A Characterization of Jacobson Radical in Γ-Banach Algebras
|
|
- Jennifer Blankenship
- 6 years ago
- Views:
Transcription
1 Advaces Pure Matheatcs Publshed Ole Noveber ( A Characterzato of Jacobso Radcal Γ-Baach Algebras Nlash Goswa Departet of Matheatcs Gauhat Uversty Guwahat Ida Eal: la_g3@yahooco Receved August 7 ; revsed Septeber 5 ; accepted October 3 ABSTRACT V V Let V ad V be two -Baach algebras ad R be the rght operator Baach algebra ad L be the left operator Baach algebra of V We gve a characterzato of the Jacobso radcal for the projectve tesor product ters of the Jacobso radcal for R L If ad V are soorphc the we show that ths characterzato ca also be gve ters of the Jacobso radcal for V R L Keywords: Γ-Algebra; Rght Quas Regularty; Tesor Product; Operator Baach Algebra Itroducto I [] usg the rght quas regularty property Kyuo ad Coppage ad Luh gave a characterzato of Jacobso radcal -rgs May terestg results o the teral propertes of Jacobso radcal for -rgs were developed [-5] by dfferet research worers I [6] soe of these results are exteded to -algebras I ths paper we cosder two -Baach algebras V ad V ad cosder ther projectve tesor product V V Let R be the rght operator Baach algebra ad L be the left operator Baach algebra of V We gve a characterzato of Jacobso radcal J V V ters of J R L Before gog to preset our a results we frst gve soe basc terologes (refer to [5-]) whch are eeded our dscusso Defto Let X be a rg havg the ut eleet e A ew ultplcato called the crcle coposto (refer to [5]) o X s defed by: x x xxxx Ths coposto aes sese eve whe X does ot have the ut eleet A eleet x of X s sad to be rght quas regular f t has a rght quas verse wrt ths coposto e there exsts xx such that x x xxxx Defto Let V ad be two lear spaces over a feld F V s sad to be a -algebra over F f for x y z V ; ; a F the followg codtos are satsfed: ) x yv ; x y z x yz ; ) a xy axy xay xay x yz x y x z x y xy xy x y z xz yz V 3) ; 4) The -algebra s deoted by If V ad are ored lear spaces over F the -algebra V s called a -ored algebra f codtos ) to 4) hold ad further 5) xy x y holds A -ored algebra V s called a -Baach algebra f V s a Baach space Ay Baach algebra ca be regarded as a -Baach algebra by sutably choosg Defto 3 A subset I of a -Baach algebra V s sad to be a rght (left) -deal of V f ) I s a subspace of V ( the vector space sese); ) ; x y I y xi xi y V e I V I V I I A rght -deal whch s a left -deal as well s called a two-sded -deal or sply a -deal Defto 4 Let V be a -Baach algebra ad let x V The the appg x defed by y x yxy V s a rght Baach space edoorphs of V The collecto R of all edoorphss geerated by x ; x V s a Baach algebra uder the operatos: x y= x y x x x Copyrght ScRes
2 44 N GOSWAMI where a F ad the or: a x ax a x x y xy x x V Ths Baach algebra s tered as the rght operator Baach algebra of -Baach algebra V We ca slarly defe the left operator Baach algebra L of V as the Baach algebra geerated by the set of all left edoorphss of V the for x where x y xyyv Defto 5 Let V ad V be -Baach algebras over F ad : V V be a appg The s called a -Baach algebra hooorphs f ) ax by ax b y ad ) xy x y for all x y V ; ad ab F Defto 6 Let X ad Y be two ored spaces The projectve tesor or o X Y s defed as: u f x y : u x y where the fu s tae over all (fte) represetatos of u The copleto of X Y s called the projectve tesor product of X ad Y ad s deoted by X Y Let V ad V be -Baach algebras over F ad F soorphc to F The projectve tesor product V V wth the projectve tesor or s a -Baach algebra over F where a ultplcato s defed by the forula: x y xy xx yy where x y V ; x yv; Defto 7 Let V be a -Baach algebra Let A eleet x V s sad to be -rght quas regular wth -rght quas verse y f x yx y x s sad to be a rght quas regular eleet of V f t s -rght quas regular for each Equvaletly a eleet x V s called rght quas regular f for ay there exst v V such that vx v v vx v vv A deal I of V s sad to be rght quas regular f each of ts eleets s rght quas regular We have rght quas regularty s a radcal property a algebra The axal rght quas regular deal s called the Jacobso radcal of V ad t s deoted by J(V) Ma Results I [6] we have the followg Lea regardg rght quas regularty of a -Baach algebra ad ts operator algebra Lea A eleet x of a -Baach algebra V s rght quas s rght quas regular the rght operator Baach algebra R of V Extedg ths result to the projectve tesor product of -Baach algebras we prove Lea regular f ad oly f for all x Let V ad V be two ad -Baach algebras respectvely Let R be the rght operator Baach algebra of V ad L be the left operator Baach algebra of V If x x s rght quas regular V V the x x s rght quas regular R L for ad coversely Proof Sce x x s rght quas regular V V so for ay there exst j j j pj xj xj V V j such that for ay q v v V V j j j j j j q x x q p q x x p v x x v v j j xj x v j j v v x x j j xj x j j v x x v v x x v v x x x xv j j j j j j j j j j () Copyrght ScRes
