PARALLELISM OF DISTRIBUTIONS AND GEODESICS ON F(±a2; ±b2)-STRUCTURE LAGRANGIAN MANIFOLD

This paper deals with the Lagrange vertical structure on the vertical space TV (E) endowed with a non null (1,1) tensor field FV satisfying (Fv2-a2)(Fv2+a2)(Fv2 - b2)(Fv2 + b2) = 0. In this paper, the authors have proved that if an almost product structure P on the tangent space of a 2n-dimensional Lagrange manifold E is defined and the F(±a2; ±b2)-structure on the vertical tangent space TV (E) is given, then it is possible to define the similar structure on the horizontal subspace TH(E) and also on T(E). In the next section, we have proved some theorems and have obtained conditions under which the distribution L and M are r-parallel, r¯ anti half parallel when r = r¯ . The last section is devoted to proving theorems on geodesics on the Lagrange manifol

Nonlinear Measures for Characterizing Rough Surface Morphologies

We develop a new approach to characterizing the morphology of rough surfaces based on the analysis of the scaling properties of contour loops, i.e. loops of constant height. Given a height profile of the surface we perform independent measurements of the fractal dimension of contour loops, and the exponent that characterizes their size distribution. Scaling formulas are derived and used to relate these two geometrical exponents to the roughness exponent of a self-affine surface, thus providing independent measurements of this important quantity. Furthermore, we define the scale dependent curvature and demonstrate that by measuring its third moment departures of the height fluctuations from Gaussian behavior can be ascertained. These nonlinear measures are used to characterize the morphology of computer generated Gaussian rough surfaces, surfaces obtained in numerical simulations of a simple growth model, and surfaces observed by scanning-tunneling-microscopes. For experimentally realized surfaces the self-affine scaling is cut off by a correlation length, and we generalize our theory of contour loops to take this into account.Comment: 39 pages and 18 figures included; comments to [email protected]

Coordinated Activation of Candidate Proto-Oncogenes and Cancer Testes Antigens via Promoter Demethylation in Head and Neck Cancer and Lung Cancer

Background: Epigenetic alterations have been implicated in the pathogenesis of solid tumors, however, proto-oncogenes activated by promoter demethylation have been sporadically reported. We used an integrative method to analyze expression in primary head and neck squamous cell carcinoma (HNSCC) and pharmacologically demethylated cell lines to identify aberrantly demethylated and expressed candidate proto-oncogenes and cancer testes antigens in HNSCC. Methodology/Principal Findings: We noted coordinated promoter demethylation and simultaneous transcriptional upregulation of proto-oncogene candidates with promoter homology, and phylogenetic footprinting of these promoters demonstrated potential recognition sites for the transcription factor BORIS. Aberrant BORIS expression correlated with upregulation of candidate proto-oncogenes in multiple human malignancies including primary non-small cell lung cancers and HNSCC, induced coordinated proto-oncogene specific promoter demethylation and expression in non-tumorigenic cells, and transformed NIH3T3 cells. Conclusions/Significance: Coordinated, epigenetic unmasking of multiple genes with growth promoting activity occurs i

Iron Behaving Badly: Inappropriate Iron Chelation as a Major Contributor to the Aetiology of Vascular and Other Progressive Inflammatory and Degenerative Diseases

The production of peroxide and superoxide is an inevitable consequence of aerobic metabolism, and while these particular "reactive oxygen species" (ROSs) can exhibit a number of biological effects, they are not of themselves excessively reactive and thus they are not especially damaging at physiological concentrations. However, their reactions with poorly liganded iron species can lead to the catalytic production of the very reactive and dangerous hydroxyl radical, which is exceptionally damaging, and a major cause of chronic inflammation. We review the considerable and wide-ranging evidence for the involvement of this combination of (su)peroxide and poorly liganded iron in a large number of physiological and indeed pathological processes and inflammatory disorders, especially those involving the progressive degradation of cellular and organismal performance. These diseases share a great many similarities and thus might be considered to have a common cause (i.e. iron-catalysed free radical and especially hydroxyl radical generation). The studies reviewed include those focused on a series of cardiovascular, metabolic and neurological diseases, where iron can be found at the sites of plaques and lesions, as well as studies showing the significance of iron to aging and longevity. The effective chelation of iron by natural or synthetic ligands is thus of major physiological (and potentially therapeutic) importance. As systems properties, we need to recognise that physiological observables have multiple molecular causes, and studying them in isolation leads to inconsistent patterns of apparent causality when it is the simultaneous combination of multiple factors that is responsible. This explains, for instance, the decidedly mixed effects of antioxidants that have been observed, etc...Comment: 159 pages, including 9 Figs and 2184 reference

