On The Symmetrical Property Of Procrustes Measure Of Distance
.\
ISSN 1311-8080
0
International Journal of Pure and
Applied Mathematics
Vol. 99, No. 3, March 2015
J
,
..,
Contents
K. Kannan: Amenable action and invariant mean
C . Promsakon: The partial order on category of semigroups
and Endo-Cayley digraphs
K . Paykan, A. Moussavi: A generalization of bear rings
S. Noeiaghdam: Numerical solution of n-th order Fredholm
integro-differential equations by integral mean value theorem
method
D.W. Yoon: On translation surfaces with zero Gaussian
curvature in H2 x R
D. Hac helfi, Y . Las kri , M.L. Sahari: Trust region with
nonlinear conjugate gradient method
T. Bakhtiar, Siswadi: On the symmetrical property of
Procrustes measure of distance
S.B. Belhaouari: The density of the process of coalescing
random walks
M.A. Alqudah: Construction of Tchebyshev-ll weighted
orthogonal polynomials on triangular
M.K. Bansal, R . Jain: Application of generalized differential
transform method to fractional order Riccati differential equation
and numerical result
S. Acharjee: Fixed point theorem in structure fuzzy metric
space
H. Rahimpoor, A. Ebadian, M.E. Gordji, A . Zohri:
Common fixed point theorems in modular metric spaces
....
227 - 244
245 - 256
257 - 276
277 - 288
289 - 298
299 - 314
315 - 324
325 - 342
343 - 354
355 - 366
367 - 372
373 - 383
ｾ＠
ｾ＠
.
International Journal of Pure and Applied Mathematics
ISSN 1311-8080, Academic Publications, Ltd., Kliment Ohridski Blvd., 8,
Sofia 1756, Bulgaria, Email: [email protected], Web: www.ijpam.eu
Founding Publisher: Drumi Bainov
Managing Editor: Svetoslav Nenov
Editorial Board:
J. Abadie {France)
R. Agarwal (USA)
A. Baker (USA)
M. Balas (USA)
R.E. Bank (USA)
H.T . Banks (USA)
V. Barbu (Romania)
P. Bates (USA)
G. Beer (USA)
A. Bensoussan (USA)
H. Berestycki (France)
M . Bohner (USA)
J. Bona (USA)
L. Bunimovich (USA)
G. Butta.zzo (Italy)
F. Calogero (Italy)
J . Cash (UK)
G.-Q. Chen (USA)
E. Cheney (USA)
F.L. Chernousko (Russia)
M. Chipot (Switzerland)
J . Conway (USA)
R. Cools (Belgium)
G. Cooperman (USA)
C . Da Prato (Italy)
C. Dafermos (USA)
K. Deimling (Germany)
F. Deutsch (USA)
E. DiBenedetto {USA)
A. Dishliev (Bulgaria)
K. Dishlieva (Bulgaria)
D. Evans (UK)
R. Finn (USA)
H. Frankowska (France)
R. Freund (USA)
B. Ga\'ish (USA)
C. Gear (USA)
L. Gelman (UK)
I. Gladwell (USA)
J. Graef (USA)
B. Gramsch (Germany)
C. Grebogi (UK)
P. Cresho (USA)
C. Groetsch (USA)
J. Henderson (USA)
C. Hess {France)
S. Hristova (Bulgaria)
M . Jri (Japan)
M. Ito (Japan)
J . Jeffers (U K)
D.S. Jones (UK)
Y. Kannai (Israel)
II. Kawarada (Japan)
N. Kenmochi (Japan)
0 . Kinderlehrer (USA)
M. Konstantinov (Bulgaria)
G. Ladas (USA)
D. Larson (USA)
C. Lcitmann (USA)
P.-L. Lions (France)
M. Luskin (USA)
M. Susai Manuel (INDIA)
N. Mastronardi (Italy)
C. Mitchell (U K)
K. Morgan (UK)
S. .\enov (Bulgaria)
H . .\icdcrreiter (Singapore)
D. O'Rcgan (Ireland)
J . Osborn (USA)
Otani (Japan)
::". Pavel (USA)
G . Pinder (USA)
A. Rahnev (Bulgaria)
S. Reich (Israel)
E. Saff (USA)
M . Sambandham (USA)
P. Sabatier (France)
M. Schechter (USA)
B.-W. Schulze (Germany)
0 . Serre (France)
J. Serrin (USA)
R. Showalter (USA)
C.-W. Shu (USA)
M . Shub (USA}
P. Souganidis (USA)
S. Suzuki (Japan)
E. Tadmor (USA)
K. Tamma (USA)
A. Tani (Japan)
R. Thomas (USA)
K.K. Tomma (USA)
M. Tsutsumi (Japan)
R. Varga (USA)
W. Vasconcelos (USA)
V. Vazirani {USA)
N. Velkov (Bulgaria)
R. Verma (USA)
J . Vines (France)
T . Ward (USA)
G . Watson (Scotland)
R. Wets (USA)
0. Widlund (USA)
ｾｦＮ＠
ernational Journal of Pure and Applied Mathematics
Scope: International Journal of P ure and Applied ｾ｡ｴｨ･ｭｬ｣ｳ＠
(IJP AM) Is a
rigorously journal for publishing early, high-impact results in the areas of mathematics
and computer science/informatics. The journal also emphasizes mathematical articles
devoted to the mathematical treatment of questions arising in physics, c hemistry,
biology, engineering and all applied sciences. Although the journal focuses on the
original research articles, it also welcomes reviews and short notes.
