In recent years, the computer graghics have improved highly. In this paper,  we present a special kind  of  the computer  graghics named  vectorial  graphics and point out  to  their  mathematical backgrounds  by using  the NURBS curves  and surfaces which are often unknown. Then, we propose the use of the presented mathematical formulas in the vectorial computer ghraghics.

Displacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, total rotation jx, and/or shear strain Uxz, as well as the variational method used (e.g., collocation, weak form Galerkin, or least-squares). When nonlinear shear deformation theories are used, the displacement finite element models experience membrane and shear locking. The present study is concerned with development of alternative beam finite elements using both uniform and non-uniform RATIONAL b-SPLINEs (NURBS) to eliminate shear and membrane locking in an hpk finite element setting for both the Euler-Bernoulli beam and Timoshenko beam theories. Both linear and non-linear analysis are performed using mixed finite element models of the beam theories studied. Results obtained are compared with analytical (series) solutions and non-linear finite element and spectral/hp solutions available in the literature, and excellent agreement is found for all cases.

In this paper a bivariate RATIONAL interpolation is developed to create a space surface using both function values and the first order partial derivatives of the function being interpolated as the interpolation data. This method has some characteristics comparing with present interpolation methods. First, the interpolation function has a simple and explicit mathematical representation. Secondly, the interpolation function can be expressed by symmetric bases. We use this method to estimate the value of double integrals. Presented examples show the pertinent features of the method.

We are... So, to reframe the inquiry: who are we on a metaphysical level? Which aspects of ourselves are the most universally representative of who we are? How do we fare in the face of the passage of time? For decades, philosophers have debated the concept of diachronic personal identity, which focuses on the question of what keeps us alive. An intricate debate has developed between those who hold the body view (animalism) and those who hold the psychological view (memory) on the question of who we are. The two groups will eventually become so firmly set in their views that they will be unable to compromise. Hylomorphic animalism, or the view that humans are RATIONAL animals, living bodies made of prime matter and a RATIONAL soul, is an alternative answer to this divisive question that I propose in this study, following in the footsteps of Aristotle and Aquinas. We only survive if matter and RATIONAL souls do.