The 3-dimensional coordinates of alpha-carbon atoms of proteins are used to distinguish the protein structural classes based on recurrence quantification analysis (RQA). We consider two independent variables from RQA of coordinates of alpha-carbon atoms, %determ1 and %determ2, which were defined by Webber et al. (2001). The variable %determ2 is used to define two new variables, %determ21 and %d...

If a d-dimensional integral involves an integrand ofthe functional form F (II (x I) + f2(X2) + ... ), then one can introduce an integral transform (Fourier or Laplace or variants on those) which allows all the integrals over the coordinates XI to factor. Thus a d-dimensional integral is reduced to a one-dimensional integral over the transform variable. This is shown to be a very powerful and pr...

cm(ρ)e ) which offers an exponential convergence in the φ direction and is naturally applicable for polar coordinates system. The coefficients (cm(ρ)) are then calculated by Finite Difference Method (FDM) in the ρ direction. We adopt the Crank-Nicholson method for the temporal propagation. The final linear system consists of a set of independent one-dimensional (ρ) linear systems and the matrix...

In this paper it will be studied the dynamical system of a rheonomic Finslerian mechanical system, whose evolution curves are given, on the phase space TM×R, by Lagrange equations. Then one can associate to the considered mechanical system a vector field S on TM ×R, which is called the canonical semispray. All geometric objects of the rheonomic Finslerian mechanical system one can be derived fr...

We review the theory of orthogonal separation of variables of the Hamilton– Jacobi equation on spaces of constant curvature, highlighting key contributions to the theory by Benenti. This theory revolves around a special type of conformal Killing tensor, hereafter called a concircular tensor. First, we show how to extend original results given by Benenti to intrinsically characterize all (orthog...

The purpose of this paper is to describe some of the features associated with a finite element computer program for approximate solutions of a gun dynamics problem. The lateral motion of a gun tube is modeled by. an Euler-Bernoulli beam. The difficulties of the problem are due to various complicated loadings and support conditions which can be nonconservative, highly discontinuous and time depe...

We perform a covariant $1+3$ split of the Newton-Cartan equations. The resulting 3-dimensional system equations, called $1+3$-Newton-Cartan is structurally equivalent to $1+3$-Einstein In particular it features momentum constraint, and choice adapted coordinates corresponds shift vector. show that these equations reduce classical Newton without need for special Galilean coordinates. solutions a...

We describe a method to recover the underlying parametrization of scattered data (mi) lying on a manifold M embedded in high-dimensional Euclidean space. The method, Hessian-based Locally Linear Embedding (HLLE), derives from a conceptual framework of Local Isometry in which the manifold M , viewed as a Riemannian submanifold of the ambient Euclidean space Rn, is locally isometric to an open, c...

We describe a method for recovering the underlying parametrization of scattered data (m(i)) lying on a manifold M embedded in high-dimensional Euclidean space. The method, Hessian-based locally linear embedding, derives from a conceptual framework of local isometry in which the manifold M, viewed as a Riemannian submanifold of the ambient Euclidean Space R(n), is locally isometric to an open, c...