Indexed/ Abstracted: With the publication of the December 2014 issue, ｉｊｐａｾｴ＠
has
concluded its 13-th year o f publication of high-quality research articles. Over the past
years, we have seen significant growth: the metric factor "cites per paper" (impact of
the journal) has become 2.80 {The ｉｊｐａｾＱ＠
indexes and impact are calculated using only
Harzing's Publish or Peris h software, based on Google Scholar on 12.12.2014). For this
success, we are thankful to our Editorial Board, authors especially, and readers. IJP Al\1
is indexed/abstracted in: ELSEVIER, Index Copernicus, Hub SciVerse, Google Scholar,
SCimago Journal & Country Rank , SCIRUS, SCOPUS. We would like to thank these
institutions for cooperation and support.
Instructions for Authors: Submission of an article for evaluation in all journals
published by Academic Publications, Ltd. implies that the work has not been published
previo usly (except in the form of an abstract or as part of a published lecture or
academic thesis or as an electronic preprint). :\itoreover, it is not under consideration
for publication elsewhere, the publication is approved by all authors, and if accepted it
will not be published elsewhere (including electronically in the same form. in English or
in any other language) without the written consent of the copyright-holder.
The manuscript should be prepared only using LaTeX processing system (please use
the LaTeX template provided in the journal web), basic font 12pt size, and must
remain legible after small reduction. The papers should be in English and typed in
frames 12x20 cm. Authors arc cordially invited to submit papers in two differe nt ways.
Online: Please visit our Submission Center. Electronically: Please, send the pdf (or
ps) file of your paper as an attachment to: ｩｪｰ｡ｭ
ｾ ｭｵ
Ｎ ｵ｣ｴｭＮ･､＠
(our primary
address) and ･｢ｾｩｪｰ｡ｭ
Ｎ ･ｵ＠
(the address is over-spammed).
Open Access: IJPA'.\l is available on-line to the reader-without any limitations for
download fu ll text of all publis hed articles. In an open access publication model , the
publication costs of an article nrc paid from author's research huclgct or hy supporting
organization in the form of page-charge. These page-charges replace subscription
charges and allow our publishing house to make the full-text of every published article
or book freely available to all interested readers.
Copyright: In order to meet recent modern public demands for publication and
electronic access to academic resources, we asking authors to agree with following
items:
• Academic Publications, Ltd. have the rights to reproduce, translate to any language
and transmit to the public the whole article or any part of it for academic purposes
• The author(s) retains the right to keep the article on servers approved by Academic
Publications, Ltd. and/ or on the author's own Web sites in its published form for
academic purposes, provided that the author(s) acknowledges that it was published
•
•
•
•
in IJP AM or its predecessors.
Upon request of the author(s), Academic Publications, Ltd. may grant the
author(s), free of charge, the right to publish the article or its revision for
publication with academic value, including the complete works of the author(s),
provided that the author(s) acknowledges that it was published in IJPAM or its
predecessors.
Upon request of a third party with intention of publication for academic purposes,
Academic Publications, Ltd. may permit them to use the rights described in the
item l.
To the author whose articles are newly accepted, we are sending a form of
agreement to be signed and sent back as promptly as possible.
