008015   Pujar S S (Mathematics Dep, Sres College of Engineering, Kopargaon-423 603, Email: satishbhati1@rediffmail.com) : Integral formulas in Riemannian geometry and their applications-II. Bull Calcutta Mathl Soc 2007, 99(2), 137-52.

Compact orientable Riemannian manifold of dimension greater than 2 is considered and investigated the integral formulas. Applications of these integral formulas are rigorously used to establish the some global results. In fact conformality and isometry of Riemannian manifolds to spheres are studied. Finally as a geometric significance, some special cases of our results are also studied.

43 ref

008014   Prasad B N;Chaubey G C;Patel G S (Mathematics Dep, St. Andrews College Gorakhpur Gorakhpur, India) : Four dimensional Finsler space with constant unified main scalar. Bull Calcutta Mathl Soc 2007, 99(2), 113-22.

Discusses the theory of four dimensional Finsler space with constant unified main scalar. The conditions have been obtained under which v-connection vectors vanish. The v-connection vectors of C-reducible, semi-C-reducible and C2-like four-dimensional Finsler space with constant unified main scalar have been determined.

10 ref

008013   Pranesachar C R (Mathematics Dep. Mathematical Olympiad Cell, Indian Institute of Science, Bangalore-560 012, Email: pran@math.iisc.ernet.in) : Euclid and 'The elements'. Resonance 2007, 12(4), 19-25.

When a crime is committed and the culprit responsible for the crime is nabbed, the job of the investigators is not over. To convince the judge, they have to prove beyond doubt that it was the accused who committed the crime. Likewise, mathematical statements require proofs for their veracity to be established. Further, to make these statements precise we need to have a set of proper definitions. It was Euclid, who more than two thousand years ago, started this tradition when he bequeathed to the world his book entitled The Elements. This tradition has continued since then. Definitions, proofs besides axioms have become an inalienable part of mathematical lore. We owe all this to Euclid, one of the greatest pioneers of rigour and reasoning. Discusses the work of Euclid.

1 illus, 1 table, 3 ref

008012   Pokley S S;Thomas K T (Mathematics Dep, Kavikulguru Institute of Technology and Science, Ramtek, Maharashtra) : Higher dimensional plane symmetrical space-time in polar coordinate system. Indian J Math mathl Sci 2007, 3(1), 2007.

5 ref

008011   Park W G (Information and Communication Engineering Dep, Tongmyong Univ, Busan 608-711, South Korea, Email: wgpark@tu.ac.kr) : On some linear transformations associated with finite binary relations. Far East J mathl Sci 2007, 24(3), 281-95.

Power set with a binary operation "+" (symmetric difference) forms a vector space over two elements field together with an appropriate scalar multiplication. Considering non-empty finite sets A and B, a fundamental one-to-one correspondence between the linear transformations from the vector space P(A) to the vector space P(B) and the relations from A to B and some related consequences have been presented.

6 ref

008010   Park W G (Information and Communication Engineering Dep, Tongmyong Univ, Busan 608-711, South Korea, Email: wgpark@tu.ac.kr) : On some homomorphisms associated with finite binary relations. Far East J mathl Sci 2007, 24(1), 121-36.

Considering non-empty finite sets A and B, Authors present a fundamental one-to-one correspondence between the homomorphisms from the pre-module P(A) to the pre-module P(B) and the relations from A to B. Some related consequences have also been presented.

3 ref

008009   Park J S;Kwun Y C (Mathematics Education Dep, Chinju National Univ Education, Jinju-600 756, Korea, Email: parkjs@cue.ac.kr) : Some fixed point theorems in the intuitionistic Fuzzy metric spaces. Far East J mathl Sci 2007, 24(2), 227-39.

Establishes some fixed point theorems in each of which the completeness of the spaces is omitted and the same conclusion is obtained as in Park, Kwun and Park's fixed point theorem in intuitionistic fuzzy metric spaces but with different sufficient conditions.

10 ref

008008   Park C H (Mathematics Dep, Ulsan Univ, Ulsan 680-749, Korea, Email: chpark@ulsan.ac.kr) : Bifuzzy subalgebras of k(g)-algebras. Far East J mathl Sci 2007, 24(1), 99-119.

Generalize the concept of fuzzy subalgebras in a right K(G) - algebra, initiated by Akram et al. [1], to the case of bifuzzy sets. The notion of bifuzzy subalgebras is introduced, and their properties are investigated. Using a collection of subalgebras with additional conditions, we construct a bifuzzy subalgebra. The concept of bifuzzy topological subalgebra is introduced, and related properties are discussed.