Second order parallel tensors on para r-Sasakian manifolds with a coefficient α

Levy [11] had proved that a second order symmetric parallel non singular tensor on a space of constant curvature is a constant multiple of the metric tensor. Sharma [6] has proved that second order parallel tensor in a Kaehler Space of constant holomorphic sectional curvature is a linear combination with constant coefficients of the Kaehlerian metric and the fundamental 2-form. In this paper, we show that a second order symmetric parallel tensor on a para r-Sasakian manifold with a coefficient α is a constant multiple of the associated metric tensor and we have also proved that there is no non zero skew symmetric second order parallel tensor on a para r-Sasakian manifold

Second Order Parallel Tensors on LP-Sasakian Manifolds with a coefficient α

In 1926, Levy [3] had proved that a second order symmetric parallel nonsingular tensor on a space of constant curvature is a constant multiple of the metric tensor. Sharma [4] has proved that a second order parallel tensor in a K¨ahler space of constant holomorphic sectional curvature is a linear combination with constant coefficient of the K¨ahlerian metric and the fundamental 2-form. In this paper, we have shown that a second order symmetric parallel tensor on Lorentzian Para Sasakian manifold (briefly LP-Sasakian) with a coefficient α (non zero Scalar function) is a constant multiple of the associated metric tensor and we have also proved that there is no non zero skew symmetric second order parallel tensor on a LP-Sasakian manifold

Submanifolds of F-structure manifold satisfying FK+(−)K+1F=0

The purpose of this paper is to study invariant submanifolds of an n-dimensional manifold M endowed with an F-structure satisfying FK+(−)K+1F=0 and FW+(−)W+1F≠0 for 1<W<K, where K is a fixed positive integer greater than 2. The case when K is odd (≥3) has been considered in this paper. We show that an invariant submanifold M˜, embedded in an F-structure manifold M in such a way that the complementary distribution Dm is never tangential to the invariant submanifold ψ(M˜), is an almost complex manifold with the induced F˜-structure. Some theorems regarding the integrability conditions of induced F˜-structure are proved

Complete lift of a structure satisfying FK−(−)K+1F=0

The idea of f-structure manifold on a differentiable manifold was initiated and developed by Yano [1], Ishihara and Yano [2], Goldberg [3] and among others. The horizontal and complete lifts from a differentiable manifold Mn of class C∞ to its cotangent bundles have been studied by Yano and Patterson [4,5]. Yano and Ishihara [6] have studied lifts of an f-structure in the tangent and cotangent bundles. The purpose of this paper is to obtain integrability conditions of a structure satisfying FK−(−)K+1F=0 and FW−(−)W+1F≠0 for 1<W<K, in the tangent bundle

Prolongations of F-structure to the tangent bundle of order 2

A study of prolongations of F-structure to the tangent bundle of order 2 has been presented

On the Integrability Conditions and Operators of the F((K

WOS: 000521938700010This paper consists of two main sections. In the first part, we find the integrability conditions of the horizontal lifts of F((K + 1), (K - 1))-structure satisfying F-K+(1) + F-K(-1) = 0, (F not equal 0, K equal to or greater than 2). Later, we get the results of Tachibana operators applied to vector and covector fields according to the horizontal lifts of F((K + 1), (K - 1))-structure in cotangent bundle T* (M-n). Finally, we have studied the purity conditions of Sasakian metric with respect to the horizontal lifts of the structure. In the second part, all results obtained in the first section were obtained according to the complete and horizontal lifts of the structure in tangent bundle T (M-n)