If we receive any message of disagreement, we arc ready to cancel the copyright
agreement and take a process to withdraw the paper from the Web site of Project
Euclid or from the Web site of OCU ｾｬ｣､ｩ｡＠
Center Library Service.
International Journal of Pure and Applied Mathematics
Volume 99 No. 3 2015, 315-324
ISSN: 1311-8080 (printed version): ISS!': 1314-3395 (on-line version)
url: http://www.ijpam.eu
doi: http://dx.doi.ol"g/10 l2732/ijpam.,·99i3.i
ｾ＠
ijpam.eu
ON THE SYMMETRICAL PROPERTY OF
PROCRUSTES MEASURE OF DISTANCE
Toni Bakhtiar 1 S, Siswadi2
L 2 Department
of ).lathematics
Bogor Agricultural University
Dramaga Campus, Bogor. 16680. INDONESIA
Abstract:
ｾｉ｣｡ｳｵｲ･ｭｮｴ＠
the degree of differe11c:e bctwl'C'n two matric:s by
using Procrustes analysis is preceded by a series of Euclidean si111ila rit.v transformations namely translation , rotation. and dilation, performed i11 rc:;pcctccl
order. for gai11i11g maximal matching. It b easy. by a counter cxainplc. to show
that Procrustes measure ､ｯ＼Ｎｾ＠
not obey the symmetrical property, something
s hould he owned by any distnne i:-. all tlw geom etrical information that remain:-. wbP11 locatio11. rotational.
T. Bakhtiar. Siswadi
316
and scaling e ffects are filtered out from a n object. Two con figura tion matri｣ｾ＠
as representation of objects ha,·e the sam e s h ape if they can be tra nslated.
ro tated, and dilated to each other so that they match exactly [3]. Procrus tes
analysis refers to a technique of comparing objects with different s hapes and
producing a m easure of the match. It eliminates possible ｩｮ ｣ｯ ｭｾｮ
･ｵｳｲ｡｢
ｩｬﾭ
ity or variables wi t hin the individual data sets and size difference:> between
data sets by employing data and configuration scalings i11 calculating the distance. rcspcd i\'cly. Thus, a series of Euclidean s imilarity tn.msfonnations. i.e..
translation- rotation-dilation, is carried-out to b est match up to their m
ISSN 1311-8080
0
International Journal of Pure and
Applied Mathematics
Vol. 99, No. 3, March 2015
J
,
..,
Contents
K. Kannan: Amenable action and invariant mean
C . Promsakon: The partial order on category of semigroups
and Endo-Cayley digraphs
K . Paykan, A. Moussavi: A generalization of bear rings
S. Noeiaghdam: Numerical solution of n-th order Fredholm
integro-differential equations by integral mean value theorem
method
D.W. Yoon: On translation surfaces with zero Gaussian
curvature in H2 x R
D. Hac helfi, Y . Las kri , M.L. Sahari: Trust region with
nonlinear conjugate gradient method
T. Bakhtiar, Siswadi: On the symmetrical property of
Procrustes measure of distance
S.B. Belhaouari: The density of the process of coalescing
random walks
M.A. Alqudah: Construction of Tchebyshev-ll weighted
orthogonal polynomials on triangular
M.K. Bansal, R . Jain: Application of generalized differential
transform method to fractional order Riccati differential equation
and numerical result
S. Acharjee: Fixed point theorem in structure fuzzy metric
space
H. Rahimpoor, A. Ebadian, M.E. Gordji, A . Zohri:
Common fixed point theorems in modular metric spaces
....
227 - 244
245 - 256
257 - 276
277 - 288
289 - 298
299 - 314
315 - 324
325 - 342
343 - 354
355 - 366
367 - 372
373 - 383
ｾ＠
ｾ＠
.