3 N GOSWAMI 45 Let x x x We tae j j x Now y x j j j x yxy v v x x j xj xj j j x x j xj xj j v v j x x v v j x j xj j v v j x x j x j xj j v v j v x xv v x x v v x x x j j j j j j j j j jx v (by ()) Proof Let x x J V V But v v V V s arbtrary The x x s a rght quas regular eleet of So x + y xy = Thus x e x x s V V By Lea for ay rght quas regular R L x x s a rght quas regular eleet of The coverse follows the sae way I [3] we have defed the followg deal for the R L e projectve tesor product of V ad V xx JR L Lea 3 Let V ad V be two ad -Baach algebras respectvely Let R be the rght operator Baach algebra of So V ad L be the left operator Baach algebra of V Let J x x JR L be a deal of R L We defe: Hece J x x V V : xx J x x J R L where x x j : j ad j x j : x j j The J s a deal of V V Usg the above defed deal ow we gve the characterzato of Jacobso radcal for the projectve tesor product of two -Baach algebras V ters of the Jacobso radcal of the projectve tesor product of correspodg rght ad left operator Baach algebras Theore 4 Let V be a -Baach algebra (over F) wth rght operator Baach algebra R ad left operator Baach algebra L respectvely The the Jacobso radcal of V J R L s gve by: J V V V Thus J V V J R L Coversely let The x x J R L x x J R L So for ay x x R L x x s a rght quas regular eleet of V V s a rght quas regular eleet of By Lea So e x x JV V Copyrght ScRes
4 46 N GOSWAMI L JV V J R Thus J V L V J R Let the -Baach algebras V ad V are soorphc I that case we have the followg result Theore 5 Let V be a -Baach algebra (over F) wth rght operator Baach algebra R ad left operator Baach algebra L respectvely If there exsts a -Baach algebra soorphs f fro V oto V the R L s a hooorphc age of R L Proof Let r lr L where l y r x We defe : R L R L by r l x y xf y where x f x x V Let r R (The dual space of R ) We defe r : R C by r x r x where x f x The r R Slarly for l L we ca defe l L by l y lf y Now let r r l l where r x l y r l r lh h hr L I partcular tag h r l we get r l l r l r r l r r l l r r l l where ad x f x x f x r x l y r x l y y y r x l f r x l f xf y r l xf y r l r lr lr l r l But r ad are arbtrary So R l L r l r l b x f y Thus s well defed Now Let ab F The arl brl arl brl a x y b x y a x y b x y a x f y f x ad where x x f x b x f y a x f y a f( x) f y b f x f y ar l br l Aga r lr l rr l l x x y y () x x y y We have x x V So there exst x x V x f x x f x such that Now x x V ad f x x f x f x x x So the expresso () s equal to Copyrght ScRes
5 N GOSWAMI 47 x x f y y x x f y f y x xf y f y xf y x f y r lr l So : R L R L s a hooorphs Sce f s oto so s also oto Also t ca be show that s oe-oe Thus R L R L Corollary 6 Let the -Baach algebras V ad V as defed Theore 4 are soorphc The we have R L J V V J Rear 7 If the soorphs f fro V oto V s soetrc the we ca show that : R L R L s also a soetry So that case R L J V V J The oto of drect suad for -rgs s dscussed [] by Booth For a -Baach algebra V a deal P s called drect suad f there exsts a -deal Q of V such that every eleet v of V s uquely expressble the for v = p + q p P qq ad V s wrtte as V PQ Clearly f V P Q the for p P qq p q Now we prove: Deducto 8 If P s the drect suad for the -Baach algebra V V the J P s the drect suad for J V V Proof Let V V PQClearly JQ J P ad x = p + q where p P qq Sce x s rght quas regular V V so for ay we have there exsts yv V such that x yx y Let y p q where p P q Q So Let x JV V pq pq pq pq p p p p + qq q q [sce p q But p p p ppad q q q q Q ad P Q So p p p p ad q q q q for ay ad q p ] Thus p s rght quas regular P ad q s rght quas regular Q e p JP ad q JQ Hece J VV = JPJQ I [4] there s a characterzato of Jacobso radcal for -rgs ters of axal regular left deals Lea 9 M Let X be a -rg The J X where the tersecto s over all axal regular left deals M of X Cosderg ths aspect we ca rase the followg proble: Let the structures of axal regular left deals of the operator Baach algebras R ad L are gve Usg ths ca we obta the structure of the Jacobso radcal for V V? I [6] Behres radcal for -Baach algebras s troduced whch cotas the Jacobso radcal Let deote the class of all subdrectly rreducble -Baach algebras V such that the tersecto of all o-zero deals of V cotas a o-zero depotet eleet The upper radcal R B detered by the class s called the Behres radcal for V Lea For a sple -Baach algebra V J V RB V Now aother proble ca be rased: Ca we derve aalogous result as Theore 4 case of the Behres radcal for V V? REFERENCES [] S Kyuo Notes o Jacobso Radcals of Gaa Rgs Matheatca Japoca Vol 7 No 98 pp 7- [] W E Coppage ad J Luh Radcals of Gaa Rgs Joural of the Matheatcal Socety of Japa Vol 3 No 97 pp 4-5 do:969/jsj/34 [3] A C Paul ad A K Azad Jacobso Radcal for Gaa Rgs Rajshah Uversty Studes Part-B Joural of Scece Vol pp 53-6 [4] A C Paul ad Md S Udd O Jacobso Radcal for Gaa Rgs Gat: Joural of Bagladesh Matheatcal Socety Vol 9 9 pp 47-6 [5] K N Raghava The Jacobso Desty Theore ad Applcatos 5 [6] H K Nath A Study of Gaa-Baach Algebras PhD Thess Gauhat Uversty Guwahat [7] W E Bares O the -Rgs of Nobusawa Pacfc Joural of Matheatcs Vol 8 No pp 4- Copyrght ScRes
