF THE SEOND KIND DANIEL YAQUI, MADJID MIRZAVAZIRI AND YASIN SAEEDNEZHAD Abstact The Stilig umbe of the secod id { } couts the umbe of ways to patitio a set of labeled balls ito
More informationLecture 9: Tolerant Testing
Lecture 9: Tolerat Testg Dael Kae Scrbe: Sakeerth Rao Aprl 4, 07 Abstract I ths lecture we prove a quas lear lower boud o the umber of samples eeded to do tolerat testg for L dstace. Tolerat Testg We have
More informationEvaluating Polynomials
Uverst of Nebraska - Lcol DgtalCommos@Uverst of Nebraska - Lcol MAT Exam Expostor Papers Math the Mddle Isttute Partershp 7-7 Evaluatg Polomals Thomas J. Harrgto Uverst of Nebraska-Lcol Follow ths ad addtoal
More informationare 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 informationAPPROXIMATE ANALYTIC WAVE FUNCTION METHOD IN ELECTRON ATOM SCATTERING CALCULATIONS. Budi Santoso
APPROXIMATE ANALYTIC WAVE FUNCTION METHOD IN ELECTRON ATOM SCATTERING CALCULATIONS Bud Satoso ABSTRACT APPROXIMATE ANALYTIC WAVE FUNCTION METHOD IN ELECTRON ATOM SCATTERING CALCULATIONS. Appoxmate aalytc
More informationSolving Constrained Flow-Shop Scheduling. Problems with Three Machines
It J Cotemp Math Sceces, Vol 5, 2010, o 19, 921-929 Solvg Costraed Flow-Shop Schedulg Problems wth Three Maches P Pada ad P Rajedra Departmet of Mathematcs, School of Advaced Sceces, VIT Uversty, Vellore-632
More informationCHAPTER 4 RADICAL EXPRESSIONS
6 CHAPTER RADICAL EXPRESSIONS. The th Root of a Real Number A real umber a s called the th root of a real umber b f Thus, for example: s a square root of sce. s also a square root of sce ( ). s a cube
More informationGeneralized Fibonacci-Lucas Sequence
Tuish Joual of Aalysis ad Numbe Theoy, 4, Vol, No 6, -7 Available olie at http://pubssciepubcom/tjat//6/ Sciece ad Educatio Publishig DOI:6/tjat--6- Geealized Fiboacci-Lucas Sequece Bijeda Sigh, Ompaash
More informationThe Pigeonhole Principle 3.4 Binomial Coefficients
Discete M athematic Chapte 3: Coutig 3. The Pigeohole Piciple 3.4 Biomial Coefficiets D Patic Cha School of Compute Sciece ad Egieeig South Chia Uivesity of Techology Ageda Ch 3. The Pigeohole Piciple
More informationON EUCLID S AND EULER S PROOF THAT THE NUMBER OF PRIMES IS INFINITE AND SOME APPLICATIONS
Joual of Pue ad Alied Mathematics: Advaces ad Alicatios Volume 0 Numbe 03 Pages 5-58 ON EUCLID S AND EULER S PROOF THAT THE NUMBER OF PRIMES IS INFINITE AND SOME APPLICATIONS ALI H HAKAMI Deatmet of Mathematics
More informationResearch Article A New Derivation and Recursive Algorithm Based on Wronskian Matrix for Vandermonde Inverse Matrix
Mathematcal Problems Egeerg Volume 05 Artcle ID 94757 7 pages http://ddoorg/055/05/94757 Research Artcle A New Dervato ad Recursve Algorthm Based o Wroska Matr for Vadermode Iverse Matr Qu Zhou Xja Zhag
More informationA NOTE ON DOMINATION PARAMETERS IN RANDOM GRAPHS
Discussioes Mathematicae Gaph Theoy 28 (2008 335 343 A NOTE ON DOMINATION PARAMETERS IN RANDOM GRAPHS Athoy Boato Depatmet of Mathematics Wilfid Lauie Uivesity Wateloo, ON, Caada, N2L 3C5 e-mail: aboato@oges.com
More information2.1.1 The Art of Estimation Examples of Estimators Properties of Estimators Deriving Estimators Interval Estimators
. ploatoy Statstcs. Itoducto to stmato.. The At of stmato.. amples of stmatos..3 Popetes of stmatos..4 Devg stmatos..5 Iteval stmatos . Itoducto to stmato Samplg - The samplg eecse ca be epeseted by a
More informationChapter 9 Jordan Block Matrices
Chapter 9 Jorda Block atrces I ths chapter we wll solve the followg problem. Gve a lear operator T fd a bass R of F such that the matrx R (T) s as smple as possble. f course smple s a matter of taste.
