The binomial transforms of the generalized (s, t )-Jacobsthal matrix sequence
|
|
- Cory Chase
- 5 years ago
- Views:
Transcription
1 Int. J. Adv. Appl. Math. and Mech. 6(3 ( (ISSN: Journal homepage: IJAAMM Internatonal Journal of Advances n Appled Mathematcs and Mechancs The bnomal transforms of the generalzed (s, t -Jacobsthal matr sequence Sukran UYGUN Mathematcs Department, Scence and Art Faculty, Gazantep Unversty, Turkey esearch Artcle eceved 11 November 2018; accepted (n revsed verson 11 January 2019 Abstract: In ths paper, we study the bnomal transforms of the generalzed (s, tjacobsthal matr sequence n+1 (s, t n N ; (s, t Jacobsthal J n+1 (s, t n N and, (s, t Jacobsthal Lucas C n+1 (s, t n N matr sequences. After thatby usng recurrence relatons of them, the generatng functons have beenfounded for these transforms. Fnally the relatons among these transforms have been demonstrated wth dervng new equaltes. MSC: 15A24 11B39 15B36 Keywords: Generalzed (s, t sequence Generalzed (s, t matr sequence (s, t Jacobsthal matr sequence (s, t Jacobsthal Lucas matr sequence The Author(s. Ths s an open access artcle under the CC BY-NC-ND lcense ( 1. Introducton and prelmnary There are so many studes n the lterature that are concern about specal nteger sequences such as Fbonacc, Lucas, Pell, Jacobsthal, Padovan. You can encounter the generalzatons of these sequences n all of the references. In [1 the author wrote a book about these nteger sequences You can see the generalzed number and matr sequences for Fbonacc and Lucas sequences n [3, 5, 6. Smlarly the author defned number and matr sequences whch generalzes Jacobsthal and Jacobsthal Lucas sequences n [7, 8. Some authors ntroduced matr based transforms for these specal sequences. Bnomal transform s one of most popular transforms. You can have detaled nformaton about bnomal transform n [9, 10. Falcon defned dfferent bnomal transforms of thek Fbonacc sequence such as fallng, rsng bnomal transforms n [4. The authors gave bnomal transform for generalzed (s, t matr sequences n [11.The authors ntroduced bnomal transforms for the Padovan and Perrn numbers n [12. And n [13 bnomal transforms of the k Jacobsthal sequence a rentroduced. In [14 the authors gave some propertes of Lucas numbers wth bnomal coeffcents.the goal of ths paper s to apply the bnomal transforms to the generalzed Jacobsthal and Jacobsthal Lucas matr sequences. Also, the generatng functon of ths transform s found by recurrence relatons. Fnally the relatons among these transforms have been demonstrated wth dervng new equaltes. In [2, the author defned the Jacobsthal and Jacobsthal Lucas sequence as follows respectvely j n+1 = j n + 2j n 1 n 1, (j 0 = 0, j 1 = 1 c n+1 = c n + 2c n 1 n 1, (c 0 = 0, c 1 = 1 Now we gve some prelmnares related to our study. For a gven nteger sequence X = { 1, 2,..., n,...} the bnomal transform Y of the sequence X;Y (X = { } y n s defned by y n = =0 E-mal address: suygun@gantep.edu.tr. 14
2 Sukran UYGUN / Int. J. Adv. Appl. Math. and Mech. 6(3 ( Defnton 1.1. Assume that a,b, s > 0, t 0 s 2 + 8t > 0. The(s, t Jacobsthal sequence {ĵ n (s, t} n N s defned by the followng recurrence relaton: ĵ n+1 (s, t = s ĵ n (s, t + 2t ĵ n 1 (s, t, (ĵ 0 (s, t = 0, ĵ 1 (s, t = 1 and, the (s, t Jacobsthal Lucas {ĉ n (s, t} n N s defned by the followng recurrence relaton ĉ n+1 (s, t = sĉ n (s, t + 2tĉ n 1 (s, t, (ĉ 0 (s, t = 2, ĉ 1 (s, t = s And the generalzed (s, tjacobsthal sequence {G n (s, t} n N s defned by the followng recurrence relaton G n+1 (s, t = sg n (s, t + 2tG n 1 (s, t, (G 0 (s, t = a, ĉ 1 (s, t = bs n [7. By choosng sutable values on a; b, we wll obtan (s, t Jacobsthal sequence;the (s, t Jacobsthal Lucas sequence by the generalzed (s, t Jacobsthal sequence: a = b = 1 { G n (s, t = ĵ n+1 (s, t a = 2, b = 1 {G n (s, t = ĉ n (s, t Defnton 1.2. Assume that a,b, s > 0, t 0 s 2 + 8t > 0. Generalzed (s, tjacobsthal matr sequence n+1 (s, t n N ; (s, t Jacobsthal J n+1 (s, t n N and, (s, t Jacobsthal Lucas C n+1 (s, t n N matr sequences are defned by the followng recurrence relatons n [8 : n+1 (s, t = s n (s, t + 2t n 1 (s, t (1 J n+1 (s, t = s J n (s, t + 2t J n 1 (s, t (2 C n+1 (s, t = sc n (s, t + 2tC n 1 (s, t (3 wth ntal condtons [ [ bs 2a bs 2 + 2at 2bs 0 = and at (b as 1 = bst 2at [ [ 1 0 s 2 J 0 (s, t = and J (s, t = t 0 [ [ s 4 s 2 + 4t 2s C 0 (s, t = and C 2t s 1 (s, t = st 4t By choosng sutable values on a; b, we wll obtan (s, t Jacobsthal matr sequence;the (s, t Jacobsthal Lucas matr sequence by the generalzed (s, tjacobsthal matr sequence: a = b = 1 { n (s, t = J n+1 (s, t a = 2, b = 1 { n (s, t = C n (s, t In the rest of ths paper, for convenence we wll use the symbols ĵ n, ĉ n,g n, J n, C n, n nstead of ĵ n (s, t,ĉ n (s, t, G n (s, t, J n (s, t, C n (s, t, n (s, t respectvely. Proposton 1.1. The relatons between the number sequences and ther matr sequences are gven as [ [ [ ĵn+1 2ĵ n ĉn+1 2ĉ n Gn+1 2G n J n =,C n = and t ĵ n 2t ĵ n 1 tĉ n 2tĉ n =. n 1 tg n 2tG n 1