6 48 N GOSWAMI 4 [8] D K Bhattacharya ad A K Maty Selear Tesor Product of -Baach Algebras Gata Vol 4 No 989 pp 75-8 [9] F F Bosall ad J Duca Coplete Nored Algebras Sprger-Verlag Berl 973 do:7/ [] G L Booth Operator Rgs of a -Rg Math Japoca Vol 3 No 986 pp [] N J Dvsy Rgs ad Radcals George Alle ad Uw Lodo 965 [] N Goswa Soe Results o Operator Baach Algebras of a -Baach Algebra Joural of Assa Acadey of Matheatcs Vol pp 4-48 [3] N Goswa O Levtzl Radcal of Gaa Baach Algebras Global Joural of Appled Matheatcs ad Matheatcal Sceces Press Copyrght ScRes
SUBCLASS OF HARMONIC UNIVALENT FUNCTIONS ASSOCIATED WITH SALAGEAN DERIVATIVE. Sayali S. Joshi
Faculty of Sceces ad Matheatcs, Uversty of Nš, Serba Avalable at: http://wwwpfacyu/float Float 3:3 (009), 303 309 DOI:098/FIL0903303J SUBCLASS OF ARMONIC UNIVALENT FUNCTIONS ASSOCIATED WIT SALAGEAN DERIVATIVE
More informationA Family of Non-Self Maps Satisfying i -Contractive Condition and Having Unique Common Fixed Point in Metrically Convex Spaces *
Advaces Pure Matheatcs 0 80-84 htt://dxdoorg/0436/a04036 Publshed Ole July 0 (htt://wwwscrporg/oural/a) A Faly of No-Self Mas Satsfyg -Cotractve Codto ad Havg Uque Coo Fxed Pot Metrcally Covex Saces *
More informationA New Method for Solving Fuzzy Linear. Programming by Solving Linear Programming
ppled Matheatcal Sceces Vol 008 o 50 7-80 New Method for Solvg Fuzzy Lear Prograg by Solvg Lear Prograg S H Nasser a Departet of Matheatcs Faculty of Basc Sceces Mazadara Uversty Babolsar Ira b The Research
More informationConnective Eccentricity Index of Some Thorny Graphs
Aals of ure ad Appled Matheatcs Vol. 7, No., 04, 59-64 IN: 79-087X (), 79-0888(ole) ublshed o 9 epteber 04 www.researchathsc.org Aals of oectve Eccetrcty Idex of oe Thory raphs Nlaja De, k. Md. Abu Nayee
More informationA Conventional Approach for the Solution of the Fifth Order Boundary Value Problems Using Sixth Degree Spline Functions
Appled Matheatcs, 1, 4, 8-88 http://d.do.org/1.4/a.1.448 Publshed Ole Aprl 1 (http://www.scrp.org/joural/a) A Covetoal Approach for the Soluto of the Ffth Order Boudary Value Probles Usg Sth Degree Sple
More information2/20/2013. Topics. Power Flow Part 1 Text: Power Transmission. Power Transmission. Power Transmission. Power Transmission
/0/0 Topcs Power Flow Part Text: 0-0. Power Trassso Revsted Power Flow Equatos Power Flow Proble Stateet ECEGR 45 Power Systes Power Trassso Power Trassso Recall that for a short trassso le, the power
More informationA Remark on the Uniform Convergence of Some Sequences of Functions
Advaces Pure Mathematcs 05 5 57-533 Publshed Ole July 05 ScRes. http://www.scrp.org/joural/apm http://dx.do.org/0.436/apm.05.59048 A Remark o the Uform Covergece of Some Sequeces of Fuctos Guy Degla Isttut
More informationInternational Journal of Mathematical Archive-5(8), 2014, Available online through ISSN
Iteratoal Joural of Mathematcal Archve-5(8) 204 25-29 Avalable ole through www.jma.fo ISSN 2229 5046 COMMON FIXED POINT OF GENERALIZED CONTRACTION MAPPING IN FUZZY METRIC SPACES Hamd Mottagh Golsha* ad
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 informationMULTIOBJECTIVE NONLINEAR FRACTIONAL PROGRAMMING PROBLEMS INVOLVING GENERALIZED d - TYPE-I n -SET FUNCTIONS
THE PUBLIHING HOUE PROCEEDING OF THE ROMANIAN ACADEMY, eres A OF THE ROMANIAN ACADEMY Volue 8, Nuber /27,.- MULTIOBJECTIVE NONLINEAR FRACTIONAL PROGRAMMING PROBLEM INVOLVING GENERALIZED d - TYPE-I -ET
More informationA Study on Generalized Generalized Quasi hyperbolic Kac Moody algebra QHGGH of rank 10
Global Joural of Mathematcal Sceces: Theory ad Practcal. ISSN 974-3 Volume 9, Number 3 (7), pp. 43-4 Iteratoal Research Publcato House http://www.rphouse.com A Study o Geeralzed Geeralzed Quas (9) hyperbolc
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 information18.413: Error Correcting Codes Lab March 2, Lecture 8
18.413: Error Correctg Codes Lab March 2, 2004 Lecturer: Dael A. Spelma Lecture 8 8.1 Vector Spaces A set C {0, 1} s a vector space f for x all C ad y C, x + y C, where we take addto to be compoet wse
More informationOn the construction of symmetric nonnegative matrix with prescribed Ritz values
Joural of Lear ad Topologcal Algebra Vol. 3, No., 14, 61-66 O the costructo of symmetrc oegatve matrx wth prescrbed Rtz values A. M. Nazar a, E. Afshar b a Departmet of Mathematcs, Arak Uversty, P.O. Box
More informationV. Hemalatha, V. Mohana Selvi,
Iteratoal Joural of Scetfc & Egeerg Research, Volue 6, Issue, Noveber-0 ISSN - SUPER GEOMETRIC MEAN LABELING OF SOME CYCLE RELATED GRAPHS V Healatha, V Mohaa Selv, ABSTRACT-Let G be a graph wth p vertces
More informationThe Mathematical Appendix
The Mathematcal Appedx Defto A: If ( Λ, Ω, where ( λ λ λ whch the probablty dstrbutos,,..., Defto A. uppose that ( Λ,,..., s a expermet type, the σ-algebra o λ λ λ are defed s deoted by ( (,,...,, σ Ω.