More informationLearning Bayesian belief networks
Lectue 6 Leag Bayesa belef etwoks Mlos Hauskecht mlos@cs.ptt.edu 5329 Seott Squae Admstato Mdtem: Wedesday, Mach 7, 2004 I class Closed book Mateal coveed by Spg beak, cludg ths lectue Last yea mdtem o
More informationTHE ANALYTIC LARGE SIEVE
THE ANALYTIC LAGE SIEVE 1. The aalytic lage sieve I the last lectue we saw how to apply the aalytic lage sieve to deive a aithmetic fomulatio of the lage sieve, which we applied to the poblem of boudig
More informationCh 3.4 Binomial Coefficients. Pascal's Identit y and Triangle. Chapter 3.2 & 3.4. South China University of Technology
Disc ete Mathem atic Chapte 3: Coutig 3. The Pigeohole Piciple 3.4 Biomial Coefficiets D Patic Cha School of Compute Sciece ad Egieeig South Chia Uivesity of Techology Pigeohole Piciple Suppose that a
More informationJohns Hopkins University Department of Biostatistics Math Review for Introductory Courses
Johs Hopks Uverst Departmet of Bostatstcs Math Revew for Itroductor Courses Ratoale Bostatstcs courses wll rel o some fudametal mathematcal relatoshps, fuctos ad otato. The purpose of ths Math Revew s
More informationBest Linear Unbiased Estimators of the Three Parameter Gamma Distribution using doubly Type-II censoring
Best Lea Ubased Estmatos of the hee Paamete Gamma Dstbuto usg doubly ype-ii cesog Amal S. Hassa Salwa Abd El-Aty Abstact Recetly ode statstcs ad the momets have assumed cosdeable teest may applcatos volvg
More informationAssignment 5/MATH 247/Winter Due: Friday, February 19 in class (!) (answers will be posted right after class)
Assgmet 5/MATH 7/Wter 00 Due: Frday, February 9 class (!) (aswers wll be posted rght after class) As usual, there are peces of text, before the questos [], [], themselves. Recall: For the quadratc form
More informationANOTHER 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 informationAuchmuty High School Mathematics Department Advanced Higher Notes Teacher Version
The Binomial Theoem Factoials Auchmuty High School Mathematics Depatment The calculations,, 6 etc. often appea in mathematics. They ae called factoials and have been given the notation n!. e.g. 6! 6!!!!!
More informationUsing Laplace Transform to Evaluate Improper Integrals Chii-Huei Yu
Available at https://edupediapublicationsog/jounals Volume 3 Issue 4 Febuay 216 Using Laplace Tansfom to Evaluate Impope Integals Chii-Huei Yu Depatment of Infomation Technology, Nan Jeon Univesity of
More information12.2 Estimating Model parameters Assumptions: ox and y are related according to the simple linear regression model
1. Estmatg Model parameters Assumptos: ox ad y are related accordg to the smple lear regresso model (The lear regresso model s the model that says that x ad y are related a lear fasho, but the observed
More informationSUFFICIENT CONDITIONS FOR MAXIMALLY EDGE-CONNECTED AND SUPER-EDGE-CONNECTED GRAPHS DEPENDING ON THE CLIQUE NUMBER
Discussiones Mathematicae Gaph Theoy 39 (019) 567 573 doi:10.7151/dmgt.096 SUFFICIENT CONDITIONS FOR MAXIMALLY EDGE-CONNECTED AND SUPER-EDGE-CONNECTED GRAPHS DEPENDING ON THE CLIQUE NUMBER Lutz Volkmann
More informationECONOMETRIC THEORY. MODULE VIII Lecture - 26 Heteroskedasticity
ECONOMETRIC THEORY MODULE VIII Lecture - 6 Heteroskedastcty Dr. Shalabh Departmet of Mathematcs ad Statstcs Ida Isttute of Techology Kapur . Breusch Paga test Ths test ca be appled whe the replcated data
More informationMultistage Median Ranked Set Sampling for Estimating the Population Median
Jounal of Mathematcs and Statstcs 3 (: 58-64 007 ISSN 549-3644 007 Scence Publcatons Multstage Medan Ranked Set Samplng fo Estmatng the Populaton Medan Abdul Azz Jeman Ame Al-Oma and Kamaulzaman Ibahm