3 16 The bnomal transforms of the generalzed (s, t -Jacobsthal matr sequence 2. Bnomal transform of the (s, t Generalzed and (s, t Jacobsthal, (s, t Jacobsthal Lucas matr sequences In ths secton, the bnomal transforms of the generalzed (s, t matr sequence, (s, t Jacobsthal and (s, t Jacobsthal Lucas matr sequences wll be ntroduced. Defnton 2.1. Let n, J n and C n be the (s, t generalzed,(s, t Jacobsthal and (s, t Jacobsthal Lucas matr sequences, respectvely. The bnomal transforms of these matr sequences can be epressed as follows: The bnomal transform of the generalzed (s, t matr sequence s B n = =0 The bnomal transforms of (s, t Jacobsthal matr sequence s Ĵ n = J =0 The bnomal transforms of (s, t Jacobsthal Lucas matr sequence s Ĉ n = C =0 Lemma 2.1. For n 0, the followng equaltes are hold: B n+1 = n n ( + +1 =0 Ĵ n+1 = n =0 Ĉ n+1 = n =0 =1 (J + J +1 (C +C +1 Proof. Frstly, n here we wll just prove (, snce ( and ( can be proved ( by usng ( the same ( method.by ( usng the n + 1 n n n defnton of bnomal transform and the well-known bnomal equalty = + and = 0 t 1 n + 1 s obtaned that B n+1 = n+1 n + 1 =0 = 0 + n+1 [ n n + =1 1 = 0 + n+1 n + n n +1 = n =0 ( + +1 =0 whch s the desred result. Note that B n+1 s also wrtten as B n+1 = B n + n =0 +1 Theorem 2.1. For n 0, the sequences {B n }, { Ĵ n }, {Ĉn } are verfed the followng recurrence relatons a B n+2 = (s + 2B n+1 (s + 1 2tB n wth ntal condtons [ bs 2a B 0 = at (b as [ bs 2 + bs + 2at 2bs + 2a, B 1 = bst + at (b as + 2at
4 Sukran UYGUN / Int. J. Adv. Appl. Math. and Mech. 6(3 ( b Ĵ n+2 = (s + 2Ĵ n+1 (s + 1 tĵ n [ [ 1 0 s Ĵ 0 = andĵ = t 1 c Ĉ n+2 = (s + 2Ĉ n+1 (s + 1 tĉ n [ [ s 4 s 2 + 4t 2s Ĉ 0 = andĉ 2t s 1 = st 4t Proof. have We only prove the frst case because the other cases can be proved wth the same way. From Lemma 2.1, we n =0 = n B n+1 = n ( + +1 n ( = = (s + 1 n =1 =1 + 2t n =1 1 ± (s From Defnton 2.1, t s obtaned that B n+1 = (s + 1B n + 2t s 0 (4 puttng n 1 nstead of n n (4 we have B n = (s + 1B n 1 + 2t n 1 n 1 = s 0 = sb n 1 + n 1 n 1 =0 + 2t n 1 n 1 = s 0 = sb n 1 + n [ n 1 n 1 + 2t = s 0 = sb n 1 + n [ n 1 n 1 n 1 + 2t ± 2t = s 0 = sb n 1 + n [ n 1 n (1 2t + 2t = s 0 = (s + 1 2tB n 1 + 2t n n s 0 =1 =1 From ths equalty we have 2t s 0 = B n (s + 1 2tB n 1 By substtutng ths epresson n (4, we obtan B n+1 = (s + 2B n (s + 1 2tB n 1 (5 whch completes the proof. The characterstc equaton of the bnomal transforms of the generalzed(s, t matr sequence B n s λ 2 (s+2λ+ (s 2t + 1 = 0.The roots of ths equaton are λ 1 = s s 2 + 8t, λ 2 = s + 2 s 2 + 8t 2 2 Bnet formula are well known n the specal nteger sequences theory. Bnetformula allows us to epress the nth term n functon of the roots of λ 1 andλ 2 of the characterstc equaton, assocated the recurrence relaton (5. So the Bnet formula for B n can be epressed as B n = X λ 1 n Y λ 2 n λ 1 λ 2 [ bs 2 λ 2 bs + 2at 2bs 2aλ 2 X = bst λ 2 at 2at λ 2 (b as (6 [ bs 2 λ 1 bs + 2at 2bs 2aλ 1 Y = bst λ 1 at 2at λ 1 (b as (7 By choosng correspondng values on a and b n (6 and (7, we can obtan the Bnet formula of Ĵ n and Ĉ n. Namely,
5 18 The bnomal transforms of the generalzed (s, t -Jacobsthal matr sequence a For a = b = 1; we get the Bnet formula for the bnomal transforms of (s, t Jacobsthal matr sequence as Ĵ n+1 = Aλ 1 n n Bλ 2 where λ 1 λ 2 [ s 2 [ λ 2 s + 2t 2(s λ 2 bs 2 λ 1 s + 2t 2(s λ 1 A =, B = t(s λ 2 2t t(s λ 1 2t b For a =2, b = 1; we get the Bnet formula for the bnomal transforms of (s, t Jacobsthal Lucas matr sequence as Ĉ n = Cλ 1 n n Dλ 2 where λ 1 λ 2 [ s 2 [ λ 2 s + 4t 2(s 2λ 2 bs 2 λ 1 s + 4t 2(s 2λ 1 C =, D =. t(s 2λ 2 4t sλ 2 t(s 2λ 1 4t sλ 1 Theorem 2.2. The generatng functons of the bnomal transforms of generalzed (s, t matr sequence, (s, t Jacobsthal matr sequence, (s, t Jacobsthal Lucas matr sequence are B n (s, t, = = n=0 [ 1 1 (s+2+(s+1 t 2 J n (s, t, = = n=0 C n (s, t, = = B n n = 0+[ 1 (s (s+2+(s+1 t 2 bs + (2at bs 2(a + (bs as a t(a + (bs as a (b as + (2at s 2 (b a s(b a ĵ n+1 n = J 0+[J 1 (s+1j 0 1 (s+2+(s+1 t 2 [ 1 s + (2t s 2(1 1 (s+2+(s+1 t 2 t(1 2t n=0 ĉ n n = C 0+[C 1 (s+1c 0 1 (s+2+(s+1 t 2 [ 1 s + (4t s 2(2 (s (s+2+(s+1 t 2 t(2 (s + 2 s + (4t + s 2 s Proof. We just prove the case ( and the others wll be omtted. Let B n (s, t, be generatng functon for the bnomal transform of generalzed (s, t Jacobsthal matr sequence. Then, B n (s, t, = B 0 + B n B n +... (8 If we multply (s + 2and (s + t 1 2 ; wth the both sdes of the equalty (8 respectvely, we obtan (s + 2 B n (s, t, = (s + 2 B 0 + (s B (s + 2 n+1 B n +... (9 (s + 1 2t 2 B n (s, t, = (s + 1 2t 2 B 0 + (s + 1 2t 3 B (s + 1 2t n+2 B n +... (10 Consderng (8, (9, (10 we get the followng equalty B n (s, t, ( 1 (s (s + 1 t 2 = B 0 + (B 1 (s + 2B 0 (11 Fnally, from Theorem 2.1, Defnton 2.1, and (11 we have the desred result. We can get the followng relatons between the generalzed (s; t- matr sequence, (s, t Jacobsthal and (s, t Jacobsthal Lucas matr sequences and the generatng functons of the bnomal transforms of these sequences, respectvely. Let r ( = 0+[ 1 s 0 be the ordnary generatng functon of the sequence { 1 s t 2 n } : By usng the transformaton of 1 f 1 we have the generatng functon of the bnomal transform sequence {Bn } n Theorem 2.2-(. Let j ( = J 0+[J 1 s J 0 be the ordnary generatng functon of the sequence {J 1 s t 2 n }: By usng the transformaton of 1 j 1 we have the generatng functon of the bnomal transform sequence {Jn }n Theorem 2.2-(.