More informationEntropy ISSN by MDPI
Etropy 2003, 5, 233-238 Etropy ISSN 1099-4300 2003 by MDPI www.mdp.org/etropy O the Measure Etropy of Addtve Cellular Automata Hasa Aı Arts ad Sceces Faculty, Departmet of Mathematcs, Harra Uversty; 63100,
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 informationA Penalty Function Algorithm with Objective Parameters and Constraint Penalty Parameter for Multi-Objective Programming
Aerca Joural of Operatos Research, 4, 4, 33-339 Publshed Ole Noveber 4 ScRes http://wwwscrporg/oural/aor http://ddoorg/436/aor4463 A Pealty Fucto Algorth wth Obectve Paraeters ad Costrat Pealty Paraeter
More informationNon-uniform Turán-type problems
Joural of Combatoral Theory, Seres A 111 2005 106 110 wwwelsevercomlocatecta No-uform Turá-type problems DhruvMubay 1, Y Zhao 2 Departmet of Mathematcs, Statstcs, ad Computer Scece, Uversty of Illos at
More informationResearch Article A New Iterative Method for Common Fixed Points of a Finite Family of Nonexpansive Mappings
Hdaw Publshg Corporato Iteratoal Joural of Mathematcs ad Mathematcal Sceces Volume 009, Artcle ID 391839, 9 pages do:10.1155/009/391839 Research Artcle A New Iteratve Method for Commo Fxed Pots of a Fte
More informationThe Lie Algebra of Smooth Sections of a T-bundle
IST Iteratoal Joural of Egeerg Scece, Vol 7, No3-4, 6, Page 8-85 The Le Algera of Smooth Sectos of a T-udle Nadafhah ad H R Salm oghaddam Astract: I ths artcle, we geeralze the cocept of the Le algera
More informationLebesgue Measure of Generalized Cantor Set
Aals of Pure ad Appled Mathematcs Vol., No.,, -8 ISSN: -8X P), -888ole) Publshed o 8 May www.researchmathsc.org Aals of Lebesgue Measure of Geeralzed ator Set Md. Jahurul Islam ad Md. Shahdul Islam Departmet
More informationUnique Common Fixed Point of Sequences of Mappings in G-Metric Space M. Akram *, Nosheen
Vol No : Joural of Facult of Egeerg & echolog JFE Pages 9- Uque Coo Fed Pot of Sequeces of Mags -Metrc Sace M. Ara * Noshee * Deartet of Matheatcs C Uverst Lahore Pasta. Eal: ara7@ahoo.co Deartet of Matheatcs
More informationANALYSIS ON THE NATURE OF THE BASIC EQUATIONS IN SYNERGETIC INTER-REPRESENTATION NETWORK
Far East Joural of Appled Mathematcs Volume, Number, 2008, Pages Ths paper s avalable ole at http://www.pphm.com 2008 Pushpa Publshg House ANALYSIS ON THE NATURE OF THE ASI EQUATIONS IN SYNERGETI INTER-REPRESENTATION
More informationThe Primitive Idempotents in
Iteratoal Joural of Algebra, Vol, 00, o 5, 3 - The Prmtve Idempotets FC - I Kulvr gh Departmet of Mathematcs, H College r Jwa Nagar (rsa)-5075, Ida kulvrsheora@yahoocom K Arora Departmet of Mathematcs,
More informationInvestigating Cellular Automata
Researcher: Taylor Dupuy Advsor: Aaro Wootto Semester: Fall 4 Ivestgatg Cellular Automata A Overvew of Cellular Automata: Cellular Automata are smple computer programs that geerate rows of black ad whte
More informationPROJECTION PROBLEM FOR REGULAR POLYGONS
Joural of Mathematcal Sceces: Advaces ad Applcatos Volume, Number, 008, Pages 95-50 PROJECTION PROBLEM FOR REGULAR POLYGONS College of Scece Bejg Forestry Uversty Bejg 0008 P. R. Cha e-mal: sl@bjfu.edu.c
More informationTHE PROBABILISTIC STABILITY FOR THE GAMMA FUNCTIONAL EQUATION
Joural of Scece ad Arts Year 12, No. 3(2), pp. 297-32, 212 ORIGINAL AER THE ROBABILISTIC STABILITY FOR THE GAMMA FUNCTIONAL EQUATION DOREL MIHET 1, CLAUDIA ZAHARIA 1 Mauscrpt receved: 3.6.212; Accepted
More informationStrong Convergence of Weighted Averaged Approximants of Asymptotically Nonexpansive Mappings in Banach Spaces without Uniform Convexity
BULLETIN of the MALAYSIAN MATHEMATICAL SCIENCES SOCIETY Bull. Malays. Math. Sc. Soc. () 7 (004), 5 35 Strog Covergece of Weghted Averaged Appromats of Asymptotcally Noepasve Mappgs Baach Spaces wthout
More informationFurther Results on Pair Sum Labeling of Trees
Appled Mathematcs 0 70-7 do:046/am0077 Publshed Ole October 0 (http://wwwscrporg/joural/am) Further Results o Par Sum Labelg of Trees Abstract Raja Poraj Jeyaraj Vjaya Xaver Parthpa Departmet of Mathematcs
More informationAn Innovative Algorithmic Approach for Solving Profit Maximization Problems
Matheatcs Letters 208; 4(: -5 http://www.scecepublshggroup.co/j/l do: 0.648/j.l.208040. ISSN: 2575-503X (Prt; ISSN: 2575-5056 (Ole A Iovatve Algorthc Approach for Solvg Proft Maxzato Probles Abul Kala
More informationCubic Nonpolynomial Spline Approach to the Solution of a Second Order Two-Point Boundary Value Problem
Joural of Amerca Scece ;6( Cubc Nopolyomal Sple Approach to the Soluto of a Secod Order Two-Pot Boudary Value Problem W.K. Zahra, F.A. Abd El-Salam, A.A. El-Sabbagh ad Z.A. ZAk * Departmet of Egeerg athematcs
More informationOn L- Fuzzy Sets. T. Rama Rao, Ch. Prabhakara Rao, Dawit Solomon And Derso Abeje.