More informationDistribution of Geometrically Weighted Sum of Bernoulli Random Variables
Appled Mathematc, 0,, 8-86 do:046/am095 Publhed Ole Novembe 0 (http://wwwscrpog/oual/am) Dtbuto of Geometcally Weghted Sum of Beoull Radom Vaable Abtact Deepeh Bhat, Phazamle Kgo, Ragaath Naayaachaya Ratthall
More informationk. s k=1 Part of the significance of the Riemann zeta-function stems from Theorem 9.2. If s > 1 then 1 p s
9 Pimes in aithmetic ogession Definition 9 The Riemann zeta-function ζs) is the function which assigns to a eal numbe s > the convegent seies k s k Pat of the significance of the Riemann zeta-function
More informationA note on random minimum length spanning trees
A ote o adom miimum legth spaig tees Ala Fieze Miklós Ruszikó Lubos Thoma Depatmet of Mathematical Scieces Caegie Mello Uivesity Pittsbugh PA15213, USA ala@adom.math.cmu.edu, usziko@luta.sztaki.hu, thoma@qwes.math.cmu.edu
More informationMachine Learning. Spectral Clustering. Lecture 23, April 14, Reading: Eric Xing 1
Machne Leanng -7/5 7/5-78, 78, Spng 8 Spectal Clusteng Ec Xng Lectue 3, pl 4, 8 Readng: Ec Xng Data Clusteng wo dffeent ctea Compactness, e.g., k-means, mxtue models Connectvty, e.g., spectal clusteng
More informationX ε ) = 0, or equivalently, lim
Revew for the prevous lecture Cocepts: order statstcs Theorems: Dstrbutos of order statstcs Examples: How to get the dstrbuto of order statstcs Chapter 5 Propertes of a Radom Sample Secto 55 Covergece
More informationJournal of Engineering Science and Technology Review 7 (2) (2014) Research Article
Jest Joual of Egeeg Scece ad echology Revew 7 () (4) 75 8 Reseach Atcle JOURNAL OF Egeeg Scece ad echology Revew www.jest.og Fuzzy Backsteppg Sldg Mode Cotol fo Msmatched Uceta System H. Q. Hou,*, Q. Mao,
More informationarxiv: v1 [math.nt] 28 Oct 2017
ON th COEFFICIENT OF DIVISORS OF x n axiv:70049v [mathnt] 28 Oct 207 SAI TEJA SOMU Abstact Let,n be two natual numbes and let H(,n denote the maximal absolute value of th coefficient of divisos of x n
More informationPTAS for Bin-Packing
CS 663: Patter Matchg Algorthms Scrbe: Che Jag /9/00. Itroducto PTAS for B-Packg The B-Packg problem s NP-hard. If we use approxmato algorthms, the B-Packg problem could be solved polyomal tme. For example,
More informationOn Eccentricity Sum Eigenvalue and Eccentricity Sum Energy of a Graph
Aals of Pure ad Appled Mathematcs Vol. 3, No., 7, -3 ISSN: 79-87X (P, 79-888(ole Publshed o 3 March 7 www.researchmathsc.org DOI: http://dx.do.org/.7/apam.3a Aals of O Eccetrcty Sum Egealue ad Eccetrcty
More informationNUMERICAL SIMULATION OF TSUNAMI CURRENTS AROUND MOVING STRUCTURES
NUMERICAL SIMULATION OF TSUNAMI CURRENTS AROUND MOVING STRUCTURES Ezo Nakaza 1, Tsuakyo Ibe ad Muhammad Abdu Rouf 1 The pape ams to smulate Tsuam cuets aoud movg ad fxed stuctues usg the movg-patcle semmplct
More informationChapter 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 informationOn Submanifolds of an Almost r-paracontact Riemannian Manifold Endowed with a Quarter Symmetric Metric Connection
Theoretcal Mathematcs & Applcatos vol. 4 o. 4 04-7 ISS: 79-9687 prt 79-9709 ole Scepress Ltd 04 O Submafolds of a Almost r-paracotact emaa Mafold Edowed wth a Quarter Symmetrc Metrc Coecto Mob Ahmad Abdullah.
More informationCISC 203: Discrete Mathematics for Computing II Lecture 2, Winter 2019 Page 9
Lectue, Wte 9 Page 9 Combatos I ou dscusso o pemutatos wth dstgushable elemets, we aved at a geeal fomula by dvdg the total umbe of pemutatos by the umbe of ways we could pemute oly the dstgushable elemets.
