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Supergroups of some hyperbolic space groups are classified as a continuation of our former works. Fundamental domains will be integer parts of truncated tetrahedra belonging to families F1 -F4, for a while, by the notation of E. Molna ' r et al. in 2006. Our paper relies basically on this work. As an application, optimal congruent hyperball packings and coverings to the truncation base planes with their very good densities are computed. This covering density is better than the conjecture of L. Fejes To ' th for balls and horoballs in 1964.

In this paper we give a new, shortened proof of NP-completeness of CSP problem for undirected, non bipartite graphs, of interest for generalization to QCSP problem. We also give some illustrative examples.

In this paper, the finite-time stability for nonlinear neutral multi-term fractional order systems with time-varying input and state delays is investigated. By use of the generalized Gronwall inequality and extended form of the generalized Gronwall inequality, new sufficient conditions for finite-time stability of such systems are obtained. Finally, numerical examples are given to illustrate the effectiveness and applicability of the proposed theoretical results.

In this paper, we consider the Kronrod extension for the Gauss-Radau and Gauss-Lobatto quadrature consisting of any one of the four Chebyshev weights. The main purpose is to effectively estimate the error of these quadrature formulas. This estimate needs a calculation of the maximum of the modulus of the kernel. We compute explicitly the kernel function and determine the locations on the ellipses where a maximum modulus of the kernel is attained. Based on this, we derive effective error bounds of the Kronrod extensions if the integrand is an analytic function inside of a region bounded by a confocal ellipse that contains the interval of integration.

In this paper, convex continuous-time programming problem with inequality type of constraints is considered. We derive new saddle point optimality conditions and classical duality results such as weak and strong duality properties, under additional regularity assumption. A fundamental tool, employed in the derivation of the necessary saddle point optimality criteria and strong duality result for convex continuous-time programming, is a new version of a theorem of the alternative in infinite-dimensional spaces.