Iteratoal Joural of Fuzzy Mathematcs ad Systems. ISSN 2248-9940 Volume 3, Number 5 (2013), pp. 375-379 Research Ida Publcatos http://www.rpublcato.com O L- Fuzzy Sets T. Rama Rao, Ch. Prabhakara Rao, Dawt
More informationSUPER GRACEFUL LABELING FOR SOME SPECIAL GRAPHS
IJRRAS 9 ) Deceber 0 www.arpapress.co/volues/vol9issue/ijrras_9 06.pdf SUPER GRACEFUL LABELING FOR SOME SPECIAL GRAPHS M.A. Perual, S. Navaeethakrsha, S. Arockara & A. Nagaraa 4 Departet of Matheatcs,
More informationTHE TRUNCATED RANDIĆ-TYPE INDICES
Kragujeac J Sc 3 (00 47-5 UDC 547:54 THE TUNCATED ANDIĆ-TYPE INDICES odjtaba horba, a ohaad Al Hossezadeh, b Ia uta c a Departet of atheatcs, Faculty of Scece, Shahd ajae Teacher Trag Uersty, Tehra, 785-3,
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 informationBounds for the Connective Eccentric Index
It. J. Cotemp. Math. Sceces, Vol. 7, 0, o. 44, 6-66 Bouds for the Coectve Eccetrc Idex Nlaja De Departmet of Basc Scece, Humates ad Socal Scece (Mathematcs Calcutta Isttute of Egeerg ad Maagemet Kolkata,
More informationSome results and conjectures about recurrence relations for certain sequences of binomial sums.
Soe results ad coectures about recurrece relatos for certa sequeces of boal sus Joha Cgler Faultät für Matheat Uverstät We A-9 We Nordbergstraße 5 Joha Cgler@uveacat Abstract I a prevous paper [] I have
More informationLecture 8. A little bit of fun math Read: Chapter 7 (and 8) Finite Algebraic Structures
Lecture 8 A lttle bt of fu ath Read: Chapter 7 (ad 8) Fte Algebrac Structures Groups Abela Cyclc Geerator Group order Rgs Felds Subgroups Euclda Algorth CRT (Chese Reader Theore) 2 GROUPs DEFINITION: A
More informationRelations to Other Statistical Methods Statistical Data Analysis with Positive Definite Kernels
Relatos to Other Statstcal Methods Statstcal Data Aalyss wth Postve Defte Kerels Kej Fukuzu Isttute of Statstcal Matheatcs, ROIS Departet of Statstcal Scece, Graduate Uversty for Advaced Studes October
More information. The set of these sums. be a partition of [ ab, ]. Consider the sum f( x) f( x 1)
Chapter 7 Fuctos o Bouded Varato. Subject: Real Aalyss Level: M.Sc. Source: Syed Gul Shah (Charma, Departmet o Mathematcs, US Sargodha Collected & Composed by: Atq ur Rehma (atq@mathcty.org, http://www.mathcty.org
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 information4 Inner Product Spaces
11.MH1 LINEAR ALGEBRA Summary Notes 4 Ier Product Spaces Ier product s the abstracto to geeral vector spaces of the famlar dea of the scalar product of two vectors or 3. I what follows, keep these key
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 information1 Onto functions and bijections Applications to Counting
1 Oto fuctos ad bectos Applcatos to Coutg Now we move o to a ew topc. Defto 1.1 (Surecto. A fucto f : A B s sad to be surectve or oto f for each b B there s some a A so that f(a B. What are examples of
More informationHájek-Rényi Type Inequalities and Strong Law of Large Numbers for NOD Sequences
Appl Math If Sc 7, No 6, 59-53 03 59 Appled Matheatcs & Iforato Sceces A Iteratoal Joural http://dxdoorg/0785/as/070647 Háje-Réy Type Iequaltes ad Strog Law of Large Nuers for NOD Sequeces Ma Sogl Departet
More informationSome Notes on the Probability Space of Statistical Surveys
Metodološk zvezk, Vol. 7, No., 200, 7-2 ome Notes o the Probablty pace of tatstcal urveys George Petrakos Abstract Ths paper troduces a formal presetato of samplg process usg prcples ad cocepts from Probablty
More informationMaps on Triangular Matrix Algebras
Maps o ragular Matrx lgebras HMED RMZI SOUROUR Departmet of Mathematcs ad Statstcs Uversty of Vctora Vctora, BC V8W 3P4 CND sourour@mathuvcca bstract We surveys results about somorphsms, Jorda somorphsms,
More informationJournal Of Inequalities And Applications, 2008, v. 2008, p