More informationConditional Convergence of Infinite Products
Coditioal Covegece of Ifiite Poducts William F. Tech Ameica Mathematical Mothly 106 1999), 646-651 I this aticle we evisit the classical subject of ifiite poducts. Fo stadad defiitios ad theoems o this
More informationJohns Hopkins University Department of Biostatistics Math Review for Introductory Courses
Johs Hopks Uverst Departmet of Bostatstcs Math Revew for Itroductor Courses Ratoale Bostatstcs courses wll rel o some fudametal mathematcal relatoshps, fuctos ad otato. The purpose of ths Math Revew s
More informationIntroduction to Matrices and Matrix Approach to Simple Linear Regression
Itroducto to Matrces ad Matrx Approach to Smple Lear Regresso Matrces Defto: A matrx s a rectagular array of umbers or symbolc elemets I may applcatos, the rows of a matrx wll represet dvduals cases (people,
More informationFIXED POINT AND HYERS-ULAM-RASSIAS STABILITY OF A QUADRATIC FUNCTIONAL EQUATION IN BANACH SPACES
IJRRAS 6 () July 0 www.apapess.com/volumes/vol6issue/ijrras_6.pdf FIXED POINT AND HYERS-UAM-RASSIAS STABIITY OF A QUADRATIC FUNCTIONA EQUATION IN BANACH SPACES E. Movahedia Behbaha Khatam Al-Abia Uivesity
More informationOn a Problem of Littlewood
Ž. JOURAL OF MATHEMATICAL AALYSIS AD APPLICATIOS 199, 403 408 1996 ARTICLE O. 0149 O a Poblem of Littlewood Host Alze Mosbache Stasse 10, 51545 Waldbol, Gemay Submitted by J. L. Bee Received May 19, 1995
More informationON THE INVERSE SIGNED TOTAL DOMINATION NUMBER IN GRAPHS. D.A. Mojdeh and B. Samadi
Opuscula Math. 37, no. 3 (017), 447 456 http://dx.doi.og/10.7494/opmath.017.37.3.447 Opuscula Mathematica ON THE INVERSE SIGNED TOTAL DOMINATION NUMBER IN GRAPHS D.A. Mojdeh and B. Samadi Communicated
More informationGeneralizations and analogues of the Nesbitt s inequality
OCTOGON MATHEMATICAL MAGAZINE Vol 17, No1, Apil 2009, pp 215-220 ISSN 1222-5657, ISBN 978-973-88255-5-0, wwwhetfaluo/octogo 215 Geealiatios ad aalogues of the Nesbitt s iequalit Fuhua Wei ad Shahe Wu 19
More informationL-MOMENTS EVALUATION FOR IDENTICALLY AND NONIDENTICALLY WEIBULL DISTRIBUTED RANDOM VARIABLES
THE PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Sees A, OF THE ROMANIAN ACADEMY Volume 8, Numbe 3/27,. - L-MOMENTS EVALUATION FOR IDENTICALLY AND NONIDENTICALLY WEIBULL DISTRIBUTED RANDOM VARIABLES
More informationQuestion 1. Typical Cellular System. Some geometry TELE4353. About cellular system. About cellular system (2)
TELE4353 Moble a atellte Commucato ystems Tutoal 1 (week 3-4 4 Questo 1 ove that fo a hexagoal geomety, the co-chael euse ato s gve by: Q (3 N Whee N + j + j 1/ 1 Typcal Cellula ystem j cells up cells
More informationRobust Regression Analysis for Non-Normal Situations under Symmetric Distributions Arising In Medical Research
Joual of Mode Appled Statstcal Methods Volume 3 Issue Atcle 9 5--04 Robust Regesso Aalyss fo No-Nomal Stuatos ude Symmetc Dstbutos Asg I Medcal Reseach S S. Gaguly Sulta Qaboos Uvesty, Muscat, Oma, gaguly@squ.edu.om
More informationRandomly Weighted Averages on Order Statistics
Apple Mathematcs 3 4 34-346 http://oog/436/am3498 Publshe Ole Septembe 3 (http://wwwscpog/joual/am Raomly Weghte Aveages o Oe Statstcs Home Haj Hasaaeh Lela Ma Ghasem Depatmet of Statstcs aculty of Mathematcal
More informationTaylor Transformations into G 2
Iteatioal Mathematical Foum, 5,, o. 43, - 3 Taylo Tasfomatios ito Mulatu Lemma Savaah State Uivesity Savaah, a 344, USA Lemmam@savstate.edu Abstact. Though out this pape, we assume that
More informationEinstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,
MB BINOMIAL THEOREM Biomial Epessio : A algebaic epessio which cotais two dissimila tems is called biomial epessio Fo eample :,,, etc / ( ) Statemet of Biomial theoem : If, R ad N, the : ( + ) = a b +
More information(n 1)n(n + 1)(n + 2) + 1 = (n 1)(n + 2)n(n + 1) + 1 = ( (n 2 + n 1) 1 )( (n 2 + n 1) + 1 ) + 1 = (n 2 + n 1) 2.
Paabola Volume 5, Issue (017) Solutions 151 1540 Q151 Take any fou consecutive whole numbes, multiply them togethe and add 1. Make a conjectue and pove it! The esulting numbe can, fo instance, be expessed
More informationUsing Difference Equations to Generalize Results for Periodic Nested Radicals
Usig Diffeece Equatios to Geealize Results fo Peiodic Nested Radicals Chis Lyd Uivesity of Rhode Islad, Depatmet of Mathematics South Kigsto, Rhode Islad 2 2 2 2 2 2 2 π = + + +... Vieta (593) 2 2 2 =
More information