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008007   Ozkan E (NO, Ataturk Universitesi Fen Edebiyat Fak. Matematik BOl, 25240 Erzurum, Turkey) : On truncated fibonacci sequences. Indian J pure appl Math 2007, 38(4), 241-51.

Proves some theorems concerning truncated Fibonacci sequences, which are defined 2. Also states some conjectures concerning the period (mod m) of truncated Fibonacci sequences, where the integer m is greater than or equal to 2. In addition Some computer-generated results that tend to support these conjectures has also been presented.

2 tables, 5 ref

008006   Okadome T (NTT Laboratotries Keihanna Science City, , Kyoto 619-0237, Japan, Email: houmi@idea.brl.ntt.co.jp) : Note of polynomial time learnability in the limit from positive data. Far East J mathl Sci 2007, 24(2), 259-69.

Definition of identifiability in the limit from polynomial positive data with a polynomial-time updating algorithm proposed is a restricted version of de la Higuera (1997)'s definition for the case of positive data only. Any language class learnable in the limit from positive data in the sense of Pitt (1989)'s definition is shown to be identifiable in the limit from polynomial positive data with a polynomial-time updating algorithm.

9 ref

008005   Nishimura H (Institute of Mathematics, Tsukuba Univ, Tsukuba, Ibaraki, 305-8571 Japan) : Lie algebra of the group of bisections a chapter in synthetic differential geometry of groupoids. Far East J mathl Sci 2007, 24(3), 329-42.

Groupoids provide a more appropriate framework for differential geometry than principal bundles. Synthetic differential geometry is the avant-garde branch of differential geometry, in which nilpotent infinitesimals are available in abundance. The principal objective in this paper Aim is to show within our favorite framework of synthetic differential geometry that the tangent space of the group of bisections of a microlinear groupoid at its identity is naturally a Lie algebra. Two proofs for its Jacobi identity have been given.

16 ref

008004   Moukamba F;Nkasa Y (Mathematiques Dep, Faculte des Sciences, Marien Ngouabi Univ, B.P. 69 Brazzaville Republique du Congo) : Pseudo-topological structure in spaces of anisotropically approximately differentiable functions. Far East J mathl Sci 2007, 24(3), 343-54.

By means of convergent filters, has been introduced convergence concept and defined a pseudotopology (or a limit structure) in spaces of anisotropically approximately differentiable functions. It has been proved that those spaces joined with the defined limit structure are pseudo-topological vector spaces.

3 ref

008003   Mojdeh D A;Hassanpour S A;Abdollahzadeh Ahangar H;Ahmadi Haji A (Mathematics Dep, Mazandaran Univ, Babolsar, Iran, Email: dmojdeh@umz.ac.ir) : On domination in Hamiltonian cubic graphs. Far East J mathl Sci 2007, 24(2), 187-200.

In 1996, Reed proved that the domination number γ(G) of every n-vertex graph G with minimum degree at least 3 is at most 3n/8. Also, he conjectured that γ(H) ≥ [n/3] for every connected 3-regular (cubic) n-vertex graph H. Reed's conjecture is obviously true for Hamiltonian cubic graphs. In this note, presents a sequence of Hamiltonian cubic graphs whose domination numbers are sharp have been presented. The connected domination number for these graphs are presented.

10 ref

008002   Mecheri S (Mathematics Dep, College of Science King Saud Univ, P. O. Box 2455, Riyadh 11451, Saudi Arabia, Email: mecherisalah@hotmail.com) : Extension of the Fuglede-Putnam theorem to semihyponormal operators. Far East J mathl Sci 2007, 24(2), 251-7.

Fuglede-Putnam theorein shows that A and B are normal operators and if X is an operator such that AX - XB, then A*X = XB*. The hypothesis on A and B can bo relaxed by using a Hilbert-Schmidt operator: Let A be semihyponormal and B* be invertible semihyponormal such that AX = XB for a Hilbert Schmidt operators. Then A*X = XB*. As a consequence of this result. range of the generalized derivation induced by this class of operators is orthogonal to its kernel has been obtained.

14 ref

008001   Matsuda M (Mathematics Dep, Faculty of Science, Shizuoka Univ, Ohya, Surugaku, Shizuoka 422-8529, Japan, Email: smmmatu@ipc.shizuoka.ac.jp) : Birkhoff integrability and generalized Pettis sets. Far East J mathl Sci 2007, 24(2), 169-86.