Ttle O verse Hlbert-tye equaltes Authors Chagja, Z; Cheug, WS Ctato Joural Of Iequaltes Ad Alcatos, 2008, v. 2008,. 693248 Issued Date 2008 URL htt://hdl.hadle.et/0722/56208 Rghts Ths work s lcesed uder
More informationfor each of its columns. A quick calculation will verify that: thus m < dim(v). Then a basis of V with respect to which T has the form: A
Desty of dagoalzable square atrces Studet: Dael Cervoe; Metor: Saravaa Thyagaraa Uversty of Chcago VIGRE REU, Suer 7. For ths etre aer, we wll refer to V as a vector sace over ad L(V) as the set of lear
More informationQ-analogue of a Linear Transformation Preserving Log-concavity
Iteratoal Joural of Algebra, Vol. 1, 2007, o. 2, 87-94 Q-aalogue of a Lear Trasformato Preservg Log-cocavty Daozhog Luo Departmet of Mathematcs, Huaqao Uversty Quazhou, Fua 362021, P. R. Cha ldzblue@163.com
More informationPrime and Semi Prime Subbi-Semi Modules of (R, R) Partial Bi-Semi Modules 1
Vol 5, o 9 September 04 ISS 079-8407 Joural of Emergg Treds Computg ad Iformato Sceces 009-04 CIS Joural All rghts reserved http://wwwcsouralorg Prme ad Sem Prme Subb-Sem Modules of (R, R) Partal B-Sem
More informationDerivation of 3-Point Block Method Formula for Solving First Order Stiff Ordinary Differential Equations
Dervato of -Pot Block Method Formula for Solvg Frst Order Stff Ordary Dfferetal Equatos Kharul Hamd Kharul Auar, Kharl Iskadar Othma, Zara Bb Ibrahm Abstract Dervato of pot block method formula wth costat
More information{ }{ ( )} (, ) = ( ) ( ) ( ) Chapter 14 Exercises in Sampling Theory. Exercise 1 (Simple random sampling): Solution:
Chapter 4 Exercses Samplg Theory Exercse (Smple radom samplg: Let there be two correlated radom varables X ad A sample of sze s draw from a populato by smple radom samplg wthout replacemet The observed
More informationMAX-MIN AND MIN-MAX VALUES OF VARIOUS MEASURES OF FUZZY DIVERGENCE
merca Jr of Mathematcs ad Sceces Vol, No,(Jauary 0) Copyrght Md Reader Publcatos wwwjouralshubcom MX-MIN ND MIN-MX VLUES OF VRIOUS MESURES OF FUZZY DIVERGENCE RKTul Departmet of Mathematcs SSM College
More informationOn 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 informationSome Different Perspectives on Linear Least Squares
Soe Dfferet Perspectves o Lear Least Squares A stadard proble statstcs s to easure a respose or depedet varable, y, at fed values of oe or ore depedet varables. Soetes there ests a deterstc odel y f (,,
More informationStrong Laws of Large Numbers for Fuzzy Set-Valued Random Variables in Gα Space
Advaces Pure Matheatcs 26 6 583-592 Publshed Ole August 26 ScRes http://wwwscrporg/oural/ap http://dxdoorg/4236/ap266947 Strog Laws of Large Nubers for uzzy Set-Valued Rado Varables G Space Lae She L Gua
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 informationLECTURES ON REPRESENTATION THEORY AND INVARIANT THEORY
LECTUES ON EPESENTATION THEOY AND INVAIANT THEOY These are the otes for a lecture course o the syetrc group, the geeral lear group ad varat theory. The a of the course was to cover as uch of the beautful
More informationDouble Dominating Energy of Some Graphs
Iter. J. Fuzzy Mathematcal Archve Vol. 4, No., 04, -7 ISSN: 30 34 (P), 30 350 (ole) Publshed o 5 March 04 www.researchmathsc.org Iteratoal Joural of V.Kaladev ad G.Sharmla Dev P.G & Research Departmet
More informationarxiv:math/ v1 [math.gm] 8 Dec 2005
arxv:math/05272v [math.gm] 8 Dec 2005 A GENERALIZATION OF AN INEQUALITY FROM IMO 2005 NIKOLAI NIKOLOV The preset paper was spred by the thrd problem from the IMO 2005. A specal award was gve to Yure Boreko
More informationOn the convergence of derivatives of Bernstein approximation
O the covergece of dervatves of Berste approxmato Mchael S. Floater Abstract: By dfferetatg a remader formula of Stacu, we derve both a error boud ad a asymptotc formula for the dervatves of Berste approxmato.
