Ab-initio crystal structure analysis and refinement approaches of oligo p-benzamides based on electron diffraction data

Ab-initio crystal structure analysis of organic materials from electron diffraction data is presented. The data were collected using the automated electron diffraction tomography (ADT) technique. The structure solution and refinement route is first validated on the basis of the known crystal structure of tri-p-benzamide. The same procedure is then applied to solve the previously unknown crystal structure of tetra-p-benzamide. In the crystal structure of tetra-p-benzamide, an unusual hydrogen-bonding scheme is realised; the hydrogen-bonding scheme is, however, in perfect agreement with solid-state NMR data

Total Problem of Constructing Linear Regression Using Matrix Correction Methods with Minimax Criterion

A linear problem of regression analysis is considered under the assumption of the presence of noise in the output and input variables. This approximation problem may be interpreted as an improper interpolation problem, for which it is required to correct optimally the positions of the original points in the data space so that they all lie on the same hyperplane. The use of the quadratic approximation criterion for such a problem led to the appearance of the total least squares method. In this paper, we use the minimax criterion to estimate the measure of correction of the initial data. It leads to a nonlinear mathematical programming problem. It is shown that this problem can be reduced to solving a finite number of linear programming problems. However, this number depends exponentially on the number of parameters. Some methods for overcoming this complexity of the problem are proposed

Linear-quadratic programming and its application to data correction of improper linear programming problems

The problem of maximizing a linear function with linear and quadratic constraints is considered. The solution of the problem is obtained in a constructive form using the Lagrange function and the optimality conditions. Many optimization problems can be reduced to the problem of this type. In this paper, as an application, we consider an improper linear programming problem formalized in the form of maximization of the initial linear criterion with a restriction to the Euclidean norm of the correction vector of the right-hand side of the constraints or the Frobenius norm of the correction matrix of both sides of the constraints