Gives some additional characterizations of generalized Pettis sets in terms of generalized Birkhoff integrability by the effective use of the notion of sets of small oscillation have been given Especially, this yields a characterization theorem of Pettis sets in terms of Birkhoff integrability, which extends Theorem 3.5 in and Theorem 2.

8 ref

008000   Mathe P;Tautenhahn U (NO, Weierstrass Institure for Applied Analysis and Stochastics Mohrenstras, Berlin, Germany, Email: mathe@wias-berlin.de) : Error bounds for regularization methods in Hilbert scales by using operator monotonicity. Far East J mathl Sci 2007, 24(1), 1-21.

For solving linear ill-posed problems with noisy data regularization methods are required. Regularized approximations are obtained by a general regularization scheme in Hilbert scales. Authors exploit operator monotonicity of certain functions for deriving order optimal error bounds that characterize the accuracy of the regularized approximations. These error bounds are obtained under general smoothness conditions.

19 ref

007999   Mao L (Institute of Mathematics, Nanjing Institute of Technology, Nanjing-211 167, People's Republic of China, Email: maolx2@hotmail.com) : Rings close to baer. Indian J pure appl Math 2007, 38(3), 129-42.

Defines two kinds of dimensions, called <65>-injective dimension and <65>-flat dimension, which measure how far away a ring is from being a Baer ring. These dimensions have nice properties when the ring in question is an AC ring, where R is said to be a left AC ring in case the left annihilator of each nonempty subset of R is a cyclic left ideal.

27 ref

007998   Lee J G;Lee D M (Mathematics Dep, Won Kwang Univ, 344-2 Shinyongdong Ik-San Chunbuk 570-749, Korea, Email: jukolee@wonkwang.ac.kr) : Approximations for Hilbert framelets. Far East J mathl Sci 2007, 24(3), 439-46.

Some equivalency relations of Hilbert framelets under approximation in terms of expansions have been considered. Our results are in spirit close to classical results for bases and unconditional convergence, due to Bessaga and Pelczynski.

15 ref

007997   Lanani A (Mathematics Dep, Mentouri Univ, Constantine 25000, Algeria, Email: Alanani1@yahoo.fr) : Mixed linear model. Far East J mathl Sci 2007, 24(3), 355-62.

The repeated measures taken on the same subject are often correlated whether they are taken over time or over space. Most of statisticians, especially those using marginal models (Liang and Zeger [7]), ignore this correlation (or the covariance between the observations) or assume this like a nuisance parameter. They are only interested in the observations mean. In this study, we analyse a set of repeated measures data has been analysed. Focus in this paper is how to choose a parsimonious model for the covariance structure. For this purpose we use a general linear model with different covariance structures has been used.

13 ref

007996   Lakshminarayan A (Physics Dep, Indian Institute of Technology, Madras Chennai-600 036, Email: arul@physics.iitm.ac.in) : Borromean triangles and prime knots in an ancient temple. Resonance 2007, 12(5), 41-7.

Deals with mathematical motifs of modern interest such as remarkable links and knots that were found at a 6th 1 century Chennai temple. Introducing these mathematical objects discusses their timeless and universal appeal as well as point to possible reasons for their symbolic use in ancient Indian temples.

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007995   Kulkarni S H (Mathematics Dep, Indian Institute of Technology, Madras Chennai-600 036, Email: shk@iitm.ac.in) : Relatively elementary proof of a characterization of polynomials. Indian J pure appl Math 2007, 38(4), 229-30.

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007994   Kim B J (Mathematics Dep, Daejin University, Pocheon-487-711, Korea, Email: bjkim@daejin.ac.kr) : Relationships among conditional transforms conditional convolutions and first variations for some conditioning functions. Far East J mathl Sci 2007, 24(3), 385-96.

Several interesting relationships involving exactly two of the three concepts of conditional integral transform, conditional convolution product and first variation for a class of functionals defined on K[0, T], the space of complex valued continuous functions on [0, T] which vanish at zero, for some conditioning functions.

12 ref

007993   Kecilioglu O;Gundogan H (Mathematics Dep, Kirikkale Univ, Kirikkale, Turkey, Email: keciliglu@kku.edu.tr) : Dual split quaternions and motions in lorentzian space R<. Far East J mathl Sci 2007, 24(3), 425-37.

Dual Lorentzian angles and dual split quaternions are defined. Then using these concepts, rotation motions, translation motions and screw motions are obtained in 3-dimensional Lorentzian space R<^>31.