More informationChapter 4 Multiple Random Variables
Revew for the prevous lecture: Theorems ad Examples: How to obta the pmf (pdf) of U = g (, Y) ad V = g (, Y) Chapter 4 Multple Radom Varables Chapter 44 Herarchcal Models ad Mxture Dstrbutos Examples:
More informationExercises for Square-Congruence Modulo n ver 11
Exercses for Square-Cogruece Modulo ver Let ad ab,.. Mark True or False. a. 3S 30 b. 3S 90 c. 3S 3 d. 3S 4 e. 4S f. 5S g. 0S 55 h. 8S 57. 9S 58 j. S 76 k. 6S 304 l. 47S 5347. Fd the equvalece classes duced
More informationStudy of Correlation using Bayes Approach under bivariate Distributions
Iteratoal Joural of Scece Egeerg ad Techolog Research IJSETR Volume Issue Februar 4 Stud of Correlato usg Baes Approach uder bvarate Dstrbutos N.S.Padharkar* ad. M.N.Deshpade** *Govt.Vdarbha Isttute of
More informationA New Measure of Probabilistic Entropy. and its Properties
Appled Mathematcal Sceces, Vol. 4, 200, o. 28, 387-394 A New Measure of Probablstc Etropy ad ts Propertes Rajeesh Kumar Departmet of Mathematcs Kurukshetra Uversty Kurukshetra, Ida rajeesh_kuk@redffmal.com
More informationJournal of Mathematical Analysis and Applications
J. Math. Aal. Appl. 365 200) 358 362 Cotets lsts avalable at SceceDrect Joural of Mathematcal Aalyss ad Applcatos www.elsever.com/locate/maa Asymptotc behavor of termedate pots the dfferetal mea value
More informationOn the Primitive Classes of K * KHALED S. FELALI Department of Mathematical Sciences, Umm Al-Qura University, Makkah Al-Mukarramah, Saudi Arabia
JKAU: Sc., O vol. the Prmtve, pp. 55-62 Classes (49 of A.H. K (BU) / 999 A.D.) * 55 O the Prmtve Classes of K * (BU) KHALED S. FELALI Departmet of Mathematcal Sceces, Umm Al-Qura Uversty, Makkah Al-Mukarramah,
More informationComplete Convergence and Some Maximal Inequalities for Weighted Sums of Random Variables
Joural of Sceces, Islamc Republc of Ira 8(4): -6 (007) Uversty of Tehra, ISSN 06-04 http://sceces.ut.ac.r Complete Covergece ad Some Maxmal Iequaltes for Weghted Sums of Radom Varables M. Am,,* H.R. Nl
More informationOPTIMALITY CONDITIONS FOR LOCALLY LIPSCHITZ GENERALIZED B-VEX SEMI-INFINITE PROGRAMMING
Mrcea cel Batra Naval Acadey Scetfc Bullet, Volue XIX 6 Issue he joural s dexed : PROQUES / DOAJ / Crossref / EBSCOhost / INDEX COPERNICUS / DRJI / OAJI / JOURNAL INDEX / IOR / SCIENCE LIBRARY INDEX /
More information2. Independence and Bernoulli Trials
. Ideedece ad Beroull Trals Ideedece: Evets ad B are deedet f B B. - It s easy to show that, B deedet mles, B;, B are all deedet ars. For examle, ad so that B or B B B B B φ,.e., ad B are deedet evets.,
More informationKURODA S METHOD FOR CONSTRUCTING CONSISTENT INPUT-OUTPUT DATA SETS. Peter J. Wilcoxen. Impact Research Centre, University of Melbourne.
KURODA S METHOD FOR CONSTRUCTING CONSISTENT INPUT-OUTPUT DATA SETS by Peter J. Wlcoxe Ipact Research Cetre, Uversty of Melboure Aprl 1989 Ths paper descrbes a ethod that ca be used to resolve cossteces
More informationOn Hilbert Kunz Functions of Some Hypersurfaces
JOURNAL OF ALGEBRA 199, 499527 1998 ARTICLE NO. JA977206 O HlbertKuz Fuctos of Soe Hypersurfaces L Chag* Departet of Matheatcs, Natoal Tawa Uersty, Tape, Tawa ad Yu-Chg Hug Departet of Matheatcs, Natoal
More informationSebastián Martín Ruiz. Applications of Smarandache Function, and Prime and Coprime Functions
Sebastá Martí Ruz Alcatos of Saradache Fucto ad Pre ad Core Fuctos 0 C L f L otherwse are core ubers Aerca Research Press Rehoboth 00 Sebastá Martí Ruz Avda. De Regla 43 Choa 550 Cadz Sa Sarada@telele.es
More informationDecomposition of Hadamard Matrices
Chapter 7 Decomposto of Hadamard Matrces We hae see Chapter that Hadamard s orgal costructo of Hadamard matrces states that the Kroecer product of Hadamard matrces of orders m ad s a Hadamard matrx of
More informationInterval extension of Bézier curve
WSEAS TRANSACTIONS o SIGNAL ROCESSING Jucheg L Iterval exteso of Bézer curve JUNCHENG LI Departet of Matheatcs Hua Uversty of Huates Scece ad Techology Dxg Road Loud cty Hua rovce 47 R CHINA E-al: ljucheg8@6co
More informationA CHARACTERIZATION OF THE CLIFFORD TORUS
PROCEEDINGS OF THE AERICAN ATHEATICAL SOCIETY Volue 17, Nuber 3, arch 1999, Pages 819 88 S 000-9939(99)05088-1 A CHARACTERIZATION OF THE CLIFFORD TORUS QING-ING CHENG AND SUSUU ISHIKAWA (Coucated by Chrstopher
More informationAlgorithms behind the Correlation Setting Window
Algorths behd the Correlato Settg Wdow Itroducto I ths report detaled forato about the correlato settg pop up wdow s gve. See Fgure. Ths wdow s obtaed b clckg o the rado butto labelled Kow dep the a scree
More informationINTEGRATION THEORY AND FUNCTIONAL ANALYSIS MM-501
INTEGRATION THEORY AND FUNCTIONAL ANALYSIS M.A./M.Sc. Mathematcs (Fal) MM-50 Drectorate of Dstace Educato Maharsh Dayaad Uversty ROHTAK 4 00 Copyrght 004, Maharsh Dayaad Uversty, ROHTAK All Rghts Reserved.
More informationDebabrata Dey and Atanu Lahiri
RESEARCH ARTICLE QUALITY COMPETITION AND MARKET SEGMENTATION IN THE SECURITY SOFTWARE MARKET Debabrata Dey ad Atau Lahr Mchael G. Foster School of Busess, Uersty of Washgto, Seattle, Seattle, WA 9895 U.S.A.