International Journal of Pure and Applied Mathematics
ISSN 1311-8080, Academic Publications, Ltd., Kliment Ohridski Blvd., 8,
Sofia 1756, Bulgaria, Email: [email protected], Web: www.ijpam.eu
Founding Publisher: Drumi Bainov
Managing Editor: Svetoslav Nenov
Editorial Board:
J. Abadie {France)
R. Agarwal (USA)
A. Baker (USA)
M. Balas (USA)
R.E. Bank (USA)
H.T . Banks (USA)
V. Barbu (Romania)
P. Bates (USA)
G. Beer (USA)
A. Bensoussan (USA)
H. Berestycki (France)
M . Bohner (USA)
J. Bona (USA)
L. Bunimovich (USA)
G. Butta.zzo (Italy)
F. Calogero (Italy)
J . Cash (UK)
G.-Q. Chen (USA)
E. Cheney (USA)
F.L. Chernousko (Russia)
M. Chipot (Switzerland)
J . Conway (USA)
R. Cools (Belgium)
G. Cooperman (USA)
C . Da Prato (Italy)
C. Dafermos (USA)
K. Deimling (Germany)
F. Deutsch (USA)
E. DiBenedetto {USA)
A. Dishliev (Bulgaria)
K. Dishlieva (Bulgaria)
D. Evans (UK)
R. Finn (USA)
H. Frankowska (France)
R. Freund (USA)
B. Ga\'ish (USA)
C. Gear (USA)
L. Gelman (UK)
I. Gladwell (USA)
J. Graef (USA)
B. Gramsch (Germany)
C. Grebogi (UK)
P. Cresho (USA)
C. Groetsch (USA)
J. Henderson (USA)
C. Hess {France)
S. Hristova (Bulgaria)
M . Jri (Japan)
M. Ito (Japan)
J . Jeffers (U K)
D.S. Jones (UK)
Y. Kannai (Israel)
II. Kawarada (Japan)
N. Kenmochi (Japan)
0 . Kinderlehrer (USA)
M. Konstantinov (Bulgaria)
G. Ladas (USA)
D. Larson (USA)
C. Lcitmann (USA)
P.-L. Lions (France)
M. Luskin (USA)
M. Susai Manuel (INDIA)
N. Mastronardi (Italy)
C. Mitchell (U K)
K. Morgan (UK)
S. .\enov (Bulgaria)
H . .\icdcrreiter (Singapore)
D. O'Rcgan (Ireland)
J . Osborn (USA)
Otani (Japan)
::". Pavel (USA)
G . Pinder (USA)
A. Rahnev (Bulgaria)
S. Reich (Israel)
E. Saff (USA)
M . Sambandham (USA)
P. Sabatier (France)
M. Schechter (USA)
B.-W. Schulze (Germany)
0 . Serre (France)
J. Serrin (USA)
R. Showalter (USA)
C.-W. Shu (USA)
M . Shub (USA}
P. Souganidis (USA)
S. Suzuki (Japan)
E. Tadmor (USA)
K. Tamma (USA)
A. Tani (Japan)
R. Thomas (USA)
K.K. Tomma (USA)
M. Tsutsumi (Japan)
R. Varga (USA)
W. Vasconcelos (USA)
V. Vazirani {USA)
N. Velkov (Bulgaria)
R. Verma (USA)
J . Vines (France)
T . Ward (USA)
G . Watson (Scotland)
R. Wets (USA)
0. Widlund (USA)
ｾｦＮ＠
ernational Journal of Pure and Applied Mathematics
Scope: International Journal of P ure and Applied ｾ｡ｴｨ･ｭｬ｣ｳ＠
(IJP AM) Is a
rigorously journal for publishing early, high-impact results in the areas of mathematics
and computer science/informatics. The journal also emphasizes mathematical articles
devoted to the mathematical treatment of questions arising in physics, c hemistry,
biology, engineering and all applied sciences. Although the journal focuses on the
original research articles, it also welcomes reviews and short notes.
Indexed/ Abstracted: With the publication of the December 2014 issue, ｉｊｐａｾｴ＠
has
concluded its 13-th year o f publication of high-quality research articles. Over the past
years, we have seen significant growth: the metric factor "cites per paper" (impact of
the journal) has become 2.80 {The ｉｊｐａｾＱ＠
indexes and impact are calculated using only
Harzing's Publish or Peris h software, based on Google Scholar on 12.12.2014). For this
success, we are thankful to our Editorial Board, authors especially, and readers. IJP Al\1
is indexed/abstracted in: ELSEVIER, Index Copernicus, Hub SciVerse, Google Scholar,
SCimago Journal & Country Rank , SCIRUS, SCOPUS. We would like to thank these
institutions for cooperation and support.
Instructions for Authors: Submission of an article for evaluation in all journals
published by Academic Publications, Ltd. implies that the work has not been published
previo usly (except in the form of an abstract or as part of a published lecture or
academic thesis or as an electronic preprint). :\itoreover, it is not under consideration
for publication elsewhere, the publication is approved by all authors, and if accepted it
will not be published elsewhere (including electronically in the same form. in English or
in any other language) without the written consent of the copyright-holder.
