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Discrete Mathematical Research & Reviews:
Structures
STM JOURNALSScientific Technical Medical
(RRDMS) May - August 2014
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I take the privilege to present the print version for the [Volume 1 Issue (2)] of Research & Reviews:
Discrete Mathematical Structures. The intension of RRDMS is to create an atmosphere that
stimulates creativeness, research and growth in the area of Discrete Mathematical Structures.
The development and growth of the mankind is the consequence of brilliant Research done by
eminent Scientists and Engineers in every field. RRDMS provides an outlet for Research findings
and reviews in areas of Discrete Mathematical Structures found to be relevant for National and
International recent developments & research initiative.
The aim and scope of the Journal is to provide an academic medium and an important reference for
the advancement and dissemination of Research results that support high level learning, teaching and
research in the domain of Discrete Mathematical Structures.
Finally, I express my sincere gratitude and thanks to our Editorial/ Reviewer board and Authors for
their continued support and invaluable contributions and suggestions in the form of authoring write
ups/ reviewing and providing constructive comments for the advancement of the journals. With
regards to their due continuous support and co-operation, we have been able to publish quality
Research/Reviews findings for our customers base.
I hope you will enjoy reading this issue and we welcome your feedback on any aspect of the Journal.
Dr. Archana Mehrotra
Director
STM Journals
Director's Desk
STM JOURNALS
1. On Symmetry Preserving Diffeomorphisms of Generalized Symmetric Finsler Spaces Reza Chavosh Khatamy, Dariush Latifi 1
2. A Study on the Sparing Number of the Corona of Certain Graphs K.P. Chithra, K.A. Germina, N. K. Sudev 5
3. On Some Triple Almost Lacunary Sequence Spaces Defined by Orlicz FunctionsAyhan Esi 16
4. On the Riemann Hypothesis in The Light of The Littlewood Criterion of EquivalenceLukasz Andrzej Glinka 26
5. Origin of Modern Mathematical Numeral – 0, 1, 2, 3, 4, 5, 6, 7, 8, 9: the Hindu-Indian-Brahmagubta, The Islamo-Arabic or the West? Auwalu Musa 36
ContentsResearch & Reviews: Discrete Mathematical Structures
RRDMS (2014)© STM Journals 2014. All Rights Reserved
Research & Reviews: Discrete Mathematical Structures
Volume 1, Issue 2
www.stmjournals.com
On Symmetry Preserving Diffeomorphisms of Generalized
Symmetric Finsler Spaces
Reza Chavosh Khatamy1, Dariush Latifi
2* 1Department of Mathematics, College of Science Tabriz branch, Islamic Azad University, Tabriz, Iran
2Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran
Abstract In this paper, we study generalized symmetric Finsler spaces. We first study symmetry
preserving diffeomorphisms, then we show that the group of symmetry preserving
diffeomorphisms is a transitive Lie transformation group. Finally we give some existence
theorems. MSC: 53C60, 53C30
Keywords: Homogeneous finsler space, generalized symmetric finsler space,
symmetry preserving diffeomorphism
RRDMS (2014)© STM Journals 2014. All Rights Reserved
Research & Reviews: Discrete Mathematical Structures
Volume 1, Issue 2
www.stmjournals.com
A Study on the Sparing Number of the Corona
of Certain Graphs
K.P. Chithra1, K.A. Germina
2, N. K. Sudev
3*
1Naduvath Mana, Nandikkara P O Thrissur - 680301, Kerala, India
2Department of Mathematics, School of Mathematical & Physical Sciences,
Central University of Kerala, Kasaragod - 671316, Kerala, India 3Department of Mathematics, Vidya Academy of Science & Technology,
Thalakkottukara, Thrissur - 680501, Kerala, India
Abstract Let ℕ0 be the set of all non-negative integers and 𝒫(ℕ0) be its the power set. An integer
additive set-indexer (IASI) is defined as an injective function 𝑓: 𝑉(𝐺) → 𝒫(ℕ0) such that
the induced function 𝑓+: 𝐸(𝐺) → 𝒫(ℕ0) defined by 𝑓+(𝑢𝑣) = 𝑓(𝑢) + 𝑓(𝑣) is also
injective, where 𝑓(𝑢) + 𝑓(𝑣) is the sum set of 𝑓(𝑢) and 𝑓(𝑣). If 𝑓+(𝑢𝑣) = 𝑘 ∀ 𝑢𝑣 ∈𝐸(𝐺), then 𝑓 is said to be a 𝑘-uniform integer additive set-indexer. An integer additive
set-indexer 𝑓 is said to be a weak integer additive set-indexer if |𝑓+(𝑢𝑣)| =
𝑚𝑎𝑥 ( |𝑓(𝑢)|, |𝑓(𝑣)|) ∀ 𝑢𝑣 ∈ 𝐸(𝐺). We have some characteristics of the graphs which admit weak integer additive set-indexers. In this paper, we study about the sparing number
of the corona of two graphs.