6 Sukran UYGUN / Int. J. Adv. Appl. Math. and Mech. 6(3 ( Let c ( = C 0+[C 1 sc 0 be the ordnary generatng functon of the sequence {C 1 s t 2 n }: By usng the transformaton of 1 c 1 we have the generatng functon of the bnomal transform sequence{cn } n Theorem 2.2-(. Theorem 2.3. Let m, n N; then Ĵ m+n = Ĵ m Ĵ n. Proof. We use the nducton method. Let n = 0, then we get Ĵ m+0 = Ĵ m Ĵ 0 = Ĵ m I.Assume that Ĵ m+n = Ĵ m Ĵ n for n N. Then we obtan Ĵ m+n+1 = (s + 2Ĵ m+n (s + 1 tĵ m+n 1 = (s + 2Ĵ m Ĵ N (s + 1 tĵ m Ĵ N 1 = Ĵ m [ (s + 2 ĴN (s + 1 tĵ N 1 = Ĵ m Ĵ N+1 Theorem 2.4. Let n N, then n+1 = 1 J n J n+1 = J 1 J n C n+1 = C 1 J n Proof. The proof s easly obtaned by usng mathematcal nducton method. Theorem 2.5. The relatons among the transforms B n, Ĵ n and Ĉ n can be demonstrated by the followng equaltes: B n+1 B n = 1 Ĵ n Ĵ n+1 Ĵ n = J 1 Ĵ n Ĉ n+1 Ĉ n = C 1 Ĵ n Proof. By consderng Defnton 2.1, Lemma 2.1, we get B n+1 = n =0 By Theorem 2.4, B n+1 B n = n ( + +1 = B n + n =0 n +1 = =0 =0 +1. ( 1 J n = 1 Ĵ n Ths completes the proof of : The others are made by usng the same method. eferences [1 T. Koshy, Fbonacc and Lucas Numbers wth Applcatons, John Wleyand Sons Inc., NY (2001. [2 A. F. Horadam, Jacobsthal representaton numbers, The Fbonacc Quarterly.,34(1, (1996, [3 S. Falcon and A. Plaza, The k-fbonacc sequence and the Pascal 2-trangle,Chaos, Soltons Fractals,33(2007, [4 S. Falcon and A. Plaza, Bnomal Transforms of the k-fbonacc sequence,internatonal Journal of Nonlnear Scences and Numercal Smulaton,10(11-12 (2009, [5 H. Cvcv,. Turkmen, On the (s, t Fbonacc and Fbonacc matr sequences, AS Combnatora, 87 ( [6 H. Cvcv,. Turkmen, Notes on the(s, t- Lucas and Lucas matr sequences, AS Combnatora, 89 ( [7 S. Uygun, The (s, t-jacobsthal and (s, t-jacobsthal Lucas sequences, Appled Mathematcal Scences, 70(9, (2015,
7 20 The bnomal transforms of the generalzed (s, t -Jacobsthal matr sequence [8 K. Uslu, ÂÿS. Uygun, The (s, t-jacobsthal and (s, t-jacobsthal-lucas Matr sequences, AS Combnatora, 108, ( [9 H. Prodnger, Some nformaton about the bnomal transform, The Fbonacc Quarterly, 32(5, 1994, [10 K. W. Chen, Identtes from the bnomal transform, Journal of NumberTheory, 124, 2007, [11 Y. YazlÄśk, N. YÄślmaz, N. Taskara, The Generalzed (s, t-matr Sequences Bnomal Transforms, Gen. Math. Notes, 24(1,(2014, [12 N. YÄślmaz, N. Taskara, Bnomal transforms of the Padovan and Perrnnumbers, Journal of Abstract and Appled Mathematcs, (2013 ArtcleID [13 S. Uygun, A. ErdoÄ du, Bnomnal transforms of k-jacobsthal sequences,journal of Mathematcal and Computatonal Scence, 7(6, (2017, [14 N. Taskara, K. Uslu, H.H. Gulec, On the propertes of Lucas numbers wth bnomal coeffcents, Appled Mathematcs Letters, 23(1, ( Submt your manuscrpt to IJAAMM and beneft from: gorous peer revew Immedate publcaton on acceptance Open access: Artcles freely avalable onlne Hgh vsblty wthn the feld etanng the copyrght to your artcle Submt your net manuscrpt at edtor.jaamm@gmal.com
arxiv: v1 [math.co] 12 Sep 2014
arxv:1409.3707v1 [math.co] 12 Sep 2014 On the bnomal sums of Horadam sequence Nazmye Ylmaz and Necat Taskara Department of Mathematcs, Scence Faculty, Selcuk Unversty, 42075, Campus, Konya, Turkey March
More informationBinomial transforms of the modified k-fibonacci-like sequence
Internatonal Journal of Mathematcs and Computer Scence, 14(2019, no. 1, 47 59 M CS Bnomal transforms of the modfed k-fbonacc-lke sequence Youngwoo Kwon Department of mathematcs Korea Unversty Seoul, Republc
More informationTHE GENERALIZED (s, t)-fibonacci AND FIBONACCI MATRIX SEQUENCES
TJMM 7 205), No 2, 37-48 THE GENERALIZED s, t)-fibonacci AND FIBONACCI MATRIX SEQUENCES AHMET İPEK, KAMIL ARI, AND RAMAZAN TÜRKMEN Abstract In ths paper, we study the generalzatons of the s, t)-fbonacc
More informationThe Jacobsthal and Jacobsthal-Lucas Numbers via Square Roots of Matrices
Internatonal Mathematcal Forum, Vol 11, 2016, no 11, 513-520 HIKARI Ltd, wwwm-hkarcom http://dxdoorg/1012988/mf20166442 The Jacobsthal and Jacobsthal-Lucas Numbers va Square Roots of Matrces Saadet Arslan
More informationA new Approach for Solving Linear Ordinary Differential Equations
, ISSN 974-57X (Onlne), ISSN 974-5718 (Prnt), Vol. ; Issue No. 1; Year 14, Copyrght 13-14 by CESER PUBLICATIONS A new Approach for Solvng Lnear Ordnary Dfferental Equatons Fawz Abdelwahd Department of
