Let Mn be a Riemannian n-manifold. Denote by S(p) and Ric(p) the Ricci tensor and the maximum Ricci curvature on Mn, respectively. In this paper we prove that every C-totally real submanifolds of a Sasakian space form M̄2m+1(c) satisfies S ≤ ( (n−1)(c+3) 4 + n 2 4 H2)g, where H2 and g are the square mean curvature function and metric tensor on Mn, respectively. The equality holds identically if ...

Maps shading terrain as if illuminated by a point light source (i.e. hill-shading) are commonly used in cartographic displays. These hill-shaded maps are especially important for representing mountainous areas, due to the rapid variations in the orientation of terrain elements. Although these hill-shaded maps reveal the coarser landforms and the finer texture of the terrain, they can be enhance...

This article explores the impact of surface area, volume, curvature, and Lennard-Jones (LJ) potential on solvation free energy predictions. Rigidity surfaces are utilized to generate robust analytical expressions for maximum, minimum, mean, and Gaussian curvatures of solvent-solute interfaces, and define a generalized Poisson-Boltzmann (GPB) equation with a smooth dielectric profile. Extensive ...

‎The object of the present paper is to study spacetimes admitting‎ ‎quasi-conformal curvature tensor‎. ‎At first we prove that a quasi-conformally flat spacetime is Einstein‎ ‎and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying‎ ‎Einstein's field equation with cosmological constant is covariant constant‎. ‎Next‎, ‎we prove that if the perfect flui...

Background: Scoliosis is a health problem that causes a side-to-side curvature in the spine. The curvature may have an “S” or “C” shape. To evaluate scoliosis, the Cobb angle has been commonly used. However, digital image processing allows the Cobb angle to be obtained easily and quickly, several researchers have determined that Cobb angle contains high variations (errors) in the measurements. ...

Roll-bending technology has a high degree of flexibility and does not require special molds. However, based on the existing plastic mechanics theory finite element simulation, it is difficult to accurately analyze complex spatial relationship profile roll forming. Therefore, fixed-curvature prediction model constructed XGBoost (extreme gradient boosting), coupling effect process parameters mate...

Engineers and researchers often use nonlinear beam-column elements to simulate the response of reinforced concrete structures. Namely, distributed plasticity elements are arguably the most attractive due to the good compromise between accuracy and computational time. Formulation wise, three types of distributed plasticity beam elements can be distinguished: displacement-based, force-based and m...

A low speed, open circuit, laboratory wind tunnel has been redesigned for use in turbine blade cooling experiments. The two dimensional contraction was designed using a sixth order polynomial. This paper outlines the process of design optimisation, using Computational Fluid Dynamics (CFD) to model the contraction. The parameters that were varied were the location of the point of inflection and ...

we establish some relative volume comparison theorems for extremal volume forms of‎ ‎finsler manifolds under suitable curvature bounds‎. ‎as their applications‎, ‎we obtain some results on curvature and topology of finsler manifolds‎. ‎our results remove the usual assumption on s-curvature that is needed in the literature‎.