In the title compound, C(11)H(15)N(3)O(3), one of the methyl groups attached to the benzamide unit is slightly twisted with a C-N-C-C torsion angle of 4.04 (13)°. The crystal packing is stabilized by weak intermolecular C-H⋯O hydrogen bonds together with a weak C-H⋯π inter-action.

In this paper, we shall study regular rings satisfying weak chain condition. As main results, we show that regular rings satisfying weak chain condition are unit-regular, and show that these rings have the unperforation and power cancellation properties for the family of finitely generated projective modules.

In volume visualization, the voxel visibitity and materials are carried out through an interactive editing of Transfer Function. In this paper, we present a two-level GPU-based labeling method that computes in times of rendering a set of labeled structures using the Adaboost machine learning classifier. In a pre-processing step, Adaboost trains a binary classifier from a pre-labeled dataset and...

Choice functions on tournaments always select the maximal element (Condorcet winner), provided they exist, but this property does not hold in the more general case of weak tournaments. In this paper we analyze the relationship between the usual choice functions and the set of maximal elements in weak tournaments. We introduce choice functions selecting maximal elements, whenever they exist. Mor...

In the title mol-ecule, C(24)H(22)O(8), the mean planes of the two coumarin units are inclined to each other at a dihedral angle of 79.93 (3)°. The attached meth-oxy groups form torsion angles of 7.65 (19) and 78.36 (14)° with respect to one coumarin unit, and angles of 9.01 (16) and 99.08 (11)° with respect to the other coumarin unit. In the crystal structure, weak inter-molecular C-H⋯O hydrog...

In the title compound, C46H50O12·2CH2Cl2, each dual 20-crown-6 unit crystallizes with two di-chloro-methane solvent mol-ecules. The crown unit mol-ecule lies about an inversion centre located at the central benzene ring. The two crown ring groups adopt an anti conformation, stabilized by weak intra-molecular C-H⋯O inter-actions. In the crystal, the crown unit mol-ecules and the solvent mol-ecul...

The situation where the available data arise from a general linear process with a unit root is discussed. We propose a modi cation of the Block Bootstrap which generates replicates of the original data and which correctly imitates the unit root behavior and the weak dependence structure of the observed series. Validity of the proposed method for estimating the unit root distribution is shown. R...

In this paper we prove two results of nonsmooth analysis involving the Fréchet subdifferential. One of these results provides a necessary optimality condition for an optimization problem which arise naturally from a class of wide studied problems. In the second result we establish a sufficient condition for the metric regularity of a set-valued map without continuity assumptions. 1. Preliminari...

The main result of this paper is that the weak membership problem in the unit ball of a given norm is NP-hard if and only if the weak membership problem in the unit ball of the dual norm is NP-hard. Equivalently, the approximation of a given norm is polynomial time if and only if the approximation of the dual norm is polynomial time. Using the NP-hardness of the approximation of spectral norm o...

Every separable nonreflexive Banach space admits an equivalent norm such that the set of the weak-extreme points of the unit ball is discrete.