More informationLOWELL JOURNAL. MUST APOLOGIZE. such communication with the shore as Is m i Boimhle, noewwary and proper for the comfort
- 7 7 Z 8 q ) V x - X > q - < Y Y X V - z - - - - V - V - q \ - q q < -- V - - - x - - V q > x - x q - x q - x - - - 7 -» - - - - 6 q x - > - - x - - - x- - - q q - V - x - - ( Y q Y7 - >»> - x Y - ] [
More informationThe Arithmetic-Geometric mean inequality in an external formula. Yuki Seo. October 23, 2012
Sc. Math. Japocae Vol. 00, No. 0 0000, 000 000 1 The Arthmetc-Geometrc mea equalty a exteral formula Yuk Seo October 23, 2012 Abstract. The classcal Jese equalty ad ts reverse are dscussed by meas of terally
More information1 Edge Magic Labeling for Special Class of Graphs
S.Srram et. al. / Iteratoal Joural of Moder Sceces ad Egeerg Techology (IJMSET) ISSN 349-3755; Avalable at https://www.jmset.com Volume, Issue 0, 05, pp.60-67 Edge Magc Labelg for Specal Class of Graphs
More informationFactorization of Finite Abelian Groups
Iteratoal Joural of Algebra, Vol 6, 0, o 3, 0-07 Factorzato of Fte Abela Grous Khald Am Uversty of Bahra Deartmet of Mathematcs PO Box 3038 Sakhr, Bahra kamee@uobedubh Abstract If G s a fte abela grou
More informationBaxter Algebras and the Umbral Calculus
Baxter Algebras ad the Ubral Calculus arxv:ath/0407159v1 [ath.ra] 9 Jul 2004 L Guo Departet of Matheatcs ad Coputer Scece Rutgers Uversty at Newar Abstract We apply Baxter algebras to the study of the
More informationOn Convergence a Variation of the Converse of Fabry Gap Theorem
Scece Joural of Appled Matheatcs ad Statstcs 05; 3(): 58-6 Pulshed ole Aprl 05 (http://www.scecepulshggroup.co//sas) do: 0.648/.sas.05030.5 ISSN: 376-949 (Prt); ISSN: 376-953 (Ole) O Covergece a Varato
More informationOn Solution of Min-Max Composition Fuzzy Relational Equation
U-Sl Scece Jourl Vol.4()7 O Soluto of M-Mx Coposto Fuzzy eltol Equto N.M. N* Dte of cceptce /5/7 Abstrct I ths pper, M-Mx coposto fuzzy relto equto re studed. hs study s geerlzto of the works of Ohsto
More informationLower Bounds of the Kirchhoff and Degree Kirchhoff Indices
SCIENTIFIC PUBLICATIONS OF THE STATE UNIVERSITY OF NOVI PAZAR SER. A: APPL. MATH. INFORM. AND MECH. vol. 7, (205), 25-3. Lower Bouds of the Krchhoff ad Degree Krchhoff Idces I. Ž. Mlovaovć, E. I. Mlovaovć,
More informationNon-degenerate Perturbation Theory
No-degeerate Perturbato Theory Proble : H E ca't solve exactly. But wth H H H' H" L H E Uperturbed egevalue proble. Ca solve exactly. E Therefore, kow ad. H ' H" called perturbatos Copyrght Mchael D. Fayer,
More informationThe internal structure of natural numbers, one method for the definition of large prime numbers, and a factorization test
Fal verso The teral structure of atural umbers oe method for the defto of large prme umbers ad a factorzato test Emmaul Maousos APM Isttute for the Advacemet of Physcs ad Mathematcs 3 Poulou str. 53 Athes
More informationLecture 3 Probability review (cont d)
STATS 00: Itroducto to Statstcal Iferece Autum 06 Lecture 3 Probablty revew (cot d) 3. Jot dstrbutos If radom varables X,..., X k are depedet, the ther dstrbuto may be specfed by specfyg the dvdual dstrbuto
More information1 Mixed Quantum State. 2 Density Matrix. CS Density Matrices, von Neumann Entropy 3/7/07 Spring 2007 Lecture 13. ψ = α x x. ρ = p i ψ i ψ i.
CS 94- Desty Matrces, vo Neuma Etropy 3/7/07 Sprg 007 Lecture 3 I ths lecture, we wll dscuss the bascs of quatum formato theory I partcular, we wll dscuss mxed quatum states, desty matrces, vo Neuma etropy
More information7.0 Equality Contraints: Lagrange Multipliers
Systes Optzato 7.0 Equalty Cotrats: Lagrage Multplers Cosder the zato of a o-lear fucto subject to equalty costrats: g f() R ( ) 0 ( ) (7.) where the g ( ) are possbly also olear fuctos, ad < otherwse
More informationK-Even Edge-Graceful Labeling of Some Cycle Related Graphs
Iteratoal Joural of Egeerg Scece Iveto ISSN (Ole): 9 7, ISSN (Prt): 9 7 www.jes.org Volume Issue 0ǁ October. 0 ǁ PP.0-7 K-Eve Edge-Graceful Labelg of Some Cycle Related Grahs Dr. B. Gayathr, S. Kousalya
More informationOn the Rational Valued Characters Table of the
Aled Mathematcal Sceces, Vol., 7, o. 9, 95-9 HIKARI Ltd, www.m-hkar.com htts://do.or/.9/ams.7.7576 O the Ratoal Valued Characters Table of the Grou (Q m C Whe m s a Eve Number Raaa Hassa Abass Deartmet
More informationAnalysis of Lagrange Interpolation Formula
P IJISET - Iteratoal Joural of Iovatve Scece, Egeerg & Techology, Vol. Issue, December 4. www.jset.com ISS 348 7968 Aalyss of Lagrage Iterpolato Formula Vjay Dahya PDepartmet of MathematcsMaharaja Surajmal
More informationInternational Journal of Mathematical Archive-3(12), 2012, Available online through ISSN
teratoal Joural of Matheatal Arhve-3(2) 22 4789-4796 Avalable ole through www.ja.fo SSN 2229 546 g-quas FH-losed spaes ad g-quas CH-losed spaes Sr. Paule Mary Hele Assoate Professor Nrala College Cobatore
More informationρ < 1 be five real numbers. The
Lecture o BST 63: Statstcal Theory I Ku Zhag, /0/006 Revew for the prevous lecture Deftos: covarace, correlato Examples: How to calculate covarace ad correlato Theorems: propertes of correlato ad covarace
More information