Abstract:
We study a null Mannheim curve with time-like or space-like Mannheim partner curve in the Minkowski 3-space 31. We get the characterization of a null Mannheim curve. Then, we investigate there is no null-helix Mannheim curve in 31.

Abstract:
Bonome et al., 1997, provided an algebraic characterization for an indefinite Sasakian manifold to reduce to a space of constant -holomorphic sectional curvature. In this present paper, we generalize the same characterization for indefinite -space forms. 1. Introduction For an almost Hermitian manifold with , Tanno [1] has proved the following. Theorem 1.1. Let , and assume that almost Hermitian manifold satisfies for every tangent vector , , and . Then has a constant holomorphic sectional curvature at if and only if for every tangent vector at . Tanno [1] has also proved an analogous theorem for Sasakian manifolds as follows. Theorem 1.2. A Sasakian manifold ≥5 has a constant -sectional curvature if and only if for every tangent vector such that . Nagaich [2] has proved the generalized version of Theorem 1.1, for indefinite almost Hermitian manifolds as follows. Theorem 1.3. Let be an indefinite almost Hermitian manifold that satisfies (1.1), then has a constant holomorphic sectional curvature at if and only if for every tangent vector at . Bonome et al. [3] generalized Theorem 1.2 for an indefinite Sasakian manifold as follows. Theorem 1.4. Let be an indefinite Sasakian manifold. Then has a constant -sectional curvature if and only if for every vector field such that . In this paper, we generalize Theorem 1.4 for an indefinite generalized -space form by proving the following. Theorem 1.5. Let be an indefinite generalized -space form. Then is of constant -sectional curvature if and only if for every vector field such that , for any . 2. Preliminaries A manifold is called a globally framed f-manifold (or -manifold) if it is endowed with a nonnull -tensor field of constant rank, such that is parallelizable; that is, there exist global vector fields , , with their dual 1-forms , satisfying and . The -manifold , , is said to be an indefinite metric -manifold if is a semi-Riemannian metric with index satisfying the following compatibility condition: for any , being according to whether is spacelike or timelike. Then, for any , one has . Following the notations in [4, 5], we adopt the curvature tensor , and thus we have and , for any , , , . We recall that, as proved in [6], the Levi-Civita connection of an indefinite -manifold satisfies the following formula: where is given by . An indefinite metric -manifold is called an indefinite -manifold if it is normal and , for any , where for any . The normality condition is expressed by the vanishing of the tensor field , being the Nijenhuis torsion of . Furthermore, the Levi-Civita connection of an indefinite

Abstract:
We study characteristic -lightlike submanifolds tangent to the characteristic vector fields in an indefinite metric -manifold, and we also discuss the existence of characteristic lightlike submanifolds of an indefinite -space form under suitable hypotheses: (1) is totally umbilical or (2) its screen distribution () is totally umbilical in .

This study presents the
numerical evaluation about the impact of flow disturbance near the intrados and
extrados regions of the 90 degree bended elbow using CFX for several practical
cases where the 90 degree bended upward elbow is located in a proximity to the
butterfly valve and the butterfly valve open angle is changed. For the change
of a butterfly valve open angle from 60% to 100% and the increase of the
distance between a valve and a 90 degree bended elbow, the effect of FAC
(Flow-Accelerated Corrosion) in the 90 degree bended elbow may be neglected
because the value and distribution of the velocity and shear stress is rapidly
decreased comparing with the present status installed in an industry, and the data
of 100% valve open (Case 3) and L/D ≈ 5 (Case 4) are very good agreement
comparing with the reference data, L/D ≈ 8 (Case 2). The reasons are that flow already
maintains a fully developed condition and a steady state in spite of less
distance than the reference case, L/D = 8. Therefore, smooth flow fields have
approached at a 90 degree bended elbow. Then, the effect of shear stress and
vortex is hardly investigated around the intrados area of 90 degree bended
elbow.

Abstract:
The shape and microscopic structure of the foot of the equilateral Venus, Gomphina veneriformis are described by light and electron microscopy along with the substrate conditions of their habitat. The habitat sediment of G. veneriformis is composed of sand (2 - 0.063 mm in diameter), mainly. The foot is wedge-shaped with multiple vertical furrows on the surface. Although the foot is composed of an epithelial layer, a connective tissue layer and a muscular layer, the boundary between the connective tissue and muscular layer is not clear. The epithelial layer was composed mostly of ciliated columnar epithelia and secretory cells. Epithelial cells forming the apical region of the fold were long columnar, while cells of the interfold were mostly short columnar. The cilia and microvilli were commonly observed on the free surface of epithelial cells, while tight junctions of apico-lateral aspect and membrane interdigitations were found between the epithelial cells. Secretory cells were found to contain acidic mucopolysaccharide, and were classified into two types in accordance with the shapes and ultrastructures of secretory granules. The muscle fibers were composed of thin and thick microfilaments, the proportions of which were 81.3% and 18.7%, respectively. It was determined that such morphology and structural characteristics of the foot of G. veneriformis would present advantageous conditions for borrowing into substrate and mobility.

Abstract:
In this paper,we present a framework for the generation and control of an Internet-based 3-dimensionai game virtual environment that allows a character to navigate through the environment.Our framework includes 3-dimensional terrain mesh data processing,a map editor,scene processing,collision processing,and waikthrough control.We also define an environment-specific semantic information editor,which can be applied using specific location obtained from the real world.Users can insert text information related to the characters real position in the real world during navigation in the game virtual environment.

Abstract:
Lightlike geometry has its applications in general relativity, particularly in black hole theory. Indeed, it is known that lightlike hypersurfaces are examples of physical models of Killing horizons in general relativity (Galloway, 2007). In this paper, we introduce the definition of generic lightlike submanifolds of an indefinite cosymplectic manifold. We investigate new results on a class of generic lightlike submanifolds of an indefinite cosymplectic manifold .

Abstract:
For submanifolds tangent to the structure vector field in Sasakian space forms, we establish a Chen's basic inequality between the main intrinsic invariants of the submanifold (namely, its pseudosectional curvature and pseudosectional curvature on one side) and the main extrinsic invariant (namely, squared pseudomean curvature on the other side) with respect to the Tanaka-Webster connection. Moreover, involving the pseudo-Ricci curvature and the squared pseudo-mean curvature, we obtain a basic inequality for submanifolds of a Sasakian space form tangent to the structure vector field in terms of the Tanaka-Webster connection.

Abstract:
We implement a one-loop analysis of the $\rho$ parameter in the Left Right Twin Higgs model, including the logarithmically enhanced contributions from both heavy fermion and scalar loops. Numerical analysis indicates that the one-loop corrections are dominant over the tree-level contributions in most regions of parameter space. The experimentally allowed values of the $\rho$-parameter divide the allowed parameter space into two regions; less than $670 {\rm GeV}$ and larger than $1100 {\rm GeV}$ roughly, for the symmetry breaking scale $f$. Therefore our result significantly reduces the parameter space which are favorably accessible to the LHC.

Abstract:
We implement a one-loop analysis of the $\rho$ parameter in the Left Right Twin Higgs model, including the logarithmically enhanced contributions from both fermion and scalar loops. Numerical results show that the one-loop contributions are dominant over the tree level corrections in most regions of parameter space. The experimentally allowed values of $\rho$-parameter divide the allowed parameter space into two regions; less than $670 {\rm GeV}$ and larger than $1100 {\rm GeV}$ roughly, for symmetry breaking scale $f$. Our numerical analysis significantly reduces the parameter space which are favorably accessible to the LHC.