The manuscript should be prepared only using LaTeX processing system (please use
the LaTeX template provided in the journal web), basic font 12pt size, and must
remain legible after small reduction. The papers should be in English and typed in
frames 12x20 cm. Authors arc cordially invited to submit papers in two differe nt ways.
Online: Please visit our Submission Center. Electronically: Please, send the pdf (or
ps) file of your paper as an attachment to: ｩｪｰ｡ｭ
ｾ ｭｵ
Ｎ ｵ｣ｴｭＮ･､＠
(our primary
address) and ･｢ｾｩｪｰ｡ｭ
Ｎ ･ｵ＠
(the address is over-spammed).
Open Access: IJPA'.\l is available on-line to the reader-without any limitations for
download fu ll text of all publis hed articles. In an open access publication model , the
publication costs of an article nrc paid from author's research huclgct or hy supporting
organization in the form of page-charge. These page-charges replace subscription
charges and allow our publishing house to make the full-text of every published article
or book freely available to all interested readers.
Copyright: In order to meet recent modern public demands for publication and
electronic access to academic resources, we asking authors to agree with following
items:
• Academic Publications, Ltd. have the rights to reproduce, translate to any language
and transmit to the public the whole article or any part of it for academic purposes
• The author(s) retains the right to keep the article on servers approved by Academic
Publications, Ltd. and/ or on the author's own Web sites in its published form for
academic purposes, provided that the author(s) acknowledges that it was published
•
•
•
•
in IJP AM or its predecessors.
Upon request of the author(s), Academic Publications, Ltd. may grant the
author(s), free of charge, the right to publish the article or its revision for
publication with academic value, including the complete works of the author(s),
provided that the author(s) acknowledges that it was published in IJPAM or its
predecessors.
Upon request of a third party with intention of publication for academic purposes,
Academic Publications, Ltd. may permit them to use the rights described in the
item l.
To the author whose articles are newly accepted, we are sending a form of
agreement to be signed and sent back as promptly as possible.
If we receive any message of disagreement, we arc ready to cancel the copyright
agreement and take a process to withdraw the paper from the Web site of Project
Euclid or from the Web site of OCU ｾｬ｣､ｩ｡＠
Center Library Service.
International Journal of Pure and Applied Mathematics
Volume 99 No. 3 2015, 315-324
ISSN: 1311-8080 (printed version): ISS!': 1314-3395 (on-line version)
url: http://www.ijpam.eu
doi: http://dx.doi.ol"g/10 l2732/ijpam.,·99i3.i
ｾ＠
ijpam.eu
ON THE SYMMETRICAL PROPERTY OF
PROCRUSTES MEASURE OF DISTANCE
Toni Bakhtiar 1 S, Siswadi2
L 2 Department
of ).lathematics
Bogor Agricultural University
Dramaga Campus, Bogor. 16680. INDONESIA
Abstract:
ｾｉ｣｡ｳｵｲ･ｭｮｴ＠
the degree of differe11c:e bctwl'C'n two matric:s by
using Procrustes analysis is preceded by a series of Euclidean si111ila rit.v transformations namely translation , rotation. and dilation, performed i11 rc:;pcctccl
order. for gai11i11g maximal matching. It b easy. by a counter cxainplc. to show
that Procrustes measure ､ｯ＼Ｎｾ＠
not obey the symmetrical property, something
s hould he owned by any distnne i:-. all tlw geom etrical information that remain:-. wbP11 locatio11. rotational.
T. Bakhtiar. Siswadi
316
and scaling e ffects are filtered out from a n object. Two con figura tion matri｣ｾ＠
as representation of objects ha,·e the sam e s h ape if they can be tra nslated.
ro tated, and dilated to each other so that they match exactly [3]. Procrus tes
analysis refers to a technique of comparing objects with different s hapes and
producing a m easure of the match. It eliminates possible ｩｮ ｣ｯ ｭｾｮ
･ｵｳｲ｡｢
ｩｬﾭ
ity or variables wi t hin the individual data sets and size difference:> between
data sets by employing data and configuration scalings i11 calculating the distance. rcspcd i\'cly. Thus, a series of Euclidean s imilarity tn.msfonnations. i.e..
translation- rotation-dilation, is carried-out to b est match up to their m