More informationh-analogue of Fibonacci Numbers
h-analogue of Fbonacc Numbers arxv:090.0038v [math-ph 30 Sep 009 H.B. Benaoum Prnce Mohammad Unversty, Al-Khobar 395, Saud Araba Abstract In ths paper, we ntroduce the h-analogue of Fbonacc numbers for
More informationDeterminants Containing Powers of Generalized Fibonacci Numbers
1 2 3 47 6 23 11 Journal of Integer Sequences, Vol 19 (2016), Artcle 1671 Determnants Contanng Powers of Generalzed Fbonacc Numbers Aram Tangboonduangjt and Thotsaporn Thanatpanonda Mahdol Unversty Internatonal
More informationSome congruences related to harmonic numbers and the terms of the second order sequences
Mathematca Moravca Vol. 0: 06, 3 37 Some congruences related to harmonc numbers the terms of the second order sequences Neşe Ömür Sbel Koaral Abstract. In ths aer, wth hels of some combnatoral denttes,
More informationOn the spectral norm of r-circulant matrices with the Pell and Pell-Lucas numbers
Türkmen and Gökbaş Journal of Inequaltes and Applcatons (06) 06:65 DOI 086/s3660-06-0997-0 R E S E A R C H Open Access On the spectral norm of r-crculant matrces wth the Pell and Pell-Lucas numbers Ramazan
More informationarxiv: v1 [math.ho] 18 May 2008
Recurrence Formulas for Fbonacc Sums Adlson J. V. Brandão, João L. Martns 2 arxv:0805.2707v [math.ho] 8 May 2008 Abstract. In ths artcle we present a new recurrence formula for a fnte sum nvolvng the Fbonacc
More informationThe Order Relation and Trace Inequalities for. Hermitian Operators
Internatonal Mathematcal Forum, Vol 3, 08, no, 507-57 HIKARI Ltd, wwwm-hkarcom https://doorg/0988/mf088055 The Order Relaton and Trace Inequaltes for Hermtan Operators Y Huang School of Informaton Scence
More informationFORMULAS FOR BINOMIAL SUMS INCLUDING POWERS OF FIBONACCI AND LUCAS NUMBERS
U.P.B. Sc. Bull., Seres A, Vol. 77, Iss. 4, 015 ISSN 13-707 FORMULAS FOR BINOMIAL SUMS INCLUDING POWERS OF FIBONACCI AND LUCAS NUMBERS Erah KILIÇ 1, Iler AKKUS, Neşe ÖMÜR, Yücel Türer ULUTAŞ3 Recently
More informationRandić Energy and Randić Estrada Index of a Graph
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 5, No., 202, 88-96 ISSN 307-5543 www.ejpam.com SPECIAL ISSUE FOR THE INTERNATIONAL CONFERENCE ON APPLIED ANALYSIS AND ALGEBRA 29 JUNE -02JULY 20, ISTANBUL
More informationApplied Mathematics Letters
Appled Matheatcs Letters 2 (2) 46 5 Contents lsts avalable at ScenceDrect Appled Matheatcs Letters journal hoepage: wwwelseverco/locate/al Calculaton of coeffcents of a cardnal B-splne Gradr V Mlovanovć
More informationThe lower and upper bounds on Perron root of nonnegative irreducible matrices
Journal of Computatonal Appled Mathematcs 217 (2008) 259 267 wwwelsevercom/locate/cam The lower upper bounds on Perron root of nonnegatve rreducble matrces Guang-Xn Huang a,, Feng Yn b,keguo a a College
More informationProjective change between two Special (α, β)- Finsler Metrics
Internatonal Journal of Trend n Research and Development, Volume 2(6), ISSN 2394-9333 www.jtrd.com Projectve change between two Specal (, β)- Fnsler Metrcs Gayathr.K 1 and Narasmhamurthy.S.K 2 1 Assstant
More informationVARIATION OF CONSTANT SUM CONSTRAINT FOR INTEGER MODEL WITH NON UNIFORM VARIABLES
VARIATION OF CONSTANT SUM CONSTRAINT FOR INTEGER MODEL WITH NON UNIFORM VARIABLES BÂRZĂ, Slvu Faculty of Mathematcs-Informatcs Spru Haret Unversty barza_slvu@yahoo.com Abstract Ths paper wants to contnue
More informationA combinatorial proof of multiple angle formulas involving Fibonacci and Lucas numbers
Notes on Number Theory and Dscrete Mathematcs ISSN 1310 5132 Vol. 20, 2014, No. 5, 35 39 A combnatoral proof of multple angle formulas nvolvng Fbonacc and Lucas numbers Fernando Córes 1 and Dego Marques
More informationGeneral viscosity iterative method for a sequence of quasi-nonexpansive mappings
Avalable onlne at www.tjnsa.com J. Nonlnear Sc. Appl. 9 (2016), 5672 5682 Research Artcle General vscosty teratve method for a sequence of quas-nonexpansve mappngs Cuje Zhang, Ynan Wang College of Scence,
More informationA summation on Bernoulli numbers
Journal of Number Theory 111 (005 37 391 www.elsever.com/locate/jnt A summaton on Bernoull numbers Kwang-Wu Chen Department of Mathematcs and Computer Scence Educaton, Tape Muncpal Teachers College, No.