Keywords: Integer additive set-indexers, mono-indexed elements of a graph, weak
integer additive set-indexers, sparing number of a graph
RRDMS (2014)© STM Journals 2014. All Rights Reserved
Research & Reviews: Discrete Mathematical Structures
Volume 1, Issue 2
www.stmjournals.com
On Some Triple Almost Lacunary Sequence Spaces
Defined by Orlicz Functions
Ayhan Esi* Department of Mathematics, University of Adiyaman, Turkey
Abstract In this paper we introduce the concept of almost lacunary strong convergent triple
sequences with respect to an Orlicz function and examine some properties of these
sequence spaces. We also introduce and study almost lacunary statistical convergence for triple sequences and also present some inclusion relations.
Keywords: Preliminaries, real numbers, Pringsheim, nondecreasing
RRDMS (2014)© STM Journals 2014. All Rights Reserved
Research & Reviews: Discrete Mathematical Structures
Volume 1, Issue 2
www.stmjournals.com
On the Riemann Hypothesis in The Light of The
Littlewood Criterion of Equivalence
Lukasz Andrzej Glinka* Science Editor, BSc Physics. Full Member at the American Association
of International Researchers, American Institute for Policy Development, New York
Abstract In 1859, Riemann extended the Euler study onto the case of a complex variable according to then new Cauchy's complex analysis. According to his point of view, all non-trivial
zeros of the Riemann zeta function are located on the critical line s=1/2+it, where t is a
real number. In 1912, Littlewood presented the equivalence criterion for the Riemann Hypothesis based on the Mertens function. In this paper, the Riemann Hypothesis is
discussed and this is shown that the Littlewood criterion can be immediately applied for
proving the Riemann Hypothesis, according to the analytic number theory.
Keywords: Analytic number theory, Riemann zeta function, rie-mann hypothesis,
Littlewood criterion, Mellin transforms, Mertens function
RRDMS (2014) 36-55 © STM Journals 2014. All Rights Reserved Page 36
Research & Reviews: Discrete Mathematical Structures
Volume 1, Issue 2
www.stmjournals.com
Origin of Modern Mathematical Numeral – 0, 1, 2, 3, 4, 5,
6, 7, 8, 9: the Hindu-Indian-Brahmagubta,
The Islamo-Arabic or the West?
Auwalu Musa* Mubi North Education Authority, Mubi North Local Government Area,
Adamawa State – Nigeria
Abstract The aim of this paper is to examine, analyze and ascertain the root of the modern
mathematical numeral system between the Indian-Hindu Brahmagubta, Islamo-Arabic
and the Western numeral systems. The paper utilized secondary source of data. The methodology adopted by the paper is content analysis. The findings of the paper revealed
that the origin of the shapes of our ten modern numerals do not concern the Indian mathematics history, as Hindus do not have full-fledged mathematical numeral system
before the development of Arabic Numerals between 8th-15th Centuries. The character of
Hindu-Indian numerals in whatever form and categories it belongs- Brahmagubta or anyone else, does not have any genealogical affiliations to the present modern
mathematical numeral versions, as well the same thing applies to the Western
mathematical systems. The paper argued that, the root/origin of the modern Arabic numeral is traced to its original and independent Arabic character versions, which
transmuted from one stage to another with some state of galvanization - from Abjadi, Mashriki to Ghubari. The paper argued that apart from the non-reliability of the thesis of
disparity in characters or shapes of the Arabic numerals compare to that of the Hindu-
Indian Brahmagubta, there is also that of philosophical caricature fiction of genealogical linkage as well as the phonological misplacement of language or terms. The paper also
argued that during the Golden-Age of Islam between 7th and 15th
centuries, European arithmeticians especially in the eleventh, twelfth and part of thirteenth centuries, knew
nothing about Arabic numerals; it was incredibly absent, they knew only the use of
antiquated Roman numerals and Abacus in counting. In that regard, the Arabic numeral symbols (or system) were developed by Islamo-Arabic mathematicians, learned by
Indians and some Europeans who cares about knowledge. In the east, the numeral system
attracted the Indian mathematicians, while in Europe, the numeral system was first employed in Italy, then later France for practical purposes after the translation of the
work of Al-Khwarizmi Mohammed Ibn Musa (Latin Algorithm) in 12th
century into Latin by Gerard of Cremona, also known as Leonardo Fibonacci.
Keywords: Abjadi, Europe, Ghubari, Hindu-Indian-Brahmagubta, modern,
mathematics, islamo-Arabic-Numeral, Origin, Science, West.