We define an invariant of welded virtual knots from each finite crossed module by considering crossed module invariants of ribbon knotted surfaces which are naturally associated with them. We elucidate that the invariants obtained are non-trivial by calculating explicit examples. We define welded virtual graphs and consider invariants of them defined in a similar way. 2000 Mathematics Subject C...

A formula is given for the Seiberg–Witten invariants of a 4–manifold that is cut along certain kinds of 3–dimensional tori. The formula involves a Seiberg– Witten invariant for each of the resulting pieces. AMS Classification numbers Primary: 57R57 Secondary: 57M25, 57N13

We use group theory to construct infinite families of maps on surfaces which are invariant under Wilson’s map operations of order 3 but not under the operations of order 2, such as duality and Petrie duality. MSC classification: Primary 05C25, secondary 05C10, 20B25.

In this paper, we discuss necessary and sufficient conditions on jumping kernels for a class of jump-type Markov processes on metric measure spaces to have scale-invariant finite range parabolic Harnack inequality. AMS 2000 Mathematics Subject Classification: Primary 60J75 , 60J35, Secondary 31C25 , 31C05. Running title: Notes on Heat Kernel Estimates and Parabolic Harnack Inequality

We consider a Lévy process in Rd (d ≥ 3) with the characteristic exponent Φ(ξ) = |ξ|2 ln(1 + |ξ|2) − 1. The scale invariant Harnack inequality and apriori estimates of harmonic functions in Hölder spaces are proved. AMS Subject Classification: Primary 60J45, Secondary 60G50, 60G51, 60J25, 60J27

We deal with some of problems posed by Monk [Mo 1], [Mo 3] and related to cardinal invariant of ultraproducts of Boolean algebras. We also introduce and investigate several new cardinal invariants. AMS 1991 Mathematics Subject Classification primary: 03G05, 03E05, secondary: 06E15, 03E35 ∗ The research was partially supported by DFG grant Ko 490/7-1. This is publication number 534 of the second...

By comparing the mitochondrial 15S rRNA sequences of four wildtype yeast strains together with their respective secondary structures, with those of the 16S-like ribosomal RNA from other organisms we detected two optional and two invariant AT-clusters. The origin of these clusters is discussed with respect to their roles as possible mobile elements.

The Rayleigh quotient of a bent function is an invariant under the action of the orthogonal group, and it measures the distance of the function to its dual. An efficient algorithm is derived that generates all bent functions of given Rayleigh quotient. The Rayleigh quotient of some bent functions obtained by primary (Maiorana McFarland, Dillon) or secondary (direct and indirect sum) constructio...

Furstenberg and Margulis conjectured classifications of invariant measures for higher rank actions on homogeneous spaces. We survey the applications of the partial measure classifications result by Einsiedler, Katok, and Lindenstrauss to number theoretic problems. Mathematics Subject Classification (2010). Primary 37A45; Secondary 37D40, 11J13, 11J04.

We compute the Chern-Simons transgressed forms of some modularly invariant characteristic forms, which are related to the elliptic genera. We study the modularity properties of these secondary characteristic forms and the relations among them. We also compute the Chern-Simons forms of some vector bundles over free loop space.