More informationA Hybrid Variational Iteration Method for Blasius Equation
Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1932-9466 Vol. 10, Issue 1 (June 2015), pp. 223-229 Applcatons and Appled Mathematcs: An Internatonal Journal (AAM) A Hybrd Varatonal Iteraton Method
More informationTHE ADJACENCY-PELL-HURWITZ NUMBERS. Josh Hiller Department of Mathematics and Computer Science, Adelpi University, New York
#A8 INTEGERS 8 (8) THE ADJACENCY-PELL-HURWITZ NUMBERS Josh Hller Departent of Matheatcs and Coputer Scence Adelp Unversty New York johller@adelphedu Yeş Aküzü Faculty of Scence and Letters Kafkas Unversty
More informationCOMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
Avalable onlne at http://sck.org J. Math. Comput. Sc. 3 (3), No., 6-3 ISSN: 97-537 COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
More informationHyper-Sums of Powers of Integers and the Akiyama-Tanigawa Matrix
6 Journal of Integer Sequences, Vol 8 (00), Artcle 0 Hyper-Sums of Powers of Integers and the Ayama-Tangawa Matrx Yoshnar Inaba Toba Senor Hgh School Nshujo, Mnam-u Kyoto 60-89 Japan nava@yoto-benejp Abstract
More informationarxiv: v1 [math.co] 1 Mar 2014
Unon-ntersectng set systems Gyula O.H. Katona and Dánel T. Nagy March 4, 014 arxv:1403.0088v1 [math.co] 1 Mar 014 Abstract Three ntersecton theorems are proved. Frst, we determne the sze of the largest
More informationSolving Fractional Nonlinear Fredholm Integro-differential Equations via Hybrid of Rationalized Haar Functions
ISSN 746-7659 England UK Journal of Informaton and Computng Scence Vol. 9 No. 3 4 pp. 69-8 Solvng Fractonal Nonlnear Fredholm Integro-dfferental Equatons va Hybrd of Ratonalzed Haar Functons Yadollah Ordokhan
More informationA FORMULA FOR COMPUTING INTEGER POWERS FOR ONE TYPE OF TRIDIAGONAL MATRIX
Hacettepe Journal of Mathematcs and Statstcs Volume 393 0 35 33 FORMUL FOR COMPUTING INTEGER POWERS FOR ONE TYPE OF TRIDIGONL MTRIX H Kıyak I Gürses F Yılmaz and D Bozkurt Receved :08 :009 : ccepted 5
More informationPower law and dimension of the maximum value for belief distribution with the max Deng entropy
Power law and dmenson of the maxmum value for belef dstrbuton wth the max Deng entropy Bngy Kang a, a College of Informaton Engneerng, Northwest A&F Unversty, Yanglng, Shaanx, 712100, Chna. Abstract Deng
More informationCombinatorial Identities for Incomplete Tribonacci Polynomials
Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1932-9466 Vol. 10, Issue 1 (June 2015, pp. 40 49 Applcatons and Appled Mathematcs: An Internatonal Journal (AAM Combnatoral Identtes for Incomplete
More informationSolution of Linear System of Equations and Matrix Inversion Gauss Seidel Iteration Method
Soluton of Lnear System of Equatons and Matr Inverson Gauss Sedel Iteraton Method It s another well-known teratve method for solvng a system of lnear equatons of the form a + a22 + + ann = b a2 + a222
More informationRestricted divisor sums
ACTA ARITHMETICA 02 2002) Restrcted dvsor sums by Kevn A Broughan Hamlton) Introducton There s a body of work n the lterature on varous restrcted sums of the number of dvsors of an nteger functon ncludng
More informationOn Finite Rank Perturbation of Diagonalizable Operators
Functonal Analyss, Approxmaton and Computaton 6 (1) (2014), 49 53 Publshed by Faculty of Scences and Mathematcs, Unversty of Nš, Serba Avalable at: http://wwwpmfnacrs/faac On Fnte Rank Perturbaton of Dagonalzable
More informationON A DETERMINATION OF THE INITIAL FUNCTIONS FROM THE OBSERVED VALUES OF THE BOUNDARY FUNCTIONS FOR THE SECOND-ORDER HYPERBOLIC EQUATION
Advanced Mathematcal Models & Applcatons Vol.3, No.3, 2018, pp.215-222 ON A DETERMINATION OF THE INITIAL FUNCTIONS FROM THE OBSERVED VALUES OF THE BOUNDARY FUNCTIONS FOR THE SECOND-ORDER HYPERBOLIC EUATION
More informationTransfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system
Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng
More informationOn the Binomial Interpolated Triangles
1 2 3 47 6 23 11 Journal of Integer Sequences, Vol. 20 (2017), Artcle 17.7.8 On the Bnomal Interpolated Trangles László Németh Insttute of Mathematcs Unversty of Sopron Bajcsy Zs. u. 4 H9400 Sopron Hungary
More informationBeyond Zudilin s Conjectured q-analog of Schmidt s problem
Beyond Zudln s Conectured q-analog of Schmdt s problem Thotsaporn Ae Thanatpanonda thotsaporn@gmalcom Mathematcs Subect Classfcaton: 11B65 33B99 Abstract Usng the methodology of (rgorous expermental mathematcs
More informationAsymptotics of the Solution of a Boundary Value. Problem for One-Characteristic Differential. Equation Degenerating into a Parabolic Equation
Nonl. Analyss and Dfferental Equatons, ol., 4, no., 5 - HIKARI Ltd, www.m-har.com http://dx.do.org/.988/nade.4.456 Asymptotcs of the Soluton of a Boundary alue Problem for One-Characterstc Dfferental Equaton
More informationFACTORIZATION IN KRULL MONOIDS WITH INFINITE CLASS GROUP
C O L L O Q U I U M M A T H E M A T I C U M VOL. 80 1999 NO. 1 FACTORIZATION IN KRULL MONOIDS WITH INFINITE CLASS GROUP BY FLORIAN K A I N R A T H (GRAZ) Abstract. Let H be a Krull monod wth nfnte class
More informationAmusing Properties of Odd Numbers Derived From Valuated Binary Tree
IOSR Journal of Mathematcs (IOSR-JM) e-iss: 78-578, p-iss: 19-765X. Volume 1, Issue 6 Ver. V (ov. - Dec.016), PP 5-57 www.osrjournals.org Amusng Propertes of Odd umbers Derved From Valuated Bnary Tree
More informationA property of the elementary symmetric functions
Calcolo manuscrpt No. (wll be nserted by the edtor) A property of the elementary symmetrc functons A. Esnberg, G. Fedele Dp. Elettronca Informatca e Sstemstca, Unverstà degl Stud della Calabra, 87036,
More informationSoft Neutrosophic Bi-LA-semigroup and Soft Neutrosophic N-LA-seigroup
Neutrosophc Sets and Systems, Vol. 5, 04 45 Soft Neutrosophc B-LA-semgroup and Soft Mumtaz Al, Florentn Smarandache, Muhammad Shabr 3,3 Department of Mathematcs, Quad--Azam Unversty, Islamabad, 44000,Pakstan.
