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Almost locally conformal Kaehler product manifolds

100%

Sahin B.

2006

tom Vol. 39, nr 1

211-218

It is known that the product of two locally conformal Kaehler manifolds is not a locally conformal Kaehler manifold, ([1], P:46 ). In this paper we introduce an almost locally conformal Kaehler product manifold and show that the product of two locally conformal Kaehler manifolds is an almost locally conformal Kaehler manifold. Moreover, we investigate properties of curvature tensors of an almost locally conformal Kaehler Product manifold.

Semi-slant submersions from almost product Riemannian manifolds

88%

Gündüzalp Y.

tom Vol. 49, nr 3

345--356

In this paper, we introduce semi-slant submersions from almost product Riemannian manifolds onto Riemannian manifolds. We give some examples, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion. We also find necessary and sufficient conditions for a semi-slant submersion to be totally geodesic.

Sleep EEG analysis utilizing inter-channel covariance matrices

63%

Gopan K. G. , Prabhu S. S. , Sinha N.

tom Vol. 40, no. 1

527--545

Background: Sleep is vital for normal body functions as sleep disorders can adversely affect a person. Electroencephalographic (EEG) signals indicate brain functions and have characteristic signatures for various sleep stages. These enable the use of EEG as an effective tool for in-depth studies about sleep. Sleep stages are broadly divided as rapid eye movement (REM) and non-rapid eye movement (NREM). NREM is further divided into 3 stages. The objective of the work is to distinguish the given EEG epoch as wake, NREM1, NREM2, NREM3 and REM. DREAMS Subject Database containing 5 EEG channels is used here. This work focuses on utilizing EEG by exploiting variations in inter-dependencies of different brain regions during sleep. New method: Covariance matrices of the wavelet-decomposed channels are used to obtain the variations in inter-dependencies. The feature sets are: (1) simple matrix properties(MF) like trace, determinant and norm, (2) eigen-values (E1), (3) eigen-vector corresponding to the largest eigen-value (E2) and (4) tangent vectors obtained using Riemann geometry (RG-TS). The features are input to ensemble classifier with bagging. Subject-specific, All-subjects-combined and Leave-one-subject-out methods of analysis are carried out. Results: In all methods of analysis, RG-TS features give maximum accuracy (80.05%, 83.05% and 61.79%), closely followed by E1 (79.49%, 77.14% and 58.34%). Comparison with existing method: The proposed method obtains higher and/or comparable accuracy. This work also ensures no biasing of classifier due to unequal class distribution. Conclusion: The performances of RG-TS and E1 features reveal that the changes in interdependencies of pre-frontal and occipital lobe along with the central lobe can be used to distinguish the different sleep stages.

Radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds

51%

Shukla S. S. , Yadav A.

tom Vol. 47, nr 4

994--1011

In this paper, we study radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds giving some non-trivial examples of these submanifolds. Integrability conditions of distributions D and RadTM on radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds, have been obtained. We also study totally contact umbilical radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds.