Abstract:The Nucleic Acid Package (NUPACK) is a growing software suite for the analysis and design of nucleic acid systems. The NUPACK web server (http://www.nupack.org) currently enables:• Analysis: thermodynamic analysis of dilute solutions of interacting nucleic acid strands.• Design: sequence design for complexes of nucleic acid strands intended to adopt a target secondary structure at equilibrium.• Utilities: evaluation, display, and annotation of equilibrium properties of a complex of nucleic acid strands.NUPACK algorithms are formulated in terms of nucleic acid secondary structure. In most cases, pseudoknots are excluded from the structural ensemble.

Abstract. Starting from the results given in [14] where the uniform treatment of the Jensen type inequalities and its converses is given, we investigate the exponential convexity of differences of the left-hand and the right-hand side of these inequalities. Using these differences, we produce new exponentially convex functions. Finally, we give several examples of the families of functions for which the obtained results can be applied, and we get some generalized Cauchy means. Results from this paper present the generalization of the results from [2].Mathematics subject classification (2010): 26D15.

The theory of dynamic equations on time scales which was formulated by Hilger is an area of mathematics which is currently receiving profuse attention. Despite the fact that the basic objective of times scales is to bring together the study of difference and differential equations, it also extends these classical cases to 'in-between' . In the present article we present a version of Feng Qi integral inequalities on time scales which are in fact generalizations of results given in different articles. MSC: 39A13; 26D15; 26E70

Abstract. Some very general identities of Abel and Popoviciu type for sumsUsing obtained identities, positivity of these expressions are characterized for convex functions of higher order. An application in terms of exponential convexity is given.Mathematics subject classification (2010): 26A51, 39B62, 26D15, 26D20, 26D99.

Extension of Montgomery's identity is used in derivation of Popoviciutype inequalities containing sums m i=1 pif (xi), where f is an n-convex function.Integral analogues and some related results for n-convex functions at a point are also given, as well as Ostrowski-type bounds for the integral remainders of identities associated with the obtained inequalities.