More informationSelf-complementing permutations of k-uniform hypergraphs
Dscrete Mathematcs Theoretcal Computer Scence DMTCS vol. 11:1, 2009, 117 124 Self-complementng permutatons of k-unform hypergraphs Artur Szymańsk A. Paweł Wojda Faculty of Appled Mathematcs, AGH Unversty
More informationDifference Equations
Dfference Equatons c Jan Vrbk 1 Bascs Suppose a sequence of numbers, say a 0,a 1,a,a 3,... s defned by a certan general relatonshp between, say, three consecutve values of the sequence, e.g. a + +3a +1
More informationAn (almost) unbiased estimator for the S-Gini index
An (almost unbased estmator for the S-Gn ndex Thomas Demuynck February 25, 2009 Abstract Ths note provdes an unbased estmator for the absolute S-Gn and an almost unbased estmator for the relatve S-Gn for
More informationDETERMINATION OF TEMPERATURE DISTRIBUTION FOR ANNULAR FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY BY HPM
Ganj, Z. Z., et al.: Determnaton of Temperature Dstrbuton for S111 DETERMINATION OF TEMPERATURE DISTRIBUTION FOR ANNULAR FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY BY HPM by Davood Domr GANJI
More informationA New Refinement of Jacobi Method for Solution of Linear System Equations AX=b
Int J Contemp Math Scences, Vol 3, 28, no 17, 819-827 A New Refnement of Jacob Method for Soluton of Lnear System Equatons AX=b F Naem Dafchah Department of Mathematcs, Faculty of Scences Unversty of Gulan,
More informationCHAPTER-5 INFORMATION MEASURE OF FUZZY MATRIX AND FUZZY BINARY RELATION
CAPTER- INFORMATION MEASURE OF FUZZY MATRI AN FUZZY BINARY RELATION Introducton The basc concept of the fuzz matr theor s ver smple and can be appled to socal and natural stuatons A branch of fuzz matr
More informationPerfect Fluid Cosmological Model in the Frame Work Lyra s Manifold
Prespacetme Journal December 06 Volume 7 Issue 6 pp. 095-099 Pund, A. M. & Avachar, G.., Perfect Flud Cosmologcal Model n the Frame Work Lyra s Manfold Perfect Flud Cosmologcal Model n the Frame Work Lyra
More informationOn quasiperfect numbers
Notes on Number Theory and Dscrete Mathematcs Prnt ISSN 1310 5132, Onlne ISSN 2367 8275 Vol. 23, 2017, No. 3, 73 78 On quasperfect numbers V. Sva Rama Prasad 1 and C. Suntha 2 1 Nalla Malla Reddy Engneerng
More informationSharp integral inequalities involving high-order partial derivatives. Journal Of Inequalities And Applications, 2008, v. 2008, article no.
Ttle Sharp ntegral nequaltes nvolvng hgh-order partal dervatves Authors Zhao, CJ; Cheung, WS Ctaton Journal Of Inequaltes And Applcatons, 008, v. 008, artcle no. 5747 Issued Date 008 URL http://hdl.handle.net/07/569
More information2E Pattern Recognition Solutions to Introduction to Pattern Recognition, Chapter 2: Bayesian pattern classification
E395 - Pattern Recognton Solutons to Introducton to Pattern Recognton, Chapter : Bayesan pattern classfcaton Preface Ths document s a soluton manual for selected exercses from Introducton to Pattern Recognton
More informationAppendix for Causal Interaction in Factorial Experiments: Application to Conjoint Analysis
A Appendx for Causal Interacton n Factoral Experments: Applcaton to Conjont Analyss Mathematcal Appendx: Proofs of Theorems A. Lemmas Below, we descrbe all the lemmas, whch are used to prove the man theorems
More informationYong Joon Ryang. 1. Introduction Consider the multicommodity transportation problem with convex quadratic cost function. 1 2 (x x0 ) T Q(x x 0 )
Kangweon-Kyungk Math. Jour. 4 1996), No. 1, pp. 7 16 AN ITERATIVE ROW-ACTION METHOD FOR MULTICOMMODITY TRANSPORTATION PROBLEMS Yong Joon Ryang Abstract. The optmzaton problems wth quadratc constrants often
More informationValuated Binary Tree: A New Approach in Study of Integers
Internatonal Journal of Scentfc Innovatve Mathematcal Research (IJSIMR) Volume 4, Issue 3, March 6, PP 63-67 ISS 347-37X (Prnt) & ISS 347-34 (Onlne) wwwarcournalsorg Valuated Bnary Tree: A ew Approach
More informationRemarks on the Properties of a Quasi-Fibonacci-like Polynomial Sequence
Remarks on the Propertes of a Quas-Fbonacc-lke Polynomal Sequence Brce Merwne LIU Brooklyn Ilan Wenschelbaum Wesleyan Unversty Abstract Consder the Quas-Fbonacc-lke Polynomal Sequence gven by F 0 = 1,
More informationON A DIOPHANTINE EQUATION ON TRIANGULAR NUMBERS
Mskolc Mathematcal Notes HU e-issn 787-43 Vol. 8 (7), No., pp. 779 786 DOI:.854/MMN.7.536 ON A DIOPHANTINE EUATION ON TRIANGULAR NUMBERS ABDELKADER HAMTAT AND DJILALI BEHLOUL Receved 6 February, 5 Abstract.
More informationA CHARACTERIZATION OF ADDITIVE DERIVATIONS ON VON NEUMANN ALGEBRAS
Journal of Mathematcal Scences: Advances and Applcatons Volume 25, 2014, Pages 1-12 A CHARACTERIZATION OF ADDITIVE DERIVATIONS ON VON NEUMANN ALGEBRAS JIA JI, WEN ZHANG and XIAOFEI QI Department of Mathematcs
More information(Online First)A Lattice Boltzmann Scheme for Diffusion Equation in Spherical Coordinate
Internatonal Journal of Mathematcs and Systems Scence (018) Volume 1 do:10.494/jmss.v1.815 (Onlne Frst)A Lattce Boltzmann Scheme for Dffuson Equaton n Sphercal Coordnate Debabrata Datta 1 *, T K Pal 1
More informationFoundations of Arithmetic
Foundatons of Arthmetc Notaton We shall denote the sum and product of numbers n the usual notaton as a 2 + a 2 + a 3 + + a = a, a 1 a 2 a 3 a = a The notaton a b means a dvdes b,.e. ac = b where c s an
More informationThe Quadratic Trigonometric Bézier Curve with Single Shape Parameter
J. Basc. Appl. Sc. Res., (3541-546, 01 01, TextRoad Publcaton ISSN 090-4304 Journal of Basc and Appled Scentfc Research www.textroad.com The Quadratc Trgonometrc Bézer Curve wth Sngle Shape Parameter Uzma
More informationDEGREE REDUCTION OF BÉZIER CURVES USING CONSTRAINED CHEBYSHEV POLYNOMIALS OF THE SECOND KIND
ANZIAM J. 45(003), 195 05 DEGREE REDUCTION OF BÉZIER CURVES USING CONSTRAINED CHEBYSHEV POLYNOMIALS OF THE SECOND KIND YOUNG JOON AHN 1 (Receved 3 August, 001; revsed 7 June, 00) Abstract In ths paper
More informationThe Degrees of Nilpotency of Nilpotent Derivations on the Ring of Matrices
Internatonal Mathematcal Forum, Vol. 6, 2011, no. 15, 713-721 The Degrees of Nlpotency of Nlpotent Dervatons on the Rng of Matrces Homera Pajoohesh Department of of Mathematcs Medgar Evers College of CUNY
More informationNeutrosophic Bi-LA-Semigroup and Neutrosophic N-LA- Semigroup
Neutrosophc Sets Systems, Vol. 4, 04 9 Neutrosophc B-LA-Semgroup Neutrosophc N-LA- Semgroup Mumtaz Al *, Florentn Smarache, Muhammad Shabr 3 Munazza Naz 4,3 Department of Mathematcs, Quad--Azam Unversty,
More informationExistence of Two Conjugate Classes of A 5 within S 6. by Use of Character Table of S 6
Internatonal Mathematcal Forum, Vol. 8, 2013, no. 32, 1591-159 HIKARI Ltd, www.m-hkar.com http://dx.do.org/10.12988/mf.2013.3359 Exstence of Two Conjugate Classes of A 5 wthn S by Use of Character Table
More informationOn the set of natural numbers
On the set of natural numbers by Jalton C. Ferrera Copyrght 2001 Jalton da Costa Ferrera Introducton The natural numbers have been understood as fnte numbers, ths wor tres to show that the natural numbers
More informationCCO Commun. Comb. Optim.
Communcatons n Combnatorcs and Optmzaton Vol. 2 No. 2, 2017 pp.87-98 DOI: 10.22049/CCO.2017.13630 CCO Commun. Comb. Optm. Reformulated F-ndex of graph operatons Hamdeh Aram 1 and Nasrn Dehgard 2 1 Department
More informationModulo Magic Labeling in Digraphs
Gen. Math. Notes, Vol. 7, No., August, 03, pp. 5- ISSN 9-784; Copyrght ICSRS Publcaton, 03 www.-csrs.org Avalable free onlne at http://www.geman.n Modulo Magc Labelng n Dgraphs L. Shobana and J. Baskar
More informationCOMBINATORIAL IDENTITIES DERIVING FROM THE n-th POWER OF A 2 2 MATRIX
COMBINATORIAL IDENTITIES DERIVING FROM THE n-th POWER OF A MATRIX J Mc Laughln 1 Mathematcs Department Trnty College 300 Summt Street, Hartford, CT 06106-3100 amesmclaughln@trncolledu Receved:, Accepted:,
More informationA Note on Bound for Jensen-Shannon Divergence by Jeffreys
OPEN ACCESS Conference Proceedngs Paper Entropy www.scforum.net/conference/ecea- A Note on Bound for Jensen-Shannon Dvergence by Jeffreys Takuya Yamano, * Department of Mathematcs and Physcs, Faculty of
More informationCOMPLEX NUMBERS AND QUADRATIC EQUATIONS
COMPLEX NUMBERS AND QUADRATIC EQUATIONS INTRODUCTION We know that x 0 for all x R e the square of a real number (whether postve, negatve or ero) s non-negatve Hence the equatons x, x, x + 7 0 etc are not
More informationA P PL I CA TIONS OF FRACTIONAL EXTERIOR DI F F ER EN TIAL IN THR EE- DI M ENSIONAL S PAC E Ξ
Appled Mathematcs and Mechancs ( Englsh Edton, Vol 24, No 3, Mar 2003) Publshed by Shangha Unversty, Shangha, Chna Artcle ID : 0253-4827 (2003) 03-0256-05 A P PL I CA TIONS OF FRACTIONAL EXTERIOR DI F
More informationOn the size of quotient of two subsets of positive integers.
arxv:1706.04101v1 [math.nt] 13 Jun 2017 On the sze of quotent of two subsets of postve ntegers. Yur Shtenkov Abstract We obtan non-trval lower bound for the set A/A, where A s a subset of the nterval [1,
More informationThe exponential map of GL(N)
The exponental map of GLN arxv:hep-th/9604049v 9 Apr 996 Alexander Laufer Department of physcs Unversty of Konstanz P.O. 5560 M 678 78434 KONSTANZ Aprl 9, 996 Abstract A fnte expanson of the exponental
More informationConvexity preserving interpolation by splines of arbitrary degree
Computer Scence Journal of Moldova, vol.18, no.1(52), 2010 Convexty preservng nterpolaton by splnes of arbtrary degree Igor Verlan Abstract In the present paper an algorthm of C 2 nterpolaton of dscrete
More informationPHASED TILINGS AND GENERALIZED FIBONACCI IDENTITIES
appeared n: Fbonacc Quarterly 38(2000), pp. 282-288. PHASED TILINGS AND GENERALIZED FIBONACCI IDENTITIES Arthur T. Benjamn Dept. of Mathematcs, Harvey Mudd College, Claremont, CA 91711 benjamn@hmc.edu
More informationThe probability that a pair of group elements is autoconjugate
Proc. Indan Acad. Sc. (Math. Sc.) Vol. 126, No. 1, February 2016, pp. 61 68. c Indan Academy of Scences The probablty that a par of group elements s autoconjugate MOHAMMAD REZA R MOGHADDAM 1,2,, ESMAT
More informationNumerical Solutions of a Generalized Nth Order Boundary Value Problems Using Power Series Approximation Method
Appled Mathematcs, 6, 7, 5-4 Publshed Onlne Jul 6 n ScRes. http://www.scrp.org/journal/am http://.do.org/.436/am.6.77 umercal Solutons of a Generalzed th Order Boundar Value Problems Usng Power Seres Approxmaton
More informationDouble Layered Fuzzy Planar Graph
Global Journal of Pure and Appled Mathematcs. ISSN 0973-768 Volume 3, Number 0 07), pp. 7365-7376 Research Inda Publcatons http://www.rpublcaton.com Double Layered Fuzzy Planar Graph J. Jon Arockaraj Assstant
More informationSection 8.3 Polar Form of Complex Numbers
80 Chapter 8 Secton 8 Polar Form of Complex Numbers From prevous classes, you may have encountered magnary numbers the square roots of negatve numbers and, more generally, complex numbers whch are the
More information3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X
Statstcs 1: Probablty Theory II 37 3 EPECTATION OF SEVERAL RANDOM VARIABLES As n Probablty Theory I, the nterest n most stuatons les not on the actual dstrbuton of a random vector, but rather on a number
More informationThe Two-scale Finite Element Errors Analysis for One Class of Thermoelastic Problem in Periodic Composites
7 Asa-Pacfc Engneerng Technology Conference (APETC 7) ISBN: 978--6595-443- The Two-scale Fnte Element Errors Analyss for One Class of Thermoelastc Problem n Perodc Compostes Xaoun Deng Mngxang Deng ABSTRACT
More informationPAijpam.eu ON THE BOUNDS FOR THE NORMS OF R-CIRCULANT MATRICES WITH THE JACOBSTHAL AND JACOBSTHAL LUCAS NUMBERS Ş. Uygun 1, S.
International Journal of Pure and Applied Mathematics Volume 11 No 1 017, 3-10 ISSN: 1311-8080 (printed version); ISSN: 1314-335 (on-line version) url: http://wwwijpameu doi: 10173/ijpamv11i17 PAijpameu
More informationAnother converse of Jensen s inequality
Another converse of Jensen s nequalty Slavko Smc Abstract. We gve the best possble global bounds for a form of dscrete Jensen s nequalty. By some examples ts frutfulness s shown. 1. Introducton Throughout
More informationOn a direct solver for linear least squares problems
ISSN 2066-6594 Ann. Acad. Rom. Sc. Ser. Math. Appl. Vol. 8, No. 2/2016 On a drect solver for lnear least squares problems Constantn Popa Abstract The Null Space (NS) algorthm s a drect solver for lnear
More informationAnti-van der Waerden numbers of 3-term arithmetic progressions.
Ant-van der Waerden numbers of 3-term arthmetc progressons. Zhanar Berkkyzy, Alex Schulte, and Mchael Young Aprl 24, 2016 Abstract The ant-van der Waerden number, denoted by aw([n], k), s the smallest
More informationON SEPARATING SETS OF WORDS IV
ON SEPARATING SETS OF WORDS IV V. FLAŠKA, T. KEPKA AND J. KORTELAINEN Abstract. Further propertes of transtve closures of specal replacement relatons n free monods are studed. 1. Introducton Ths artcle
More informationAn application of generalized Tsalli s-havrda-charvat entropy in coding theory through a generalization of Kraft inequality
Internatonal Journal of Statstcs and Aled Mathematcs 206; (4): 0-05 ISS: 2456-452 Maths 206; (4): 0-05 206 Stats & Maths wwwmathsjournalcom Receved: 0-09-206 Acceted: 02-0-206 Maharsh Markendeshwar Unversty,
More informationarxiv: v1 [quant-ph] 6 Sep 2007
An Explct Constructon of Quantum Expanders Avraham Ben-Aroya Oded Schwartz Amnon Ta-Shma arxv:0709.0911v1 [quant-ph] 6 Sep 2007 Abstract Quantum expanders are a natural generalzaton of classcal expanders.
More informationBIVARIATE JACOBSTHAL AND BIVARIATE JACOBSTHAL-LUCAS MATRIX POLYNOMIAL SEQUENCES SUKRAN UYGUN, AYDAN ZORCELIK
Available online at http://scik.org J. Math. Comput. Sci. 8 (2018), No. 3, 331-344 https://doi.org/10.28919/jmcs/3616 ISSN: 1927-5307 BIVARIATE JACOBSTHAL AND BIVARIATE JACOBSTHAL-LUCAS MATRIX POLYNOMIAL
More informationOne-sided finite-difference approximations suitable for use with Richardson extrapolation
Journal of Computatonal Physcs 219 (2006) 13 20 Short note One-sded fnte-dfference approxmatons sutable for use wth Rchardson extrapolaton Kumar Rahul, S.N. Bhattacharyya * Department of Mechancal Engneerng,
More informationNon-Ideality Through Fugacity and Activity
Non-Idealty Through Fugacty and Actvty S. Patel Deartment of Chemstry and Bochemstry, Unversty of Delaware, Newark, Delaware 19716, USA Corresondng author. E-mal: saatel@udel.edu 1 I. FUGACITY In ths dscusson,
More informationResearch Article Relative Smooth Topological Spaces
Advances n Fuzzy Systems Volume 2009, Artcle ID 172917, 5 pages do:10.1155/2009/172917 Research Artcle Relatve Smooth Topologcal Spaces B. Ghazanfar Department of Mathematcs, Faculty of Scence, Lorestan
More informationSTATIC ANALYSIS OF TWO-LAYERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION
STATIC ANALYSIS OF TWO-LERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION Ákos József Lengyel István Ecsed Assstant Lecturer Emertus Professor Insttute of Appled Mechancs Unversty of Mskolc Mskolc-Egyetemváros
More informationSome Concepts on Constant Interval Valued Intuitionistic Fuzzy Graphs
IOS Journal of Mathematcs (IOS-JM) e-issn: 78-578, p-issn: 39-765X. Volume, Issue 6 Ver. IV (Nov. - Dec. 05), PP 03-07 www.osrournals.org Some Concepts on Constant Interval Valued Intutonstc Fuzzy Graphs
More informationBallot Paths Avoiding Depth Zero Patterns
Ballot Paths Avodng Depth Zero Patterns Henrch Nederhausen and Shaun Sullvan Florda Atlantc Unversty, Boca Raton, Florda nederha@fauedu, ssull21@fauedu 1 Introducton In a paper by Sapounaks, Tasoulas,
More informationDiscrete Mathematics. Laplacian spectral characterization of some graphs obtained by product operation
Dscrete Mathematcs 31 (01) 1591 1595 Contents lsts avalable at ScVerse ScenceDrect Dscrete Mathematcs journal homepage: www.elsever.com/locate/dsc Laplacan spectral characterzaton of some graphs obtaned
More informationSOME RESULTS ON TRANSFORMATIONS GROUPS OF N-LINEAR CONNECTIONS IN THE 2-TANGENT BUNDLE
STUDIA UNIV. BABEŞ BOLYAI MATHEMATICA Volume LIII Number March 008 SOME RESULTS ON TRANSFORMATIONS GROUPS OF N-LINEAR CONNECTIONS IN THE -TANGENT BUNDLE GHEORGHE ATANASIU AND MONICA PURCARU Abstract. In
More informationPAijpam.eu SOME NEW SUM PERFECT SQUARE GRAPHS S.G. Sonchhatra 1, G.V. Ghodasara 2
Internatonal Journal of Pure and Appled Mathematcs Volume 113 No. 3 2017, 489-499 ISSN: 1311-8080 (prnted verson); ISSN: 1314-3395 (on-lne verson) url: http://www.jpam.eu do: 10.12732/jpam.v1133.11 PAjpam.eu
More informationLecture 13 APPROXIMATION OF SECOMD ORDER DERIVATIVES
COMPUTATIONAL FLUID DYNAMICS: FDM: Appromaton of Second Order Dervatves Lecture APPROXIMATION OF SECOMD ORDER DERIVATIVES. APPROXIMATION OF SECOND ORDER DERIVATIVES Second order dervatves appear n dffusve
More informationSINGLE OUTPUT DEPENDENT QUADRATIC OBSERVABILITY NORMAL FORM
SINGLE OUTPUT DEPENDENT QUADRATIC OBSERVABILITY NORMAL FORM G Zheng D Boutat JP Barbot INRIA Rhône-Alpes, Inovallée, 655 avenue de l Europe, Montbonnot Sant Martn, 38334 St Ismer Cedex, France LVR/ENSI,
More information